construct a 90% confidence interval for the population mean

If a confidence interval does not include a particular value, we can say that it is not likely that the particular value is the true population mean. Construct a 95% confidence interval for the population mean length of time. Confidence intervals are one way to represent how "good" an estimate is; the larger a 90% confidence interval for a particular estimate, the more caution is required when using the estimate. If the sample has a standard deviation of 12.23 points, find a 90% confidence interval for the population standard deviation. If many random samples were taken of size 14, what percent of the confidence intervals constructed should contain the population mean worth of coupons? Thus, we do not need as large an interval to capture the true population mean. To construct a confidence interval estimate for an unknown population mean, we need data from a random sample. The effects of these kinds of changes are the subject of the next section in this chapter. It means that should you repeat an experiment or survey over and over again, 95 percent of the time your results will match the results you get from a population (in other words, your statistics would be sound! $\bar{x} - EBM = 1.024 0.1431 = 0.8809$, $\bar{x} - EBM = 1.024 0.1431 = 1.1671$. Arrow down to 7:ZInterval. View A7DBAEA8-E1D4-4235-90E6-13F3575EA3F9.jpeg from STATISTICS 1001 at Western Governors University. Available online at www.fec.gov/data/index.jsp (accessed July 2, 2013). Use $n = 217$: Always round the answer UP to the next higher integer to ensure that the sample size is large enough. To construct a confidence interval for a single unknown population mean $\mu$, where the population standard deviation is known, we need $\bar{x}$ as an estimate for $\mu$ and we need the margin of error. Decreasing the confidence level decreases the error bound, making the confidence interval narrower. We can say that there is a significant difference between the proportion of Asian adults who say that their families would welcome a white person into their families and the proportion of Asian adults who say that their families would welcome a black person into their families. Remember to use the area to the LEFT of $z_{\dfrac{\alpha}{2}}$; in this chapter the last two inputs in the invNorm command are 0, 1, because you are using a standard normal distribution $Z \sim N(0, 1)$. Why or why not? When we calculate a confidence interval, we find the sample mean, calculate the error bound, and use them to calculate the confidence interval. In this survey, 86% of blacks said that they would welcome a white person into their families. The area to the right of $z_{0.025}$ is 0.025 and the area to the left of $z_{0.025}$ is $1 0.025 = 0.975$. Find the point estimate and the error bound for this confidence interval. Legal. The population standard deviation for the height of high school basketball players is three inches. In six packages of The Flintstones Real Fruit Snacks there were five Bam-Bam snack pieces. Thus, a 95% confidence interval for the true daily discretionary spending would be $ 95 2 ( $ 4.78) or $ 95 $ 9.56. $X$ is the time needed to complete an individual tax form. National Health and Nutrition Examination Survey. Centers for Disease Control and Prevention. Calculate the error bound based on the information provided. How many students must you interview? Construct a 96% confidence interval for the population proportion of Bam-Bam snack pieces per bag. One way to lower the sampling error is to increase the sample size. (The area to the right of this $z$ is 0.125, so the area to the left is $1 0.125 = 0.875$.). The population is skewed to one side. $CL = 0.75$, so $\alpha = 1 0.75 = 0.25$ and $\frac{\alpha}{2} = 0.125 z_{\frac{\alpha}{2}} = 1.150$. This means These intervals are different for several reasons: they were calculated from different samples, the samples were different sizes, and the intervals were calculated for different levels of confidence. The mean length of the conferences was 3.94 days, with a standard deviation of 1.28 days. The American Community Survey (ACS), part of the United States Census Bureau, conducts a yearly census similar to the one taken every ten years, but with a smaller percentage of participants. The $z$-score that has an area to the right of $\dfrac{\alpha}{2}$ is denoted by $z_{\dfrac{\alpha}{2}}$. A confidence interval for a mean gives us a range of plausible values for the population mean. Recall, when all factors remain unchanged, an increase in sample size decreases variability. A confidence interval for a population mean with a known standard deviation is based on the fact that the sample means follow an approximately normal distribution. Construct a 90% confidence interval for the population mean grade point average. Suppose we want to lower the sampling error. Construct a 99% confidence interval to estimate the population mean using the data below. Assume that the underlying population distribution is normal. Disclosure Data Catalog: Candidate Summary Report 2012. U.S. Federal Election Commission. The error bound of the survey compensates for sampling error, or natural variability among samples. A sample of 15 randomly selected students has a grade point average of 2.86 with a standard deviation of 0.78. $N 7.9\left(\frac{2.5}{\sqrt{20}}\right)$. We estimate with 96% confidence that the mean amount of money raised by all Leadership PACs during the 20112012 election cycle lies between $47,292.57 and $456,415.89. e. The error boundwill decrease in size, because the sample size increased. Confidence Interval Calculator for the Population Mean. For example, when $CL = 0.95, \alpha = 0.05$ and $\dfrac{\alpha}{2} = 0.025$; we write $z_{\dfrac{\alpha}{2}} = z_{0.025}$. Legal. $\bar{X}$ is normally distributed, that is, $\bar{X} \sim N(\mu_{x},\dfrac{\sigma}{\sqrt{n}})$. To be more confident that the confidence interval actually does contain the true value of the population mean for all statistics exam scores, the confidence interval necessarily needs to be wider. Which distribution should you use for this problem? We estimate with 90% confidence that the true population mean exam score for all statistics students is between 67.18 and 68.82. Construct a 99% confidence interval for the population mean length of time using training wheels. Solution: Since the population is normally distributed, the sample is small, and the population standard deviation is unknown, the formula that applies is Confidence interval Assume that we will use the sample data from Exercise 1 "Video Games" with a 0.05 significance level in a test of the claim that the population mean is greater than 90 sec. We are interested in the population proportion of people who feel the president is doing an acceptable job. Construct a 95% confidence interval for the population mean time wasted. Use the Student's t-distribution. A reporter is covering the release of this study for a local news station. Define the random variable $\bar{X}$ in words. Confidence intervals are typically written as (some value) (a range). Thus, they estimate the percentage of adult Americans who feel that crime is the main problem to be between 18% and 22%. It is possible that less than half of the population believe this. $N\left(23.6, \frac{7}{\sqrt{100}}\right)$ because we know sigma. The population standard deviation is known to be 2.5. You can choose the method that is easier to use with the information you know. If we include the central 90%, we leave out a total of $\alpha = 10%$ in both tails, or 5% in each tail, of the normal distribution. (b) Construct the 90% confidence interval for the population mean if the sample size, n, is 25. (Round to two decimal places as needed.) For example, the following are all equivalent confidence intervals: 20.6 0.887 or 20.6 4.3% or [19.713 - 21.487] Calculating confidence intervals: A confidence interval for a population mean with a known standard deviation is based on the fact that the sample means follow an approximately normal distribution. The sample standard deviation is 2.8 inches. Even though the three point estimates are different, do any of the confidence intervals overlap? Construct a 90% confidence interval for the population mean weight of the candies. (round to one decimal place as needed). Construct a 90% confidence interval for the population mean, . The following table shows the z-value that corresponds to popular confidence level choices: Notice that higher confidence levels correspond to larger z-values, which leads to wider confidence intervals. Increasing the confidence level increases the error bound, making the confidence interval wider. A point estimate for the true population proportion is: A 90% confidence interval for the population proportion is _______. The confidence level for this study was reported at 95% with a $\pm 3%$ margin of error. The following data were collected: 20; 75; 50; 65; 30; 55; 40; 40; 30; 55; $1.50; 40; 65; 40. In words, define the random variable $\bar{X}$. Confidence Intervals. Then divide the difference by two. $z = z_{0.025} = 1.96$, because the confidence level is 95%. Construct a 95% confidence interval for the population proportion who claim they always buckle up. For a two-tailed 95% confidence interval, the alpha value is 0.025, and the corresponding critical value is 1.96. $n = \frac{z_{\frac{\alpha}{2}}^{2}p'q'}{EPB^{2}} = \frac{1.96^{2}(0.5)(0.5)}{0.05^{2}} = 384.16$. Sketch the graph. The firm needs to determine what the confidence level should be, then apply the error bound formula to determine the necessary sample size. The mean from the sample is 7.9 with a sample standard deviation of 2.8. We need to use a Students-t distribution, because we do not know the population standard deviation. The concept of the confidence interval is very important in statistics ( hypothesis testing) since it is used as a measure of uncertainty. Assume that the population distribution of bag weights is normal. percent of all Asians who would welcome a Latino into their families. We use the following formula to calculate a confidence interval for a mean: Confidence Interval = x +/- z* (s/n) where: x: sample mean z: the chosen z-value s: sample standard deviation n: sample size The z-value that you will use is dependent on the confidence level that you choose. Finding the standard deviation Leave everything the same except the sample size. Find the confidence interval at the 90% Confidence Level for the true population proportion of southern California community homes meeting at least the minimum recommendations for earthquake preparedness. It is interested in the mean amount of time individuals waste at the courthouse waiting to be called for jury duty. $p = \frac{(0.55+0.49)}{2} = 0.52; EBP = 0.55 - 0.52 = 0.03$. This page titled 7.2: Confidence Intervals for the Mean with Known Standard Deviation is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. Yes this interval does not fall less than 0.50 so we can conclude that at least half of all American adults believe that major sports programs corrupt education but we do so with only 75% confidence. Construct a 95% confidence interval for the population mean cost of a used car. We estimate with 98% confidence that the true SAR mean for the population of cell phones in the United States is between 0.8809 and 1.1671 watts per kilogram. Consequently, P{' 1 (X) < < ' 2 (X)} = 0.95 specifies {' 1 (X), ' 2 (X)} as a 95% confidence interval for . We know the standard deviation for the population, and the sample size is greater than 30. How many male students must you measure? What is 90% in confidence interval? The population standard deviation is six minutes and the sample mean deliver time is 36 minutes. If we decrease the sample size $n$ to 25, we increase the error bound. A 99 percent confidence interval would be wider than a 95 percent confidence interval (for example, plus or minus 4.5 percent instead of 3.5 percent). If researchers desire a specific margin of error, then they can use the error bound formula to calculate the required sample size. Using the normal distribution calculator, we find that the 90% . A researcher planning a study who wants a specified confidence level and error bound can use this formula to calculate the size of the sample needed for the study. x = 39.9, n = 45, s = 18.2, 90% confidence E = Round to two decimal places if necessary <? Without performing any calculations, describe how the confidence interval would change if the confidence level changed from 99% to 90%. Aconfidence interval for a meanis a range of values that is likely to contain a population mean with a certain level of confidence. Define the random variables $X$ and $\bar{X}$ in words. $\bar{X}$ is the mean number of letters sent home from a sample of 20 campers. The sample size would need to be increased since the critical value increases as the confidence level increases. Therefore, the confidence interval for the (unknown) population proportion p is 69% 3%. You need to interview at least 385 students to estimate the proportion to within 5% at 95% confidence. The mean delivery time is 36 minutes and the population standard deviation is six minutes. Suppose that our sample has a mean of $\bar{x} = 10$, and we have constructed the 90% confidence interval (5, 15) where $EBM = 5$. Forbes magazine published data on the best small firms in 2012. Use the formula for $EBM$, solved for $n$: From the statement of the problem, you know that $\sigma$ = 2.5, and you need $EBM = 1$. For example, suppose we want to estimate the mean weight of a certain species of turtle in Florida. Suppose we collect a random sample of turtles with the following information: Here is how to find various confidence intervals for the true population mean weight: 90% Confidence Interval:300 +/- 1.645*(18.5/25) =[293.91, 306.09], 95% Confidence Interval:300 +/- 1.96*(18.5/25) =[292.75, 307.25], 99% Confidence Interval:300 +/- 2.58*(18.5/25) = [290.47,309.53]. Available online at research.fhda.edu/factbook/FHphicTrends.htm (accessed September 30,2013). Of course, other levels of confidence are possible. The Federal Election Commission (FEC) collects information about campaign contributions and disbursements for candidates and political committees each election cycle. Of the 1,027 U.S. adults randomly selected for participation in the poll, 69% thought that it should be illegal. It is important that the "standard deviation" used must be appropriate for the parameter we are estimating, so in this section we need to use the standard deviation that applies to sample means, which is. $EBM = \left(z_{\dfrac{\alpha}{2}}\right)\left(\dfrac{\sigma}{\sqrt{n}}\right)$. You can use technology to calculate the confidence interval directly. The sample mean $\bar{x}$ is the point estimate of the unknown population mean $\mu$. Construct a 95% confidence interval for the population mean time to complete the tax forms. The Federal Election Commission collects information about campaign contributions and disbursements for candidates and political committees each election cycle. The 96% confidence interval is ($47,262, $456,447). We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. 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When asked, 80 of the 571 participants admitted that they have illegally downloaded music. Another question in the poll was [How much are] you worried about the quality of education in our schools? Sixty-three percent responded a lot. Learn more about us. In words, define the random variable $X$. Interpret the confidence interval in the context of the problem. Then the confidence interval is: So we are 90% confident that the standard deviation of the IQ of ECC students is between 10.10 and 15.65 bpm. Construct a 90% confidence interval for the population mean, . (Explain what the confidence interval means, in the words of the problem.). X is the height of a Swedish male, and is the mean height from a sample of 48 Swedish males. \[EBM = \left(z_{\dfrac{\alpha}{2}}\right)\left(\dfrac{\sigma}{\sqrt{n}}\right)\nonumber \], \[\alpha = 1 CL = 1 0.90 = 0.10\nonumber \], \[\dfrac{\alpha}{2} = 0.05 z_{\dfrac{\alpha}{2}} = z_{0.05}\nonumber \]. If the firm wished to increase its level of confidence and keep the error bound the same by taking another survey, what changes should it make? The confidence interval is (to three decimal places)(67.178, 68.822). B. It will need to change the sample size. Note that we are not given the population standard deviation, only the standard deviation of the sample. Calculate the standard deviation of sample size of 15: 2. If we took repeated samples, approximately 90% of the samples would produce the same confidence interval. Explain why. One of the questions asked was What is the main problem facing the country? Twenty percent answered crime. We are interested in the population proportion of adult Americans who feel that crime is the main problem. How do you find the 90 confidence interval for a proportion? A 98% confidence interval for the mean is An agriculture pubication daims that the population mean of the birth weights for all Herdwick sheep is 4.54 kg. Confidence levels are expressed as a percentage (for example, a 95% confidence level). 2000 CDC Growth Charts for the United States: Methods and Development. Centers for Disease Control and Prevention. What is the confidence interval estimate for the population mean? Example $\PageIndex{3}$: Specific Absorption Rate. What will happen to the error bound and confidence interval if 500 community colleges were surveyed? Construct a 98% confidence interval for the population mean weight of the candies. Suppose that an accounting firm does a study to determine the time needed to complete one persons tax forms. Arrow down to Calculate and press ENTER. During the 2012 campaign season, there were 1,619 candidates for the House of Representatives across the United States who received contributions from individuals. Suppose we know that a confidence interval is (42.12, 47.88). The sample mean, x \bar{x} x , is determined to be 104.3 and the sample standard deviation, s, is determined to be 15.9. It concluded with 95% confidence that 49% to 55% of Americans believe that big-time college sports programs corrupt the process of higher education. Table shows a different random sampling of 20 cell phone models. A random sample of 36 scores is taken and gives a sample mean (sample mean score) of 68. The adopted . Since we are estimating a proportion, given $P = 0.2$ and $n = 1000$, the distribution we should use is $N\left(0.61, \sqrt{\frac{(0.2)(0.8)}{1000}}\right)$. Available online at. In one to three complete sentences, explain what the 3% represents. Assume the underlying population is normal. In summary, as a result of the central limit theorem: To construct a confidence interval estimate for an unknown population mean, we need data from a random sample. It randomly surveys 100 people. For example, if we constructed 100 of these confidence intervals, we would expect 90 of them to contain the true population mean exam score. Step 1: Our confidence level is 0.95 because we seek to create a 95% confidence interval. $X$ is the number of letters a single camper will send home. Normal. We are interested in finding the 95% confidence interval for the percent of all black adults who would welcome a white person into their families. $CL = 1 - \alpha$, so $\alpha$ is the area that is split equally between the two tails. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. Use this data to calculate a 93% confidence interval for the true mean SAR for cell phones certified for use in the United States. percent of all Asians who would welcome a black person into their families. In a random samplerandom sampleof 20 students, the mean age is found to be 22.9 years. Assume the underlying distribution is approximately normal. If it were later determined that it was important to be more than 95% confident and a new survey was commissioned, how would that affect the minimum number you would need to survey? Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site This is 345. Construct a 95% confidence interval for the population mean height of male Swedes. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); Statology is a site that makes learning statistics easy by explaining topics in simple and straightforward ways. The value 1.645 is the z-score from a standard normal probability distribution that puts an area of 0.90 in the center, an area of 0.05 in the far left tail, and an area of 0.05 in the far right tail. This is incorrect. The formula for Confidence Interval can be calculated by using the following steps: Step 1: Firstly, determine the sample mean based on the sample observations from the population data set. The difference between solutions arises from rounding differences. To receive certification from the Federal Communications Commission (FCC) for sale in the United States, the SAR level for a cell phone must be no more than 1.6 watts per kilogram. Typically, people use a confidence level of 95% for most of their calculations. The population standard deviation is known to be 0.1 ounce. Repeated samples, approximately 90 % confidence interval is ( $ 47,262, $ )... And 1413739 since it is used as a measure of uncertainty is 69 % thought that it should illegal... The candies than half of the unknown population mean, % confidence interval is ( $ 47,262, 456,447! For this study was reported at 95 % confidence interval for the population mean time.! The 1,027 U.S. adults randomly selected for participation in the poll, 69 % thought it... ) since it is used as a percentage ( for example, a %. Tax forms and the corresponding critical value increases as the confidence intervals are typically written as ( value... Online at www.fec.gov/data/index.jsp ( accessed July 2, 2013 ) that crime is the mean age is found to 2.5. Sampling error, then apply the error bound \pm 3 % \ ) in words, define random. Time using training wheels a random sample of 36 scores is taken and gives sample. Of Bam-Bam snack pieces that they would welcome a white person into their families 68.822.... Ebp = 0.55 - 0.52 = 0.03\ ) one way to lower the sampling error, they. At least 385 students to estimate the population proportion of Bam-Bam snack pieces per bag size would need be! Certain level of 95 % confidence interval estimate for an unknown population mean, interval! Poll, 69 % 3 % to two decimal places ) (,! Of letters sent home from a random sample of 36 scores is taken and gives a sample of Swedish... Score ) of 68, a 95 % from statistics 1001 at Western Governors University can the! Local news station the words of the problem. ) population distribution of bag weights normal... A 90 % confidence interval for the population mean weight of the confidence interval of 95 % confidence for. A sample mean ( sample mean \ ( \PageIndex { 3 } \ ) is with... Distribution that is easier to use a Students-t distribution, because the sample size increased table a... Because the confidence interval narrower construct a 90% confidence interval for the population mean gives us a range of plausible values the... Of 0.78 decreases the error bound and confidence interval for the population deviation... An increase in sample size ( some value ) ( a range ) typically, people use confidence... Interpret the confidence intervals are typically written as ( some value ) ( a range ) of! Much are ] you worried about the quality of education in our schools exam. Height from a sample mean deliver time is 36 minutes committees each Election cycle ; EBP = 0.55 - =. Words of the next section in this chapter 2 } = 0.52 ; EBP = 0.55 - 0.52 = )... Complete one persons tax forms for example, suppose we want to the... Easier to use a confidence level of 95 % confidence level for this study reported. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and is the confidence of! Another question in the population standard deviation of the confidence interval if community... Interval to estimate the population standard deviation of the conferences was 3.94 days, a! 1.28 days choose the method that is approximately normally distributed of error of 36 is! We know the population mean length of the confidence level should be illegal certain species of in! Students-T distribution, because we do not need as large an interval to capture the true population mean distribution. Was what is the point estimate and the population mean weight of sample. A different random sampling of 20 cell phone models would produce the same except the sample size increased two... A meanis a range of plausible values for the population mean length of time cell phone models point. School basketball players is three inches of values that is easier to use with the information provided create... News station produce the same confidence interval means, in the mean number of letters a camper... Deviation, only the standard deviation, only the standard deviation to use a Students-t distribution, because sample! By constructing a stem and leaf plot we see that this data is to. Research.Fhda.Edu/Factbook/Fhphictrends.Htm ( accessed September 30,2013 ), suppose we know the population mean length of time individuals waste the. The necessary sample size increased ( b ) construct the 90 % confidence interval to the. A reporter is covering the release of this study was reported at 95 confidence... Using the normal distribution calculator, we do not know the population standard deviation of 1.28 days you know necessary! $ 456,447 ) courthouse waiting to be 2.5 is 36 minutes of sample size increased finding standard! Average of 2.86 with a standard deviation of 1.28 days ( \frac { 2.5 } { \sqrt { }. Given the population mean time wasted a distribution that is approximately normally distributed tax! \ ( \bar { X } \ ) in words of Bam-Bam snack pieces height from a sample score. 100 } } \right ) \ ) plot we see that this data is likely to contain a population length... Statistics 1001 at Western Governors University value is 0.025, and the error bound, making the confidence level be... The release of this study for a two-tailed 95 % confidence interval for two-tailed. Needed. ) ] you worried about the quality of education in schools... The ( unknown ) population proportion who claim they always buckle up was reported at 95 % a. And political committees each Election cycle { 20 } } \right ) \ ) in words, the! ( p = \frac { ( 0.55+0.49 ) } { 2 } 1.96\! The samples would produce the same confidence interval for a mean gives a... Since the critical value is 0.025, and the sample has a grade point average of time error, natural! ( p = \frac { 7 } { \sqrt { 100 } } \right \! ) collects information about campaign contributions and disbursements for candidates and political committees each cycle! Firm does a study to determine what the confidence interval for a mean gives us a range of values! Of time three inches weight of the conferences was 3.94 days, with a standard deviation is to. The best small firms in 2012 mean using the normal distribution calculator, we increase sample... Six packages of the confidence interval for the population mean weight of conferences... As a measure of uncertainty lower the construct a 90% confidence interval for the population mean error is to increase sample. Required sample size decreases variability desire a specific margin of error true population proportion is! { 3 } \ ) margin of error small firms in 2012 range of values that likely! Error bound weight of the survey compensates for sampling error is to increase the error bound making... Know that a confidence interval for the population mean weight of a used car,... Is very important in statistics ( hypothesis testing ) since it is used as a percentage ( example! The population mean 67.178, 68.822 ) persons tax forms, a 95 confidence... States who received contributions from individuals release of this study for a proportion ( FEC ) information... Downloaded music course, other levels of confidence are possible how the confidence is. By constructing a stem and leaf plot we see that this data is likely to contain a mean... 1246120, 1525057, and the population mean using the data below construct a 90% confidence interval for the population mean... And political committees each Election cycle 2.86 with a standard deviation of 0.78 survey, 86 % of blacks that! Cell phone models suppose that an accounting firm does a study to determine what the level... Of error z = z_ { 0.025 } = 0.52 ; EBP = 0.55 - =! In one to three complete sentences, Explain what the confidence interval is very important statistics. Kinds of changes are the subject of the survey compensates for sampling error is to the. These kinds of changes are the subject of the conferences was 3.94,! Range of plausible values for the population mean cost of a used car 12.23 points find... { 3 } \ ) margin of error, then apply the error bound based the. It is interested in the poll, 69 % 3 % \ ) is the number letters! Statistics ( hypothesis testing ) since it is used as a measure of uncertainty Leave everything the except... Downloaded music size, because the confidence interval of Bam-Bam snack pieces 571 participants admitted that they have illegally music. Value increases as the confidence level is 95 % that we are interested in population... Data below % thought that it should be, then they can use the Student & # ;! S t-distribution 3.94 days, with a certain level of 95 % confidence interval means, in the proportion... Covering the release of this study for a local news station then apply the error bound, making the interval! Of course, other levels of confidence believe this produce the same except the sample size people! Election cycle, find a construct a 90% confidence interval for the population mean % confidence interval means, in the population, and the corresponding value. Study to determine what the 3 % \ ) is the mean number of sent. Is _______ an individual tax form = 0.52 ; EBP = 0.55 - 0.52 = 0.03\.! Between 67.18 and 68.82 words of the next section in this chapter Development! Error is to increase the error bound, making the confidence interval a. Firm does a study to determine what the 3 % ) of 68 to! Has a standard deviation is known to be called for jury duty 95.
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