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SYSTOLIC BLOOD PRESSURE Chapter 8 – Confidence Intervals about a Population Mean μ 3) We want to estimate the mean systolic blood pressure of a group of overweight 18-24 year old women. Thirty-six women from this group were selected at random and their mean systolic blood pressure was 121 mm Hg. Assume systolic blood pressures of women of this age group have a standard deviation of σ = 13.1 mm Hg. a) What is the point estimate? The point estimate is the sample mean, that is x-bar = 121 b) Verify that the requirements for constructing a confidence interval about x-bar are satisfied. The sample is a simple random sample The value of the population standard deviation σ is known. (we’ll use z) The sample size is larger than 30 c) Construct a 99% confidence interval estimate for the systolic blood pressure of all overweight women of this age group. (Are you using z or t? Why?) The value of the population standard deviation σ is known. (We’ll use z) x z* n x z* n 13.1 13.1 121 2.575* 36 36 121 5.622 121 5.622 121 2.575* 115.378 126.622 For calculator feature use STAT, arrow to TESTS, and select 7:ZInterval, select Stats enter the required information, and CALCULATE d) The statement “99% confident” means that, if 100 samples of size __36___ were taken, about __99___ intervals will contain the parameter μ and about __1__ will not. e) We are __99___% confident that the mean systolic blood pressure of overweight 18-24 year old women is between ___115.38 __ and ____126.62 mm Hg__ f) With 99% confidence we can say that the mean systolic blood pressure of overweight 1824 year old women is ___121 mm Hg __ with a margin of error of __5.62_____ g) For 99% of such intervals, the sample mean would not differ from the actual population mean by more than __5.62 mm Hg_____ h) What would be necessary in order to construct a more precise 99% confidence interval estimate for the systolic blood pressure of this group? If we want to keep the same degree of confidence, we have to select a larger sample from the population. Or, if we don’t mind sacrificing our confidence, use a lower confidence level. 1 i) You know that the mean systolic blood pressure of women aged 18-24 is 114.8 mm Hg. What does the interval constructed in part (c) suggest? Explain. The interval (115.38, 126.62) is completely above 114.8, which suggests, with 99% confidence, that the mean systolic blood pressure of the group of women from which the sample was selected is higher than 114.8 mm Hg. j) How large of a sample should be selected in order to be 99% confident that the point estimate x-bar will be within 4 units of the true population mean? z * 2.575*13.1 n 72 4 E 2 2 The margin of error of the interval constructed in part (c) was 5.622. If we want our estimate to be more precise with an error of at most 4 units we should select a sample of size 72 If we select a simple random sample of 72 women from a group of overweight 18-24 year old women and measure their systolic blood pressures, we could say with 99% confidence that the xbar from the selected sample will be within 4 units of the true population mean systolic blood pressure of ALL overweight 18-24 year old women k) Circle the correct choice: Increasing the confidence level produces a longer/shorter Increasing the confidence level increases/decreases Increasing the sample size increases/decreases interval. the precision. the precision. 2