Download Confidence Intervals for Head Circumference in 2-Month-Old Babies: Girls vs Boys - Prof. M and more Papers Statistics in PDF only on Docsity! HEAD CIRCUMFERENCE Chapter 8 – Confidence Intervals about a Population Mean mu 6) a) Estimate the mean head circumference of all baby-girls that are two months old by constructing a 99% confidence interval. We start by selecting a simple random sample of size n. In our calculator we actually have one such a sample labeled FHED We calculate the mean of the selected sample. This is our point estimate. Our point estimate is x = 40.048 (Do STAT, CALC, 1-Var Stats on FHED to get the statistics) To fine-tune our estimate, we find a confidence interval which is a range (or interval) of values that is likely to contain the true value of the population mean. Show all work, and then check with a calculator feature (Are you using z or t? Why?) We are using t because we are not given the standard deviation of the population σ; we have the standard deviation of the sample which is 1.639 (Our sample statistics are: x = 40.048, s = 1.639, n = 50) The degrees of freedom are 49. Since we don’t have that value in our table we’ll use 49. The t-score for a 99% confidence interval is 2.69 (see t-table on the back cover of book) * * 1.639 1.639 40.048 2.69* 40.048 2.69* 50 50 40.048 .62351 40.048 .62351 39.42 40.67 s s x t x t n n For calculator feature use STAT, arrow to TESTS, and select 8:TInterval, select DATA option enter the required information, and CALCULATE b) Complete the following: (i) With 99% confidence we can say that the mean head circumference of two-month-old baby girls is __40.048 cm____ with a margin of error of __.624 cm_____ (ii) We are _99___% confident that the interval from ___39.42_ to ___40.67___ actually does contain the true value of the population mean μ. This means that if we were to select many different samples of the same size and construct the corresponding confidence intervals, in the long run __99____% of them would actually contain the value of μ. (iii) For 99% of such intervals, the sample mean would not differ from the actual population mean by more than __.624 cm_____ Page 6 HEAD CIRCUMFERENCE Chapter 8 – Confidence Intervals about a Population Mean mu 7) a) Estimate the mean head circumference of all baby-boys that are two months old by constructing a 99% confidence interval. We start by selecting a simple random sample of size n. In our calculator we actually have one such a sample labeled MHED We calculate the mean of the selected sample. This is our point estimate. Our point estimate is x = 41.098 (Do STAT, CALC, 1-Var Stats on MHED to get the statistics) To fine-tune our estimate, we find a confidence interval which is a range (or interval) of values that is likely to contain the true value of the population mean. Show all work, and then check with a calculator feature. (Are you using z or t? Why?) We are using t because we are not given the standard deviation of the population σ; we have the standard deviation of the sample which is 1.498 (Our sample statistics are: x = 41.098, s = 1.498, n = 50) The degrees of freedom are 49. Since we don’t have that value in our table we’ll use 49. The t-score for a 99% confidence interval is 2.69 (see t-table on the back cover of book) * * 1.498 1.498 41.098 2.69* 41.098 2.69* 50 50 41.098 .56987 41.098 .56987 40.53 41.67 s s x t x t n n For calculator feature use STAT, arrow to TESTS, and select 8:TInterval, select DATA option enter the required information, and CALCULATE b) Complete the following: (i) With 99% confidence we can say that the mean head circumference of two-month-old baby boys is _41.098 cm_ with a margin of error of __.57 cm____ (ii) We are _99___% confident that the interval from ___40.53 to ____41.67__ actually does contain the true value of the population mean μ. This means that if we were to select many different samples of the same size and construct the corresponding confidence intervals, in the long run ___99___% of them would actually contain the value of μ. (iii) For 99% of such intervals, the sample mean would not differ from the actual population mean by more than ___.57 cm____ 2
