The following data represent the age (in weeks) at which babies first crawl based on a survey of 12 mothers conducted by Essential Baby (Source: www.essentialbaby.com). The ages are normally distributed. The Age (in weeks) When a Baby First Crawled 30 47 52 44 35 39 26 28 37 56 26 39 a) Using technology (calculator or Excel), find the sample mean and the sample standard deviation. (Round two decimal places) b) Find the 95% confidence interval for the population mean by hand. Show all work by writing the formula and substituting in the appropriate values. (Round two decimal places) c) Find the 95% confidence interval for the population mean using technology (calculator). (Round four decimal places) d) Interpret the solution in the context of the problem.

a. Sample mean and standard deviation: Enter the values of age when a baby first crawled in columns A of an excel. The sample mean is 38.25 (using the Excel function, =AVERAGE(A1:A12). The sample standard deviation is 10.00 (using the Excel function, =STDEV.S(A1:A12)). b. Confidence interval: Since the population standard deviation is unknown and the sample size is small, t distribution can be used for the computation of confidence interval. The sample size, n is 12. The degrees of freedom is 12-1 =11. From the EXCEL, using the formula, =T.INV.2T(0.05,11), the critical value is 2.201. The 95% confidence interval can be calculated as follows: CI=x¯±tsn=38.25±2.2011012=38.25±6.354=31.90,44.60 The 95% confidence interval for the population mean is (31.90,44.60). Lower Limit = 31.90 Upper Limit = 44.60c. Step-by-step procedure to obtain the confidence interval using MINITAB software: Enter the values of age when a baby first crawled in column c1. Go to Stat > Basic statistics > one sample t. Select “One or more samples, each in a column”. Select the column “Age when a baby first crawled” Under options, Enter confidence level as 95.0. Click OK on all dialogue boxes. The output obtained from MINITAB is given below:d. One can be 95% confident that the population mean age when a baby first crawled is between (31.90,44.60).