The data set below is a random sample of the heights (in meters) of women belonging to a certain ethnic subgroup. Assume the population is normally distributed. 1.60 1.44 1.61 1.54 1.58 1.47 C a) Find the mean and standard deviation of the data. (Give your answers to three decimal places.) C Answers: mean = standard deviation = b) Conduct a hypothesis test at the 0.10 significance level to test the claim that the population mean is less than 1.58. The critical region runs from to Answers: The value of the test statistic is The correct conclusion is At the 0.1 significance level, the sample data support the claim that the population mean is less than 1.58. At the 0.1 significance level, there is not sufficient sample evidence to support the claim that the population mean is less than 1.58. At the 0.1 significance level, there is sufficient sample evidence to reject the claim that the population mean is less than 1.58. At the 0.1 significance level, there is not sufficient sample evidence to reject the claim that the population mean is less than 1.58