Answer all the questions and provide a step-by-step solutions
Question 8. 25 new mothers were investigated about their sleeping hours per day before and after having a baby. Researchers want to know if new mothers’ sleeping hours have been significantly reduced.
Sample average and sample standard deviation of D (before - after) are computed 𝑋̅𝐷= 2.5 , 𝑆𝐷=4. Please test this hypothesis at 5% significance level and calculate the p-value.
Question 9.A primary school claims that their average class size is equal to 35 students. This claim is being tested with a level of significance alpha = 0.02 using the following sample of class sizes: 42, 28, 36, 47, 35, 41, 33, 30, 39, and 48. Assume class sizes are normally distributed.
Question 10.
Answer the following questions
(a) (3pt) Researchers determined that 60 tissues is the mean number of tissues used during a cold. Suppose a random sample of 41 tissue users yielded the following data on the number of tissues used during a cold: 𝑥̅ = 52, S = 22. Using the sample information provided, calculate the value of the test statistic.
(b) (3pt) Researchers determined that 60 tissues is the mean number of tissues used during a cold. The population standard deviation is unknown. Suppose a random sample of 41 tissue users yielded the following data on the number of tissues used during a cold: 𝑥̅ = 52, S = 22. Suppose the alternative you wanted to test was H1: mu < 60. State the correct rejection region for alpha = 0.05.
(c) (4pt) Researchers determined that 60 tissues is the mean number of tissues used during a cold. Suppose a random sample of 41 tissue users yielded the following data on the number of tissues used during a cold: 𝑥̅ = 52, S = 22. Suppose the test statistic falls in the rejection region with significance level alpha = 0.05. Provide a conclusion for the hypothesis test.