Question

show work please

Problem 2: Use the following to answer questions a)-e): A random sample of 48 students at a large university reported getting an average of 7 hours of sleep on weeknights, with standard deviation 1.62 hours. A dotplot of the data is provided. 9.6 Weekniaht Sleep a. Briefly explain why it is reasonable to use a t-distribution to perform inference about the mean amount of weeknight sleep for students at this university. (2 points) The research question: It is recommended, for most college age students, to get 8 hours of sleep each night. Does this sample provide evidence that college students at this university get significantly less sleep, on average, than what is recommended? b. State the hypotheses for testing if this data provides evidence that college students at this university get significantly less sleep, on average, than what is recommended. Use proper notation. (3 points) c. Use the provided formula sheet to identify the appropriate test statistic formula. Then calculate the test statistic. Please show all of your work including the formula that you are using. (4 points) d. Use StatKey and your result from parte) to obtain the p-value. (3 points) e. Using a significance level of a = 0.05, clearly state the conclusion of the hypothesis test in the context of this problem. (4 points)

Answer 1

(a) The t-distribution is appropriate here since the population standard deviation is unknown.

(b) The hypothesis being tested is:

H₀: µ = 8

H_a: µ < 8

(c) The test statistic, t = (x - µ)/s/√n

t = (7 - 8)/1.62/√42

t = -4

(d) The p-value is 0.0001.

(e) Since the p-value (0.0001) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that µ < 8.