Instructions
The following assignment should be typed and printed or handwritten and turned in to the CA office in room 201 TMCB. If there is no one in the CA Office, you can slip your assignment through the slot in the door. You must follow the instructions below or you will not receive credit. You can turn in the assignment up until 5:00 PM on the due date.
Important Notices:
If you do not staple multiple pages, you may lose points.
If you do not put your section number on the paper, you may lose points.
As shown below, please fold your paper lengthwise and on the outside write (a) your name, (b) Stat 121, (c) your section number, and (d) the assignment number. (An example is available outside the CA Office.)
The situation is as follows:
University personnel are concerned about the sleeping habits of students and the negative impact on academic performance. In a random sample of 377 U.S. college students, 209 students reported experiencing excessive daytime sleepiness (EDS). Is there sufficient evidence to conclude that more than half of U.S. college students experience EDS? Use a 5% level of significance.
Part A. Test of Significance
STATE:
At the α = 0.05 level, is there sufficient evidence to conclude that more than half of U.S. college students experience EDS? (Put this verbatim on your paper.)
Answer all the following questions in complete sentences when applicable.
PLAN:
(1) State the name of the appropriate test procedure you will use (e.g., one-sample t test for means).
(2) Describe the parameter of interest in the context of the problem.
(3) State the null and alternative hypotheses.
(4) Write down the significance level.
SOLVE:
(5) List and check the conditions for the test procedure you named above.
(6) Obtain the value of the sample proportion. (Round your answer to FOUR decimal places).
(7) Write the calculated test statistic (including your calculations) and its associated P-value using the appropriate table, not from statistical software. Do not round any numbers used in your calculations for the test statistic, and round your final answer for the test statistic to two decimal places.
CONCLUDE:
(8) Answer the question posed in the STATE step in context, by including these three parts in your conclusion:
- Compare P-value with α
- Decide whether to reject or fail to reject the null hypothesis
- State your conclusion in context
Part B. Confidence Interval Estimation
STATE:
What is a 90% confidence interval estimate for the proportion of all of U.S. college students who experience excessive daytime sleepiness? (Please add this verbatim on your paper)
PLAN:
(1) State the name of the appropriate estimation procedure (e.g. one-sample t confidence interval for estimating the mean difference).
(Note) You have already described the parameter being estimated in part A, so you don't have to repeat it here.
SOLVE:
(2) You have already listed the conditions, now check the condition for the normality of the sampling distribution of p-hat for confidence interval estimation.
(3) Write down the confidence level and the z* critical value.
(4) Calculate the confidence interval in interval form. Be sure to show your work. Do not round any numbers used in your calculations for the confidence interval, and round your final answer for the lower and upper limits to three decimal places.
CONCLUDE:
(5) Interpret your confidence interval in context, by including these three parts in your conclusion:
- Level of confidence
- Parameter of interest in context
- The interval estimate