1. Text Exercise 1.38 (a) (b) (Hint: Find the probability of the event in question of occurring.) In the statement of this exercise, you are instructed to estimate  and  by taking them to be equal to the sample values reported in the study. However, the following misprint needs to be corrected: “  = 4.29” should read “  = 4.59”. Since practically no samples of size n = 50 CAHS scores have a mean more than 6, we do not expect to observe this. Actually observing a sample of size n = 50 with mean of 6.2 would make us conclude that  = 4.59 is not true. Homework #4Score____________/ 15Name ______________

2. Text Exercise 1.42 (a) (b) (c) (No matter what method you use to do the necessary calculations, you should be able to verify that y = 1.073 and s = 0.2316.) n = y =s = 6 1.0730.2316 df = t 0.025 = 5 2.571 1 –  =  — = 2  — = 2 0.95 0.025 1.073 – (2.571)(0.2316/  6), 1.073 + (2.571)(0.2316/  6) We can be 95% confident that the mean decay rate of fine particles produced from oven cooking or toasting is between 0.830 and 1.316 m/hour, 0.830, 1.316 Among all possible samples of size n = 6, 95% of these samples yield a confidence interval that actually contains the population mean. Either the population of decay rates has a normal distribution the sample size n = 6 is sufficiently large so that y has a normal (or approximate) distribution.

3. Text Exercise 1.46 (a) (b) Text Exercise 1.48 Answer this question by considering a hypothesis test H 0 :  = 8 vs. H 1 :   8 where the t test statistic is used. Indicate whether or not each of the following changes could affect the rejection region for this hypothesis test: The hypothesized mean value 8 is changed to 20. The sample size n is changed. The significance level  is changed. The alternative hypothesis is changed to H 1 :  > 8. Write each hypothesis first in words, then using the appropriate symbol(s). H 0 : H 1 : The rejection region remains the same. The rejection region could change. Rejecting H 0 provides strong evidence to support H 1 but does not prove H 1 is true. The mean listening time is equal to 9 seconds, that is,  = 9. The mean listening time is different from 9 seconds, that is,   9.

4. (b)Find and interpret a 95% confidence interval for the mean yearly income ($1000s) of voters in the state. Step 15: The output title Means can be deleted. Use the File> Print options to obtain a printed copy of the sample statistics. Since there is no need for you to save the output, you may close the SPSS output window without saving the results, after you have your printed copy of the output. Attach this printed copy to this assignment before submission. Exit from SPSS. n = y =s = These statistics are on the SPSS output. 30 45.4015.895 df = t 0.025 = 29 2.045 1 –  =  — = 2  — = 2 0.95 0.025 45.40 – (2.045)(15.895/  30), 45.40 + (2.045)(15.895/  30) We can be 95% confident that the mean yearly income of voters in the state is between 39.465 and 51.335 thousand dollars, 39.465, 51.335 Additional HW Exercise #1.9 - continued