Fall 2011 Exam Score: /69. Exam 4

Transcription

1 Math 12 Fall 2011 Name Exam Score: /69 Total Class Percent to Date Exam 4 For problems 1-8, circle the letter next to the response that best answers the question or completes the sentence. You do not have to show any work or write any explanations here. Make sure to read each statement carefully! (2 pts each) 1. The alternative hypothesis is a claim about a: A) parameter, where the claim is assumed to be true until it is declared false B) parameter, where the claim is assumed to be true if the null hypothesis is declared false C) statistic, where the claim is assumed to be true if the null hypothesis is declared false D) statistic, where the claim is assumed to be false until it is declared true 2. A two-tailed hypothesis test contains: A) one rejection region and two non-rejection regions B) two rejection regions and one non-rejection region C) two rejection regions and two non-rejection regions D) one rejection region and one non-rejection region 3. In a left-tailed hypothesis test, the sign in the alternative hypothesis is: A) not equal to B) greater than C) less than D) less than or equal to 4. For a two-tailed test, the P-value is: A) the area under the curve between the mean and the observed value of the sample statistic B) twice the area under the curve between the mean and the observed value of the sample statistic C) the area in the tail under the curve on the side which the sample statistic lies D) twice the area in the tail under the curve on the side which the sample statistic lies 5. In a hypothesis test, the P-value is: A) the probability of rejecting the null hypothesis when the null hypothesis is true B) the probability of not rejecting the null hypothesis when the alternative hypothesis is true C) the probability of selecting a sample whose test statistic is at least as extreme as the observed test statistic, assuming the null hypothesis is true D) the probability of selecting a sample whose test statistic is at least as extreme as the observed test statistic, assuming the null hypothesis is false

2 6. If we get a P-value of in a hypothesis test with 5% significance level, then we would A) REJECT the null hypothesis B) NOT REJECT the null hypothesis C) not know whether or not to reject unless we knew if it was a one or two tailed test D) not know whether or not to reject unless we knew the sample size 7. A bank manager claims that 90% of its customers are satisfied with the services provided by the bank. A simple random sample of 200 customers at this bank, shows that 83% of them are satisfied with the services provided by the bank. If we wanted to test the claim that less than 90% of the bank s customers are satisfied, we A) could use the ZTest program on our TI83/84 calculators B) could use the TTest program on our TI83/84 calculators C) could use the 1-PropZtest program on our TI83/84 calculators D) don't have enough information to test this claim 8. A study was made to find the difference in income between spouses. The data consisted of male vs. female incomes for each couple in the sample (gay marriages were not included in the study). This study contains A) independent samples B) matched pairs C) non of the above 9. Suppose you want to test, at the α = 0.05 significance level, if the proportion of female Cabrillo students differs from 60%. (8 pts) a) State what your null and alternative Hypotheses would be H 0 : H 1: b) Explain what a Type I Error would be in this context (do not use H 0 or H 1 in your answer, but describe the situation with words). c) Explain what a Type II Error would be in this context (do not use H 0 or H 1 in your answer, but describe the situation with words). d) Interpret α = 0.05 in this test.

3 For problems you need to show work in order to receive credit! Make sure to clearly state what parameters, formulas and calculator programs you are using. Make sure to use correct symbols! Write your answer using a complete sentence with correct units that indicates that you understand the answer. For hypotheses tests, follow the 5 step process as stated in class: 1.State the null and alternative hypotheses. 2.State which distribution and test to use, and why. 3.Draw a picture and label the critical values along with the rejection and non-rejection region(s). 4.Calculate the test statistics and p-value. 5.Make a decision and write a complete sentence answer with correct units. Unless stated otherwise, include at least 3 significant digits in your final answers (remember that this is not the same as three decimal places), which means you will want to include more than that in your mid-calculations. 10. A restaurant claims that it serves food to its customers, on average, within 15 minutes after the order is placed. A sample of 36 customers showed that the mean time taken to serve food to them was minutes with a standard deviation of 2.4 minutes. (10 pts) Using the sample statistics and a 5% significance level, test whether the restaurant's claim is false.

4 11. Listed below are the costs (in dollars) of flights from New York (JFK) to San Francisco for seven different airlines. Use a 0.01 significance level to test the claim that flights scheduled one day in advance cost more than flights scheduled 30 days in advance. Flight scheduled one day in advance Flight scheduled 30 days in advance We will assume that the population of differences is normally distributed. Use a 0.01 significance level to test the claim that flights scheduled one day in advance cost more than flights scheduled 30 days in advance. (14 pts)

5 12. A simple random sample of front-seat occupants involved in car crashes is obtained. Among 2823 occupants not wearing seat belts, 31 were killed. Among 7765 occupants wearing seat belts, 16 were killed. (11 pts) a) What is the point estimate of the difference between the population proportions p1 p2? b) Construct a 98% confidence interval for the difference between the population proportions p1 p2.

6 For the following problem you can use your calculator for all of it - no formulas needed! But you have to specify your hypotheses, say what programs you are using and why, and write whole sentence answers. It is up to you if you want to use the critical value approach or P-value approach. 13. A random sample of 1500 female workers who are not union members, showed average earnings of $388 per week, with a standard deviation of $30. A random sample of 2000 female workers who are union members, showed average earnings of $505 per week, with a standard deviation of $35. (10 pts) a) Construct a 95% confidence interval for the difference between the two population means. b) Test at the 2.5% significance level whether the mean weekly earning of female workers who are not union members are less than those of female workers who are union members.