Math 2311 EMCF Homework 13 Sections 8.1 - 8.6 Honework will NOT be accepted through email or in person. Homework must be submitted through CourseWare, https://www.casa.uh.edu, before the deadline. Submit this assignment on CourseWare under \"EMCF\" and choose ehw13. For each of the following situations in problems 1-7, determine which of the following tests should be used. Assume necessary conditions have been met. (Answers may be used more than once or not at all.) A. 1 sample z test E. 1 proportion z test B. 1 sample t test F. 2 proportion z test C. 2 sample t test G. matched pairs t test D. Chi-squared 1. Consumer Reports (January 1993) stated that the mean retail cost of an AT&T model 3730 cellular phone was $600. A random sample of 10 stores in Los Angeles had a mean cost of $586.50 with standard deviation of $26.77. Does this indicate that the mean cost in Los Angeles is less than $600? 2. Athabasca Fishing Lodge is located on Lake Athabasca in northern Canada. In one of their recent brochures, the lodge advertises that 75% of their guests catch northern pike over 20 pounds. Suppose last summer 64 out of a random sample of 83 guests did in fact catch northern pikes weighing over 20 pounds. Does this indicate that the population proportion of guests who catch pikes over 20 pounds is different from 75%? 3. A new law has been passed giving city police greater powers in apprehending suspected criminals. For six neighborhoods, the numbers of reported crimes one year before and one year after the new law are shown. Does this indicate that the number of reported crimes have dropped? Neighborhood Before After 1 18 21 2 35 23 3 44 30 4 28 19 5 22 24 6 37 29 4. A machine has a record of producing 80% excellent, 16% good, and 4% unacceptable parts. After extensive repairs, a sample of 200 produced 157 excellent, 42 good, and 1 unacceptable part. Have the repairs changed the nature of the output of the machine? 5. A random sample of 378 hotel guests was taken one year ago, and it was found that 178 requested nonsmoking rooms. Recently, a random sample of 516 hotel guests showed that 320 requested nonsmoking rooms. Do these data indicate that the proportion of hotel guests requesting nonsmoking rooms has increased? 6. Based on information from Consumer Reports (October 1993), a random sample of 86 thirty-gram servings of Duncan Hines Chocolate Chip Cookies had a mean of 132 calories with standard deviation 27 calories. A random sample of 75 Pepperidge Farm Chocolate Chip Cookies (30-gram servings) had a mean of 124 calories and standard deviation of 33 calories. Does this information indicate that there is a difference in the average number of calories for these two cookies brands? 7. Math Horizons is a publication of the Mathematical Association of America. The 1993 issue reports that in the U.S., graduating math majors who also have studied actuarial science (statistics) have a mean first-year salary of $27,600. Suppose that a random sample of 36 such graduates in the Denver region showed that they were earning an average of $27,810 with standard deviation $915. Does this indicate that the population mean salary in the Denver region is higher than the national average? 1 8. A polling organization announces that the proportion of American voters who favor congressional term limits is 64 percent, with a 95% confidence margin of error of 3 percent. If the opinion poll had announced the margin of error for 80% confidence rather than 95% confidence, this margin of error would be a. b. c. d. e. 3%, because the same sample is used. Less than 3%, because we require less confidence. Less than 3%, because the sample size is smaller. Greater than 3%, because we require less confidence. Greater than 3%, because the sample size is smaller. 9. The following are percentages of fat found in 5 samples of each of two brands of ice cream: Brand A Brand B 5.7 6.3 4.5 5.7 6.2 5.9 6.3 6.4 7.3 5.1 Which of the following procedures is appropriate to test the hypothesis of equal average fat content in the two types of ice cream? a. b. c. d. matched pairs t-test with 5 degrees of freedom two sample t-test with 9 degrees of freedom matched pairs t-test with 4 degrees of freedom two sample t-test with 4 degrees of freedom 10. In the previous problem, a Type II error would be: a. b. c. d. to to to to conclude conclude conclude conclude that that that that the the the the fat fat fat fat content content content content is is is is different when it actually is. different when it actually is not. the same when it actually is. the same when it actually is not. For questions 11 and 12, use the two-way table specifying favorite ice cream flavors by gender. Chocolate Vanilla Strawberry Male 32 14 3 Female 16 4 10 11. What is the expected number of females who prefer vanilla? a. b. c. d. e. 18.2 6.8 4.9 11.2 none of these 12. We wish to test if there is an association between gender and flavor choice. Which of the following is a valid conclusion from this information? a. We have sufficient evidence of an association between gender and ice cream flavor preference at the 5% level. b. There is insufficient evidence of a relationship between gender and ice cream preference. c. We have sufficient evidence that there is no association between gender and ice cream flavor preference at the 5% level. d. There is insufficient evidence to support the claim that gender and ice cream preference are independent. 2 13. A researcher wants to determine whether there is a difference between the proportions of males and females who believe in aliens. The sample information is: Sample Size number who said "yes" Male 75 50 Female 100 45 Based on the results of a significance test you should a. Reject H0 at the 1% significance level. b. Fail to reject H0 at the 1% significance level but reject H0 at the 5% significance level. c. Fail to reject H0 at the 5% significance level. 14. There are 4 TV sets in the student center of a large university. At a particular time each day, four different soap operas (1, 2, 3 and 4) are viewed on these TV sets. It is believed that the percentages of the audience captured by these shows are 25%, 30%, 25%, and 20%, respectively. 300 students are surveyed and the summary of their response follows: Observed 1 80 2 88 3 79 4 53 Do these observed data fit the belief of percentages who watch each show ( = 0.05)? a. Yes b. No 15. An association of college bookstores reported that the average amount of money spent by students on textbooks for the Fall 2010 semester was $325.16. A random sample of 75 students at the local campus of the state university indicated an average bill for textbooks for the semester in question to be $312.34 with a standard deviation of $76.42. Do these data provide significant evidence that the actual average bill is different from the $325.16 reported? Based on the results of the significance test, you should a. Reject H0 at the 1% significance level. b. Fail to reject H0 at the 1% significance level but reject H0 at the 5% significance level c. Fail to reject H0 at the 5% significance level 3