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QNT 561 Week 3 Individual Mystatslab Problem Set 1. Which hypothesis, the null or the alternative, is the status-quo hypothesis? 2. A university economist conducted a study of elementary school lunch menus. During the state-mandated testing period, school lunches averaged 890 calories. The economist claimed that after the testing period ended, the average caloric content of the school lunches increased/dropped significantly. Set up the null and alternative hypothesis to test the economist’s claim. 3. Suppose the mean GPA of all students graduating from a particular university in 1975 was 2.40. The register plans to look at records of graduating last year to see if the mean GPA has decreased. Define notation and state the null and alternative hypothesis for this investigation. 4. A random sample of 100 observations from a population with standard deviation 58 yielded a sample mean of 111. Complete parts a through c. 5. A final scores of games of a certain sport were compared against the final point spreads established by oddsmakers. The difference between the game outcome and point spread (called a point-spread error) was calculated for 250 games. The mean and standard deviation of the point-spread errors are = 1.7 and s = 13.1. Use this information to test the hypothesis that the true mean point-spread error for all games differs from 0. Conduct the test at α = 0.10 and interpret the result. 6. If a hypothesis test were conducted using α = 0.025, for which of the following p-values would the null hypothesis be rejected? 7. For the α and observed significance level (p-value) pair, indicate whether the null hypothesis would be rejected. α = 0.10, p-value = 0.001 8. In a test of the hypothesis H0:µ = 40 versus Ha: µ ≠ 40, a sample of n = 50 observations possessed mean = 40.7 and standard deviation s = 3.8. Find the p-value for this test. 9. In a study it was found that the averge age of cable TV shoppers was 55 years. Suppose you want to test the null hypothesis, H0:µ = 55, using a sample of n = 60 cable TV shoppers. 10. A sample of seven mesurements, randomly selected from a normally distributed population, resulted in the summary statistics = 4.6 and s = 1.2. Complete parts athrough c. 11. A study analysis recent incidents involving terrorist attacks. Data on the number of individual suicide bombings that occurred in each of 20 sampled terrorist group attcks against a country is reproduced in the data table below. An Excel/DDXL printout is shown to the right. Complete parts a through e. 12. When planning for a new forest road to be used for tree harvesting, planners must select the location to minimize tractor skidding distance. The skidding distances (in meters) were measured at 20 randomly selected road sites. The data are given below. A logger working on the road claims the mean skidding distance is atleast 424 meters. Is there sufficient evidence to refute this claim? Use α = 0.10 / α = 0.01.
13. For the binomial sample sizes and null hypothesized values of p in each part, determine whether the sample size is large enough to meet the required conditions for using the normal approximation to conduct a valid large-sample hypothesis test of the null hypothesis H 0: p = p0. Complete parts a through e. 14. Suppose a consumer group rated 49 brands of toothpaste based on whether or not the brand carries an American Dental Association (ADA) seal verifying effective decay prevention. The results of a hypothesis test for the proportion of brands with the seal are shown to the right. Complete parts a through c. 15. In order to compare the means of two populations, independent random samples of 410 observations are selected from each population, with the results found in the table to the right. Complete parts a through e. 16. To use the t-statistic to test for a difference between the means of two populations, what assumptions must be made about the two populations? About the two samples? 17. 18. Independent random samples are selected from two populations and are used to test the hypothesis H0: (µ1 - µ2) = 0 against the alternative Ha: (µ1 - µ2) ≠ 0. An analysis of 234 observations from population 1 and 310 from population 2 yielded a p-value of 0.113. Complete parts a and b below. 19. A study was done to examine whether the perception of service quality at hotels differd by gender. Hotel guests were randomly selected to rate service items on a 5-point scale. The sum of the items for each guest was determined and a summary of the guest scores are provided in the table. Complete parts a and b. 20. To determine if winning a certain award leads to a challenge in life expectancy, researches sampled 748 award winners and matched each one with another person of the same sex who was in the same profession and was born in the same era. The lifespan of each pair was compared. Complete parts a through c below. 21. A new testing method was developed to reduce a certain ratio. The data in the table show the ratios that resulted from testing six components using the standard method and the new method. Compare the two methods with a 90% confidence interval. Which method has the smaller mean ratio? 22. Consider making an interference about p1 – p2 , where there are x1 successes in n1 binomial trails and x2 succeseses in n2 binomial trails. 23. Construct a 90% confidence interval for (p1 – p2) in each of the following situations. 24. In auction bidding the “winner’s curse” is the phenomenon of the winning (or highest) bid price being above the expected value of the item being auctioned. A study was conducted to see if less-experienced bidders were more likely to be impacted by the curse than super-experienced biders. The study showed that of the 180 bids by super-experienced bidders, 26 winning bids were above the item’s expected value, and of the bids by the 140 less-experienced bidders, 31 winning bids were above the item’s expected value. Complete parts athrough d. 25. School buying is a form of aggressive behavior that occurs when a student is exposed repeatedly to negative actions from another student. In order to study the effectivenss of an antibullying policy at elementary schools, a survey of over 2,000 elementary school children was conducted. Each student was asked if he or she ever bullied another student. In a sample of 1358 boys, 745 Claimed they had never bullied another student. In a sample of 1379 girls, 966 claimed they had never bullied another student. Complete parts a through f below. 26. A study was conducted to determine the demographics of two types of product managers. Independent samples of n1 = 99 consumer/commercial group, 41%( 1) of the product managers are 40 years of age or older; in the industrial group, 55%(
2
) are 40 or more years
old. Make an interference about the differnce between the true proportions of consumer/commercial and industrial product managers who are at least 40 years old.