# Hypothesis Test

1. A maker of golf balls has developed a new ball technology and is interested in estimating the mean difference in driving distance for this new ball versus its existing best-seller. To conduct the test the developers selected six professional golfers and had each golfer hit each ball one time. The distances travelled were:

Golfer Distance with existing ball distance with new ball

1 278 285

2 299 301

3 280 276

4 295 300

5 268 276

6 305 315

Given that distances are normally distributed, test the hypothesis that there is no difference in distance travelled by both types of golf balls. Note that the same golfer hit each of the two balls, so the distance a ball travels depends to some extent upon the individual hitting the ball.This violates the requirement of independence necessary for all of the two-sample tests. In the two-sample cases the data from each population must be drawn independently and randomly from that population. With a paired model the differences between the populations must be independent of each other.

2. A random sample of ten advertisements taken from news magazines had the following reading difficulty levels:

9.7 5.6 6.0 5.5 8.2 6.1 4.8 6.5 6.0 6.7

A second random sample of 12 advertisements taken from financial magazines had the following reading difficulty levels:

9.4 7.6 6.9 7.2 7.5 8.0 6.9 6.6 7.5 7.8 6.8 6.0

Test, at a .05 level of significance, the hypothesis that advertisements published in news magazines had greater variation in reading difficulty levels than those published in financial magazines.

3. A random of 8 female high school Juniors and a random sample of 8 male high school. Juniors at a particular school took the SAT and made the following scores:

Student Female SAT Scores Male Sat Scores

1 640 530

2 590 550

3 590 580

4 640 620

5 590 490

6 585 500

7 575 550

8 550 500

Test, at a .05 level of significance, the hypothesis that female Juniors at this school score 25 points higher on the SAT than do males, given SAT scores are normally distributed.

4. A think tank research team was studying the relationship between idea generation by groups with and without a moderator. For a random sample of 40 groups with a moderator the mean number of ideas generated per group was 78.0 with a standard deviation of 24.4. For a random sample of 30 groups without a moderator the mean number of ideas generated was 63.5 with a standard deviation of 20.2. Test, at a .05 level of significance, the hypothesis that groups with a moderator generate over 10 more ideas than groups without a moderator.

5. The United Way raises money for community charity activities. In one particular community the fund raising committee was concerned about whether there is a difference in the average contribution of private-sector employees and government employees. Random samples of people who had been contacted about contributing last year were selected. It was found that of the 50 private-sector employees the average contribution was $309.45 with a standard deviation of $67.75. For the 60 government employees the average contribution was $230.25 with a standard deviation of $51.52. Given that charitable contribution amounts are known to be normally distributed, can we be 95% confident that private sector employees contribute $100 more on average than government employees?

6. Datatrac reported that a random sample of 30 credit unions charged an average interest rate of 12.15% with a standard deviation of 2.86% on credit cards they had issued, while a random sample of 40 banks charged an average of 15.08% interest with a standard deviation of 1.90 % on credit cards they had issued. Test, at a .01 level of significance, the hypothesis that credit unions charge less interest on their credit cards than do banks.

7. A random sample of 337 homeowners in Los Angeles County contained 133 who had purchased earthquake insurance, while a random sample of 521 homeowner in Contra Costa county in California contained 117 who had purchased earthquake insurance. Los Angeles County is the closest of the two to a major earthquake fault. Do the sample results support the contention that closer proximity to major earthquake faults result in higher proportions of earthquake-insured residents?

8. The number of hours per week students claim to spend studying for introductory finance and accounting classes were obtained from a random sample of 12 finance students and another of 10 accounting students. The numbers reported were:

Finance 10 6 8 10 12 13 11 9 11 11 8 9

Accounting 13 17 14 12 16 19 15 16 11 5

Test, at a .05 level of significance, the hypothesis that finance students spend fewer hours studying that do accounting students, given normality.

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#### Solution Summary

This solution is comprised of detailed explanation and step-by-step calculation of the given problems. Calculations have been shown both in text and EXCEL for better understanding. The solution provides students with a clear perspective of the underlying concepts.