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# Hypothesis testing problems

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Having trouble figuring out how to work some problems from Elementary Statistics. See attachment for problems.

In the following exercises examine the given statement, and then express the null hypothesis H&#959; and alternative hypothesis H1 in symbolic form.

12 The mean top of knee height of a sitting male is 20.7 inches.

15 Plain M&M candies have a mean weight that is at least 0.8535

16 The percentage of workers who got a job through their college is no more than 2%.

In the following exercises, find the critical z values. In each case, assume that the normal distribution applies.

19 Right - tailed test; &#945;= 0.01

20 Left handed test &#945;= 0.05

In the following exercises, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method.

12 Among 734 randomly selected Internet users, it was found that 360 of them use the Internet for making travel plans (based on data from a Gallup poll). Use a 0.01 significance level to test the claim that among Internet users, less than 50% use it for making travel plans. Are the results important for travel agents?

13 Technology is dramatically changing the way we communicate. In 1997, a survey of 880 U.S. households showed that 149 of them use email (based on data from The World Almanac and Book of Facts). Use those sample results to test the claim that more than 15% of U.S. households use email. Use a 0.05 significance level. Is the conclusion valid today?

In the following exercises, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method.

13 Randomly selected statistics students of the author participated in an experiment to test their ability to determine when 1 minute has passed. Forty students yielded a sample mean of 58.3 seconds. Assuming that &#963; = 9.5 seconds, use a 0.05 significance level to test the claim that the population mean is equal to 60 seconds. Based on the result, does there appear to be an overall perception of 1 minute that is reasonably accurate?

17 When 14 different second year medical students at Bellevue Hospital measured the systolic blood pressure of the same person, they obtained the results listed below (in mmHg). Assuming that the population standard deviation is known to be 10 mmHg, use a 0.05 significance level to test the claim that the mean blood pressure is less than 140 mmHg.

138 130 135 140 120 125 120 130 130 144 143 140 130 150

Comparing Variation

11 Researchers conducted a study to determine whether magnets are effective in treating back pain, with results given below. The values represent measurements of pain using the visual analog scale. Use a 0.05 significance level to test the claim that those given a sham treatment (similar to a placebo) have pain reductions that vary more than the pain reductions for those treated with magnets.

Reduction in pain level after sham treatment: n = 20, x = 0.44, s = 3.6
Reduction in pain level after magnet treatment: n = 35, x = 51.3, s = 4.5