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Hypothesis Tests with Critical Values

This text provides an explanation of how to perform hypothesis tests using critical values. It includes examples related to mean scores on standardized tests, meal costs for vacationers, ACT scores, weight loss competition, asthma prevalence, helmet usage among motorcyclists, and birth distribution.

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Hypothesis Tests with Critical Values

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  1. Hypothesis Tests with Critical Values

  2. Critical Value: • Based on the alpha level. Use the z or t chart and look it up. This goes on the graph. • Reject the Ho if the observed test statistic is bigger than the absolute value of the critical test value.

  3. The mean score on a standardized test is 1100 with a standard deviation of 100 points. We sampled a group of 50 honor students and found their mean was 1150. Do the honor students score higher on this test. Use a 5% level of significance.

  4. A travel association claims that the mean daily meal cost for two adults traveling together on vacation in San Francisco is $105. A random sample of 20 such groups of adults has a mean daily meal cost of $110 and a standard deviation of $8.50. Is there enough evidence to reject the claim at  = 0.01?

  5. The mean ACT scores for 43 male high school students is 21.1 and the standard deviation is 5.0. The mean ACT score for 56 female high school students is 20.9 with a standard deviation of 4.7. At  = 0.01, can you reject the claim that male and female high school students have equal ACT scores?

  6. On a tv show, eight contestants try to lose the highest percentage of weight in order to win a cash prize. The table shows the times (sec) of the contestants at the beginnings of the season and at the end of the season. At  = 0.01, is there enough evidence to conclude that the contestants’ times have improved?

  7. A medical researcher claims that 5% of children under 18 years of age have asthma. In a random sample of 250 children under 18 years of age, 9.6% say they have asthma. At  = 0.10, is there enough evidence to support the center’s claim?

  8. In a survey of 600 motorcyclists, 404 wear a helmet. In another survey of 500 motorcyclists taken one year before, 317 wore a helmet. At  = 0.05, can you support the claim that the proportion of motorcyclists who wear a helmet is now greater?

  9. A doctor believes that the number of births by day of the week is uniformly distributed. Test using a 5% level of significance.

  10. Homework • Worksheet

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