2. With inferential reasoning is is easier to demonstrate that a hypothesis is false than to prove it is true. The null hypothesis states that there is no effect and we try to show that this hypothesis is false.
4. a. The dependent variable is SAT score and the independent variable is whether they take the special course or not.
b. Ho: mu = 500, Ha: mu not equal 500. The critical boundaries are z = plus/minus 1.96. For these data, z = 2.16, so our decision is to reject Ho and conclude that the course did affect ACT scores.
c. With alpha = .01, the critical region consists of z-score values greater than 2.58 or less than - 2.58.
d. With alpha = .01, the decision is to fail to reject Ho. With alpha = .01, you have less risk of a Type I error. Therefore, the test requires a larger treatment effect in order to reject Ho.
6. The null hypothesis states that the mean IQ for children whose mothers had German measles is no different from the general population mean; Ho: mu = 100. The critical region consists of z-scores beyond plus/minus 1.96. For this sample mean, the standard error is 3.36 and z = -.80 if the null hypothesis is true. Fail to reject the null hypothesis.
8. The null hypothesis states that the mean completion time the brain-damaged population is not diffrent from the mean time for the regular population; Ho: mu = 92 seconds. With alpha = .01 the critical value is z = plus/minus 2.58. For this sample mean, the standard error is 4.91 and z = 4.68. Reject the null hypothesis and conclude that the brain-damaged population is significantly different.
10. Ho: mu = 98.6 (no change during withdrawal)
Ha: mu not equal 98.6 (there is a change)
The critical region consists of z-score values greater than 2.58 or less than z = -2.58. For these data, the sample mean is 99.57, the standard error is .16, and z = 6.06 which is in the critical region so we reject the null hyporthesis and conclude that there is a significant change in temperature during withdrawal.
12. Ho: mu = 12 (no change during hot weather)
Ha: mu not equal 12 (there is a change)
The critical region consists of z-score values greater than 1.96 or less than z = -1.96. For these data, the standard error is 1.5, and z = 2.33 which is in the critical region so we reject the null hypothesis and conclude that there is a significant change in the number of hit players during hot weather.
14. The null hypothesis states that scientists do not differ from the general public on the literacy scale, that is, the mean for scientists is mu = 22. The critical region consists of z-score values beyond plus/minus 1.96. For this sample mean = 23.5 which corresponds to z = 1.06 if Ho is true. Fail to reject Ho.
16. Ho: mu = 7 feet (English social distance is no different from that in the United States). The critical region consists of z-scores greater than 1.96 or less than - 1.96. For these data, the standard error is .50- and z = 2.00. Reject the null hypothesis. Social distance in England is significantly different from social distance in the United States.
18. a. Ho: mu greater than or equal to 26 (no decrease). The critical region consists of z-scores less than - 2.33. For these data, the standard error is 2.07 and z = -2.47. Reject the null hypothesis and conclude that anxiety significantly reduces the number of anagrams solved.
b. Ho: mu = 26 (no difference). For a two-tailed test, the critical region consists of z-scores greater than 2.58 or les than -2.58. The data produce z = -2.47 which is not in the critical region. Fail to reject the null hypothesis.
20. Power increases.
22. As the size of the treatment effect gets smaller, the treatment distribution moves closer to the null distribution and power decreases. When the difference between the two distributions is extremely small, the size of the critical region (alpha) corresponds almost exactly with the portion of the treatment distribution that is located in the critical region (power). Thus, the smallest possible power is equal to alpha.
24. Ho: mu greater than/equal to 50 (scores are not reduced). The critical region consists of z-score values less than -2.33. With n = 22 the standard error is 1.28 and z = -2.34. Reject Ho and conclude that chronic alcohol abuse significantly reduces memory scores.
26. Ho: mean less than/equal 100 (not above average), and Ha: mu
greater
than 100 (above average). The critical region consists of z-score values
greater than 2.33. For these data the standard error is 1.875 and the
z-score
is z = 2.61. Reject Ho.