Question

A certain IQ test is known to have a population mean of 100 and standard deviation of 15 in the general population. You want to test whether psychology majors have a different average IQ than the population as a whole. Assume the variance of IQ is the same for Psych majors as it is in the general population. Suppose that Psychology majors actually have an average IQ of 108. If you do a 2-tailed test at α= .05 with a sample of 56 Psychology majors, you will be able to reject the null hypothesis if the mean IQ of your sample is below [L] or above [H].

Selected Answer: A certain IQ test is known to have a population mean of 100 and standard deviation of 15 in the general population. You want to test whether psychology majors have a different average IQ than the population as a whole. Assume the variance of IQ is the same for Psych majors as it is in the general population. Suppose that Psychology majors actually have an average IQ of 108. If you do a 2-tailed test at α= .05 with a sample of 56 Psychology majors, you will be able to reject the null hypothesis if the mean IQ of your sample is below 111.92 or above 111.92. Response Feedback: You need to find the values above and below which you will reject the H0 using Excel or the inverse normal calculator http://onlinestatbook.com/2/calculators/normal.html

Answer 1

Sample size = n = 56

Sample mean = = 108

Population standard deviation = = 15

Claim: Psychology majors have a different average IQ than the population as a whole.

The null and alternative hypothesis is

Level of significance = 0.05

Here population standard deviation is known so we have to use z-test statistic.

Test statistic is

Critical value = 1.96 ( Using z table)

Critical value < Test statistic | z | we reject the null hypothesis.

Conclusion:

Psychology majors have a different average IQ than the population as a whole.

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