A researcher theorizes that first-born children of African-American families are

Question

A researcher theorizes that first-born children of African-American families are more intelligent than other African-American children. A sample of 50 first-born children of African-American families is found to have an average IQ of 105, while based on other studies we can assume that IQ of other African-American children is 100 on average and has standard deviation of 15.

1. What is the population of interest in this study? (A. All African-American families, B. All African-American children, C.  IQ of African-American children, D. IQ of all first-born African-American children)

2. Which method researcher can use to check her idea? (A. Hypothesis testing - Z test, B. Hypothesis testing - t test, C. Sample size estimation for average, D. None of the above)

3. If she conducts hypothesis testing, she has to consider: (A. one-tailed test, B. two-tailed test, C. one-tailed test because sample size is large, D. two-tailed test because sample size is large)

4. What would be the null hypothesis of this study? (A. H0: Mean= 50, B. H0: Mean = 105, C. H0: Mean = 15, D. H0: Mean > 105, E. None of the above)

5. What would be the alternative hypothesis of this study? (A. Ha: Mean= 50, B. Ha: Mean = 105, C.  Ha: Mean > 100, D. Ha: Mean > 105, E. None of the above)

6. What level of significance do you choose for this test? (A. 50, B. 10, C. 95%, D. 99%, E. None of the Above.

7. What is the computed value of test statistic? (A. -2.4, B. -1.5, C. +1.5, D. +2.4)

8. Which one of the following is a correct conclusion based on the data given? Use 5% significance level.

A. Reject H0. First-born children of African-American families are more intelligent than other children.

B. Do not reject H0. First-born children of African-American families are not more intelligent than other children.

C. Reject H0. First-born children of African-American families are not more intelligent than other children.

D. None of the above.

Explanation / Answer

Solution:-

1) (B)The population of interest in this study is All African-American children.

2) (A) Hypothesis testing - Z test

3) A. one-tailed test

4)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: < 100
Alternative hypothesis: > 100

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a one-sample z-test.

Analyze sample data. Using sample data, we compute the standard error (SE), z statistic test statistic (z).

SE = s / sqrt(n)

S.E = 2.121
z = (x - ) / SE

z = 2.36

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a z statistic test statistic of 2.36.

Thus the P-value in this analysis is 0.0091.

Interpret results. Since the P-value (0.0091) is less than the significance level (0.01), we have to reject the null hypothesis.

Reject H0. First-born children of African-American families are more intelligent than other children.

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