 Statistics Questions: Steps to Hypotheses Testing

Subject Mathematics Applied Statistics

Question

Research Scenario

IQ scores from the general population form a normal distribution with a mean = 100 and standard deviation = 15. However, data indicate that children’s intelligence may be affected if their mothers have German measles during pregnancy. Using hospital records, a researcher obtained a sample of n = 25 school children whose mothers all had German measles during their pregnancies. The average IQ for this sample was x̅ = 96.4. Do these data indicate that German measles have a significant effect on IQ? Test with p=.01.

Step 1: Set up your hypothesis and determine the level of significance

State the alternative/research hypothesis
1. In written format
2. In mathematical format

State the null hypothesis
3. In written format
4. In mathematical format

Determine the Level of significance

5. Based on information in the scenario, what is the level of significance to be used?

Step 2: Select the appropriate test statistic

6. The appropriate test statistic for the above scenario is the one-sample z test. What values are compared in a one-sample z test?

Step 3: Set up the decision rule

7. Based on the level of significance you set in Step 1 and whether your alternative hypothesis is directional or non-directional, what is your decision rule?

Step 4: Compute the test statistic

8. Calculate the z statistic.

Step 5: Conclusion

9. Do you reject or fail to reject the null hypothesis?

10. Is a child’s intelligence affected if the mother has German measles during pregnancy?

Solution Preview

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Determine the Level of significance

5. Based on information in the scenario, what is the level of significance to be used?
Answer: 0.01 with one-sided.

Step 2: Select the appropriate test statistic

6. The appropriate test statistic for the above scenario is the one-sample z test. What values are compared in a one-sample z test?
Answer: 2.3263 (or -2.3263) because it is a one-sided test....

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