4. Describe how level of significance, type I error, p value and 95% confidence level are related to each other.
5. Write down the general format for calculating confidence intervals. Provide the critical values for different levels of confidence under a normal distribution assumption.
6. A researcher informed classroom teachers that some of their students showed unusual potential for intellectual gains. An IQ test was done on such children and compared with a control group. Is there any significant difference at the 95% significance level? Use the stepwise approach to select the test, make sure the test that you use satisfies its assumptions and explain why u chose this test.
Experimental Control
35 2
40 27
12 38
15 31
21 1
14 19
46 1
10 34
28 3
48 1
16 2
30 3
7. Verbal SAT scores of a random sample of 250 high school students had a mean of 470.3 and a standard deviation of 138. Construct a 95% and a 99% confidence interval and explain the reason for the difference in these intervals. List the factors that affect the confidence interval.
8. The president of a large company (5,000 employees) is certain that a significant majority of his employees is in favor of the new health plan that will go into effect in January. The labor union (3,000 members) is not so certain that a significant majority of labor union members are in favor of this health plan. A stratified random sample of 300 union members and 200 non-union members (from the remaining 2,000 employees) indicated that 153 union members were in favor of the new health plan and 122 non-union members were in favor of the new health plan.
- Is there a significant majority of union members in favor of the new health plan?
- Is there a significant majority of non-union members in favor of the new health plan?
- Was the president of the company correct in his assumption?