Question

Practice Problems (Chapters 9 and 11)

Chapter 9

1.         Given a sample mean of 12.5 based on 25 cases and a population variance of 10, construct a 95% confidence interval for the population mean. Interpret the resulting interval.

2.         What can be expected to happen to the length of a confidence interval as the size of the sample used to construct it increases. Explain.

3.         In a short paragraph, explain the logic of confidence intervals.

4.         Can confidence intervals be used to test hypotheses? Explain.

Chapter 11

5.         Describe a research study appropriate for an independent measures t-test.

6.         Describe a research study appropriate for a dependent samples t-test.

7.         Consider the data in problem 4 in Chapter 11 (p. 273). Enter these data into SPSS and conduct a test of the null hypothesis. Compute a measure of effect size and construct a 95% confidence interval for your study.

8.         Consider the data in problem 5 in Chapter 11 (p. 273). Enter these data into SPSS and conduct a test of the null hypothesis. Compute a measure of effect size and construct a 95% confidence interval for your study.

Answer 1

1) Given sample mean = 12.5, sample size n = 25, Population variance = 10

95% confidence interval for the population mean =

Z_0.025 = 1.96

95%CI = (12.5-1.96*sqrt(10/25) , 12.5+1.96*sqrt(10/25) ) = ( 11.260, 13.740)

2) If the length of sample increases then the confidence interval length decreases because the margin of error decreases as the sample size is in the denominator of the margin of error expression.

3) The confidence intervals reports the range of parameter with the required confidence level. The 95% confidence intervals can be interpreted as " We are 95% CONFIDENT that the range of population parameter will line in the confidence limit values".

4) yes we can use the confidence intervals for hypothesis testing. If the 95% confidence interval on single mean captures the population mean value then we fail to reject null hypothesis and vice versa. Similarly for confidence interval on difference of means if the confidence interval captures the ZERO value then we fail to reject null hypothesis and vice versa.

5) independent measures t-test:-

The test on mean height difference between the boys and girls in a class is an example of the independent measures t-test, because the values are not dependent on each other as the observations will be collected for different subjects.

6) dependent samples t-test :-

The test on mean difference of test score before the coaching and after the coaching of the students is an example of the dependent measures t-test, because the values are dependent on each other as the observations will be collected for same subjects before and after the coaching class.

***for rest questions data is required*** which is not provided.