# Confidence Interval and ANOVA

Problem Set 1: Chapter 12, problems 2, 4, 6, 12; Chapter 13, problems 4, 10, 14, 20, 26

Chapter 12

2. Explain why it would not be reasonable to use estimation after a hypothesis test for which the decision was to 'fail to reject Ho".

4. A researcher has constructed an 80% confidence interval of µ = 45 +/- 8, using a sample of n = 25 scores.

a. What would happen to the width of the interval if the researcher had used a larger sample size?

b. What would happen to the width of the interval if the researcher had used a 90% confidence interval instead of 80%?

c. What would happen to the width of the interval if the sample variance increased?

6. An elementary school principle would like to know how many hours the students spend watching TV each day. M = 3.1, n = 25, s = 3.

a. Make a point estimate of the mean number of hours of TV per day for the population of elementary school children.

b. Make an interval estimate of the mean so that you are 90% confident that the true mean is in your interval. An elementary school principle would like to know how many hours the students spend watching TV each day. M = 3.1, n = 25, s = 3.

12. A developmental psychologist would like to determine how much fine motor control skill improves for children from age 3 to age 4. Three Year old sample: M = 35.4, n = 15, SS = 410; Four year old sample: M = 40.6, n = 15, SS = 430.

a. Make a point estimate of the population mean difference.

b. Make a 95% confidence interval estimate of the population mean difference

c. Make a 99% confidence interval estimate of the population mean difference

d. Based on your answers from b and c, do these data indicate a significant change using a two-tailed test with ? = .05? Is the difference significant at ? = .01?

Chapter 13

4. Explain why you should use ANOVA instead of several t-tests to evaluate mean differences when an experiment consists of three or more treatment conditions?

10. The following data are from an experiment comparing three treatment conditions with a separate sample of n = 4 in each treatment.

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Treatment

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l ll lll

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2 3 7 N = 12

6 7 5 G = 60

2 6 4 ?X2 = 344

6 4 8

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a. Use an ANOVA with ? = .05 to determine whether there are any significant differences among the three treatments

b. Compute eta2 for these data.

14. A researcher reports an F-ratio with df = 2, 24 for an independent-measures research study.

a. How many treatment conditions were compared in the study?

b. How many subjects participated in the study?

20. The following summary table presents the results from an ANOVA comparing three treatment conditions with n = 12 participants in each condition. Complete all the missing values.

26. One possible explanation for why some birds migrate and others do not...

Non Migrating Short Distance Migrants Long distance migrant

18 6 4

13 11 9

19 7 5

12 9 6

16 8 5

12 13 7

M = 15 M= 9 M= 6 N = 18

T= 90 T=54 T=36 G = 180

SS= 48 SS=34 SS=16 ?X2 = 2150

a. Do the data indicate significant differences among the four levels of severity? Test with ? = .05.

b. Compute eta2, the percentage of variance explained by the group differences.

c. Use the Tukey HSD posttest to determine which groups are significantly different.

#### Solution Summary

The solution provides a step by step method for the calculation of confidence interval for population mean and ANOVA. Formula for the calculation and interpretations of the results are also included.