# ANOVA & Confidence Interval

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

2. An elementary school principal would like to know how many hours the students spend watching TV each day. A sample of n = 25 children is selected, and a survey is sent to each child's parents. The results indicate an average of M = 3.1 hours per day with a standard deviation of s = 3.0

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.

3. A developmental psychologist would like to determine how much fine motor skill improves for children from age 3 to age

4. A random sample of n = 15 3-year-old children and a second sample of n = 15 4 year olds are obtained. Each child is given a manual dexterity test that measures fine motor skills. The average score for the older children was M = 40.6 with SS = 430 and the average for the younger children was M = 35.4 with SS = 410. Using these data,

a. Make a point estimate of the population mean difference in fine motor skills.

b. Make an interval estimate so you are 95% confident that the real mean difference is in your interval.

c. Make an interval estimate so you are 99% confident that the real mean difference is in your interval.

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

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.

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#### Solution Summary

The solution provides step by step method for the calculation of confidence interval for mean and mean difference. The solution also provides reason-ability of the estimation of hypothesis after the decision "fail to reject Ho" and the advantage of using ANOVA instead of several t tests. Formula for the calculation and Interpretations of the results are also included.