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# ANOVA & Confidence Interval

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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.

https://brainmass.com/statistics/confidence-interval/anova-confidence-interval-315856

#### 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.

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## ANOVA and SPC

Need help on the following problems

(1) Freshman 15 Weight gains. (Attached Data set 3)
Based on the sample results, find the best point estimate of the percentage of college students who gain weight in their freshman year.

a. Construct a 95% confidence interval estimate of the percentage of college students who gain weight in their freshman year.

b.Assuming that you are a newspaper reporter, write a statement that describes the results. Include all of the relevant information.

(2) NCAA Football coach salaries. A simple random sample of 40 salaries of NCAA football coaches has a mean of \$415,953. Assume that o- = \$463,364.

a. Find the best point estimate of the mean salary of all NCAA football coaches.

b. Construct a 95% confidence interval estimate of the mean salary of an NCAA football coach.
c. Does the confidence interval contain the actual population mean of \$474,477?

(3) Acupuncture for Migraines. In a study designed to test the effectiveness of acupuncture for treating migraines, 142 subjects were treated with acupuncture and 80 subjects were given a sham treatment. The numbers of migraine attacks for the acupuncture treatment group had a mean of 1.8 and a standard deviation of 1.4. The number of migraine attacks for the sham treatment group had a mean of 1.6 and a standard deviation of 1.2.

a. Construct the 95% confidence interval estimate of the mean number of migraine attacks for those treated with acupuncture.
b. Construct the 95% confidence interval estimate of the mean number of migraine attacks for those given a sham treatment.
c. Compare the two confidence intervals. What do the results suggest about the effectiveness of acupuncture?

(4) Weights of M&Ms. (Data Set 18) lists 100 weights (in grams) of M&M candies. The minimum weight is 0.696 g and the maximum weight is 1.015 g.

a. Use the range rule of thumb to estimate o, the standard deviation of weights of all such M&Ms.
b. The 100 weights have a standard deviation of 0.0518 g. Construct a 95% confidence interval estimate of the standard deviation of weights of all M&MS.
c. Does the confidence interval from part b contain the estimated value of o- from part a? What do the results suggest about the estimate from part a?

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