Question

i) State the Hypotheses to Test. ii) Make a decision based on the information given. iii) What would be Type I and Type II errors. 1. An investigator hypothesizes that cholesterol levels in children might be affected by educating their parents on proper nutrition and exercise. A sample of 40 families with a child between the ages of 10-15 who has been diagnosed with high cholesterol agree to participate in the study. All parents are provided educational information on nutrition and exercise. After following the prescribed program, their child's total cholesterol level is measured. The children's mean cholesterol level is 175 with a standard deviation of 19.5. Is there significant evidence of a reduction in total cholesterol in the children? The Z test p-value is 0.0674. The initial children's mean total cholesterol level was 180.

Answer 1

n = 40, $\mu$ = 180, $\bar{x}$ = 175, s = 19.5. p value = 0.0674

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(i) The Hypothesis:

H0: $\mu$ = 180

Ha: $\mu$ < 180

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(ii) Since p value is low (lower than 0.01 and 0.05), we reject the Null Hypothesis.

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(iii) The Type I error is the incorrect rejection of a true null hypothesis. In this case it would mean that we have accepted that the cholesterol levels are less than 180, when actually they are equal to 180.

The Type II error is the incorrect retention of a false null hypothesis. In this case it would mean that we have accepted that the cholesterol levels are equal to 180, when actually they are less than 180.

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