Nutritional researchers conducted an investigation of two high-fiber diets inten

Question

Nutritional researchers conducted an investigation of two high-fiber diets intended to reduce cholesterol levels. Twenty men with high serum cholesterol were randomly allocated to receive an “oat” diet or a “bean” diet for 21 days. The table below gives the results. Assume (unknown) equal population standard deviations for the two groups. Note that because the sample sizes are equal the pooled standard error and the un-pooled estimate give the same results. diet n mean standard deviation oat 10 53.6 31.1 bean 10 55.5 29.4 Conducted a (two-sided) hypothesis test with = 0.05.

QUESTION: Use the t table to bracket the p-value. That is, using the t table, find a lower and upper bound for the p-value.

I know how to find p value and t statistic already.

Explanation / Answer

n1 =n2=10

Mean_oat = 53.6

Mean_bean = 55.5

SD_oat = 31.1

SD_bean = 29.4

Pooled SD = sqrt(SD_oat^2/n1 + SD_bean^2/n2) = sqrt(31.1^2/10+29.4^2/10) = 13.533

Degrees of freedom = n1+n2-2 = 18

H0: mean_oat = mean_bean

H1 : mean_oat not equal to mean_bean

t = (mean_oat - mean_bean)/Pooled SD = (53.6-55.5)/13.533 = -0.14

p value = 2*P(t<=-0.14) = 2*0.4451(2 tailed test) = 0.8902>0.05

Hence we cannot reject the null hypothesis

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