A study was conducted to show that eating oat bran reduces bad cholesterol. 12 s

Question

A study was conducted to show that eating oat bran reduces bad cholesterol. 12 subject were given the diet without oat bran and then diet with oat bran. Cholesterol level were measured in both cases and difference recorded. Test the claim that there is an improvement in the cholesterol level( that is the bad cholesterol is lower) when eating a diet with bran. D= ldl cholesterol before- ldl cholesterol after N=12 mean difference = -0.381 std dev of difference = 0.4335 True or false A study was conducted to show that eating oat bran reduces bad cholesterol. 12 subject were given the diet without oat bran and then diet with oat bran. Cholesterol level were measured in both cases and difference recorded. Test the claim that there is an improvement in the cholesterol level( that is the bad cholesterol is lower) when eating a diet with bran. D= ldl cholesterol before- ldl cholesterol after N=12 mean difference = -0.381 std dev of difference = 0.4335 True or false D= ldl cholesterol before- ldl cholesterol after N=12 mean difference = -0.381 std dev of difference = 0.4335 True or false

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: d> 0

Alternative hypothesis: d < 0

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a matched-pairs t-test of the null hypothesis.

Analyze sample data. Using sample data, we compute the standard deviation of the differences (s), the standard error (SE) of the mean difference, the degrees of freedom (DF), and the t statistic test statistic (t).

s = sqrt [ ((di - d)2 / (n - 1) ]

s = 0.4335

SE = s / sqrt(n)

S.E = 0.125

DF = n - 1

D.F = 11

t = [ (x1 - x2) - D ] / SE

t = - 3.05

where di is the observed difference for pair i, d is mean difference between sample pairs, D is the hypothesized mean difference between population pairs, and n is the number of pairs.

Since we have a two-tailed test, the P-value is the probability that a t statistic having 11 degrees of freedom less than - 3.05.

Thus, the P-value = 0.025

Interpret results. Since the P-value (0.025) is less than the significance level (0.05), we have to reject the null hypothesis.

True

From the above test we have sufficient evidence in the favor of the claim that there is an improvement in the cholesterol level that is the bad cholesterol is lower) when eating a diet with bran.

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