(8) It has been long believed that eating oatmeal regularly lowers blood cholest
ID: 3375857 • Letter: #
Question
(8) It has been long believed that eating oatmeal regularly lowers blood cholesterol. To test this claim, a scientist with the FDA measured the change in blood cholesterol levels of a randomly chosen sample of 25 people in a certain age-group (who ate oatmeal for breakfast for a month) and found a sample-average reduction of 15 points with a standard deviation of 6 points. Is it believable at a 5% significance level that the population-mean reduction in all people of that age-group is more than 10 points? Hint: First construct a 95% lower confidence bound for the population mean and then see if the number 10 is below it.] [3.5Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: u < 10
Alternative hypothesis: u > 10
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = s / sqrt(n)
S.E = 1.20
DF = n - 1
D.F = 24
t = (x - u) / SE
t = 4.17
where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.
The observed sample mean produced a t statistic test statistic of 4.17.
Thus the P-value in this analysis is less than 0.0001.
Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we have to reject the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that population mean reduction in all people of that age group is more than 10 points.
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