Question

The cholesterol levels of women aged 21-40 in Canada are approximately Normally distributed with a mean of 190 miligrams per decilitre (mg/dl). In July of 2007, a clinical assessment applied in Toronto to random sample of twenty–nine Asian female immigrants aged 21-40 had a mean level of 179.52 mg/dl and a standard deviation of 38 mg/dl.

(a) At the 10% level of significance test whether the mean cholesterol level of Asian women is the same as the national average.

(b) With minor changes to the previous part, is there evidence that the mean cholesterol level of Asian women is lower than the national average?

(c) Repeat part (a) utilizing the fact that the standard deviation of the cholesterol levels for all Canadian women aged 21-40 is 32.4 mg/dl.

Answer 1

Sample Size = n = 29

Sample mean = = 179.52 mg/dl

sample standard deviation = 38 mg/dl

Here we want to  test whether the mean cholesterol level of Asian women is the same as the national average or not.

Let's write null hypothesis ( H₀ ) and the alternative hypothesis ( H₁ ) from the above statement.

Here population standard deviation is not given and we use sample standard deviation(s) instead of population

standard deviation . So here we can used one sample t test because we assume data comes from normal distribution.

Let's use Minitab:

Step 1) Click on Stat>>>Basic Statistics >>1 sample t...

Step 2) Select summarized data

Sample size : 29

Mean:179.52

Standard deviation : 38

then click on Perform hypothesis test enter hypothesis mean ( 190)

Step 3)then click on Option select level of confidence = 1 - alpha = 1 - 0.10 = 0.90

So put it as 95

Alternative " not equal "

Look the following image:

Click on OK

again Click on Ok

So we get the following output

From the above minitab output

t test statistic = T = -149

P-value = 0.149

Decision rule: 1) If p-value < level of significance (alpha) then we reject null hypothesis

2) If p-value > level of significance (alpha) then we fail to reject null hypothesis.

Here p value = 0.149 > 0.10 so we used seond rule.

That is we fail to reject null hypothesis and accept alternative hypothesis.

Conclusion: At 10% level of significance we don't have sufficient evidence to reject the claim from the sample data.

(b) With minor changes to the previous part, is there evidence that the mean cholesterol level of Asian women is lower than the national average?

Do the same procedure, just replace "not equal" by "lower than"

So we get the following result:

From the above output we get

p-value = 0.074 which is less than 0.10 so we reject the null hypothesis and conclude that there evidence that the mean cholesterol level of Asian women is lower than the national average.