A study was conducted to test the hypothesis that people with glaucoma have high

Question

A study was conducted to test the hypothesis that people with glaucoma have higher average systolic blood pressure than people without glaucoma. The study included a simple random sample of 15 people with glaucoma. Their average systolic blood pressure was 143 mm Hg. The sample standard deviation was 25 mm Hg. The average systolic blood pressure for all people without glaucoma is 130 mm Hg. At 1% significance level, do the given data provide sufficient evidence to conclude, that average systolic blood pressure in glaucoma population is significantly higher than 130 mm Hg? Interpret your answer from part (a). Determine the p-value of the test.

Explanation / Answer

Solution:

Part a

Here, we have to use one sample t test for population mean.

H0: µ = 130

Ha: µ > 130

We are given

Level of significance = alpha = 0.01

Sample size = n = 15

Sample mean = Xbar = 143

Sample Standard deviation = S = 25

Degrees of freedom = n - 1 = 15 – 1 = 14

Upper critical value = 2.6245

Test statistic = t = (Xbar - µ)/[S/sqrt(n)]

Test statistic = t = (143 – 130) / [25/sqrt(15)] = 2.0140

Test statistic value t = 2.0140 < critical value 2.6245

So, we do not reject the null hypothesis

Part b

We conclude that there is insufficient evidence that average systolic blood pressure in glaucoma population is significantly higher than 130 mm Hg.

Part c

Level of significance = alpha = 0.01

Sample size = n = 15

Degrees of freedom = n - 1 = 15 – 1 = 14

Test statistic value t = 2.0140

P-value = 0.0318

(By using t-table)

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