Question

Exercise 9: A researcher is interested in the relationship between oral contraceptive (OC) use and blood pressure in women. Suppose a sample of ten 35-to 39 year old nonpregnant, premenopausal OC users who work in a company and have a mean systolic blood pressure (SBP) of 132.86 mm Hg and sample standard deviation of 15.34 mm Hg are identified. A sample of 21 nonpregnant, premenopausal, non-OC users in the same age group are similarly identified who have mean SBP of 127. 44 mm Hg and a sample standard deviation of 18.23 mm Hg. A
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Answer 1

1. The hypothesis being tested is:

H₀: µ₁ = µ₂

H₁: µ₁ ≠ µ₂

sp2 = (10 - 1)*15.34^2 + (21 - 1)*18.23^2/(10 + 21 - 2) = 302.22408

se = $\sqrt{}$ 302.22408*(1/10 + 1/21) = 6.67937

The test statistic, t = (132.86 - 127.44)/6.67937 = 0.811

The p-value is 0.4237.

Since the p-value (0.4237) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that µ₁ ≠ µ₂.

2. The 95% confidence interval will be:

= (132.86 - 127.44) ± 2.05* 6.67937

= (-8.24, 19.08)