Question

Previous research has indicated that patients with hypertension are overweight by a mean of 35 pounds (assume σ = 8.6). Yaisha is researching a new program that has the goal of reducing the mean amount by which hypertensive patients are overweight. Yaisha takes a random sample of 40 hypertensive patients to participate in the program over the next several months and finds the sample mean by which these patients are overweight is 31.7 pounds.

Answer 1

Given that, population standard deviation (σ) = 8.6 pounds

sample size (n) = 40 and sample mean = 31.7 pounds

The null and alternative hypotheses are,

H0 : μ = 35 pounds

Ha : μ < 35 pounds

This hypothesis test is a left-tailed test.

Test statistic is,

=> Test statistic = Z = -2.43

p-value = P(Z < -2.43) = 1 - P(Z < 2.43) = 1 - 0.9925 = 0.0075

=> p-value = 0.0075

Since, p-value is less than 0.05 level of significance, we Reject the null hypothesis (H0).

Conclusion : There is sufficient evidence to conclude that the new program reduced the mean amount by which hypertensive patients are overweight.