Question

A clinician claims that, on average, the blood pressure of hypertensive patients is 150. A particular doctor believes the amount is more than 150. Then he selected a random sample of 100 patients and found that the sample have average of 155 with standard deviation of 10. Conduct the test at the 0.05 of significance.

f) How large a sample is needed for a one-sample z test with 80% power and α = 0.05 (two-tailed) when σ = 10 ?

Answer 1

Sample size = n = 100

Sample mean = = 155

Sample standard deviation = s = 10

Claim: doctor believes the amount is more than 150.

The null and alternative hypothesis is

Here population standard deviation is known so we have to use z-test statistic.

Level of significance = 0.05

Here population standard deviation is unknown so we have to use the t-test statistic.
Test statistic is

Degrees of freedom = n - 1 = 100 - 1 = 99

Critical value = 1.984 ( Using t table)

Test statistic > critical vaue we reject null hypothesis.

Conclusion: A particular doctor believes the amount is more than 150.