Question

Previous studies on sleep tendencies report that, on average, an adult American will sleep for 6 hours each night with a standard deviation of 0.75 hours. You survey a SRS of 100 adult Americans and determine that the mean sleep time is 5 hours. Which Hypothesis Test should be used here?

a. One-sample t-test for means.
b. One-sample z-test for means.
c. One sample z-test for proportions.
d. One sample t-test for proportions.
e. Chi-squared goodness of fit test.

Answer 1

b) One sample z-test for means

Explanation:

Normal Distribution

we have μ₀ (population mean from previous studies)

sample size n = 100

standar deviation of population σ = 0.75

And it was determined from sample, that μ = 5 : so we want to know if, at some significance level that value (which is smaller than population mean ) could help in relation to decide about rejecting hypothesis H₀

We should use a z one tail-test for means (left tail)