Answer to Question #141442 in Statistics and Probability for soong

Question

50 smokers were questioned about the number of hours they sleep each day. We want to test the hypothesis that the smokers need less sleep than the general public which needs an average of 7.7 hours of sleep. If the sample mean is 7.5 and known population standard deviation is 0.5, what can you conclude using significance level of 0.05?

Answer 1

$H_0:\mu=7.7$

$H_a:\mu<7.7$

$Z=\frac{\bar{X}-\mu}{\frac{\sigma}{\sqrt{n}}}$

$Z=\frac{7.5-7.7}{\frac{0.5}{\sqrt{50}}}=-2.8284$

$Cv=Z_{0.05}$ Left tailed

$=-1.645$

Since the absolute value of the test statistic z=2.8284 is greater than the absolute critical value Cv=1.645, we reject the null hypothesis and conclude that there is enough evidence to support the claim that smokers need less sleep than general public.