Question

it is recommended that adults get 8 hours of sleep each night. a researcher hypothesized college students got less than the recommended number of hours of sleep each night, on average. the researcher randomly sampled 50 college students and calculated a sample mean of 7.9 hours per night. the researcher performed a hypothesis test. what is the null hypothesis? choose the correct answer below. a. ( h_{0}: mu_{x}=7.9 ) hours per night b. ( h_{0}: mu_{x}<7.9 ) hours per night c. ( h_{0}: mu_{x}=8 ) hours per night d. ( h_{0}: mu_{x}<8 ) hours per night

Explanation:

In hypothesis testing, the null hypothesis \(H_0\) is a statement of no difference or no effect. Here, the recommended amount of sleep is 8 hours. The null hypothesis should be about the population mean \(\mu_x\) (average sleep of college students) being equal to the recommended value. The sample mean of 7.9 is just an observed value from the sample. Options A and B use the sample - mean value which is incorrect. Option D is a one - sided alternative - type statement (but in the wrong place as the null should be an equality).

Answer:

C. \(H_0:\mu_x = 8\) hours per night