It is recommended that adults get 8 hours of sleep each night A researcher hypot

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 20 college students and calculated a sample mean of 7 5 hours par night. If the researcher wanted to perform a one-sample t-test, which of the following is a correct statement? Choose the correct answer below. A. The number of hours of sleep per night for all college students must be normally distributed because the sample size is small. B. By taking a random sample, the researcher has guaranteed that the distribution of sample means is normal. C. By taking a random sample, the researcher has guaranteed that the distribution of number hours of sleep per night for all college students is normal. D. The distribution of sample means will be normal even if the distribution of the data in the population is not normal.

Explanation / Answer

According to Central limit theorem, the distribution of sample mean will always be normal, even if the distribution of the parent population is not normal.

Therefore, in this case also, Central Limit Theorem will hold true and the correct answer is option d.

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