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