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 obtained a p-value of 0.10. suppose the researcher sampled more college students and that the sample mean and sample standard deviation stayed the same. would the p-value be lower, be higher, or stay the same?

The p-value becomes lower.

Step-by-step explanation:

Let (unknown) be the true mean of number of hours of sleep each night. If we have the hypothesis vs , the test statistic for a small sample size n = 20 is , where   and S are the sample mean and standard deviation respectively. If is true, we know that T has a t distribution with n-1 degrees of freedom. The p-value for the lower-tail alternative is computed as , where is the observed value for the given sample. If we increase the size of the sample and the sample mean and sample standard deviation stayed the same, then, the value becomes smaller, besides, this quantity is always positive. The absolute value of stays the same, and the absolute value of the observed value becomes bigger.  

If is negative, then, is also negative and smaller than , therefore, becomes lower.