Question

The observed sample mean,

x
ˉ
, of 90 random samples is 4.6. It is hypothesized that
x
ˉ
=3.82, and it is known that the population variance is 16. Determine the p-value of the data set (round to the third decimal place).

a. 0.237
b. 0.135
c. 0.068
d. 0.319

Answer 1

The p-value of the data set is 0.068.

Step-by-step explanation:

The p-value is a measure of the evidence against a null hypothesis. In this case, we are given the observed sample mean of 4.6 and the population variance of 16. Our null hypothesis is that the population mean is 3.82.

To calculate the p-value, we find the probability of obtaining a sample mean of 4.6 or more extreme (greater than or equal to) if the null hypothesis is true.

Using a t-distribution with degrees of freedom equal to the number of samples minus one (90-1=89), we can calculate the p-value. The p-value is the probability to the right tail of 4.6, which is approximately 0.068. Therefore, the p-value of the data set is 0.068.