Question

A sample of size 50 is taken, which produces a mean value of 36. A hypothesis test is conducted on the null hypothesis that the mean value of the population from which the sample is taken is 40. A p-value (or significance probability) is calculated.

Which one of the following statements is true?

A) The p-value will be smaller if the variance of the sample is lower and it will be higher if the variance of the sample is higher.

B) As the sample mean is 10% below the hypothesized population mean, the p-value will be low.

C) The p-value will be higher if the variance of the sample is lower and it will be smaller if the variance of the sample is higher.

D) If the p-value is 0.5, there is an equal chance of the null hypothesis being true or false.

Answer 1

The p-value will be higher if the variance of the sample is lower and it will be smaller if the variance of the sample is higher.

Step-by-step explanation:

The correct statement among the options is:

C) The p-value will be higher if the variance of the sample is lower and it will be smaller if the variance of the sample is higher.

The p-value is determined by the observed test statistic and the null hypothesis. A lower variance in the sample would result in a smaller test statistic, which in turn leads to a higher p-value. Conversely, a higher variance in the sample would result in a larger test statistic, which leads to a smaller p-value. Therefore, option C is true.