Suppose that for a right-tailed test of significance for a population mean with unknown standard deviation the sample mean exceeds the hypothesized mean and the sample standard deviation remains fixed. What happens to the test statistic and p-values as the sample size increases?

Question

BlackTom AI · Accepted Answer

When conducting a right-tailed t-test for a population mean with unknown standard deviation, the test statistic is t = (x̄ − μ0) / (s / √n).

Since the sample mean x̄ exceeds the hypothesized mean μ0, the numerator (x̄ − μ0) is positive. 
As the sample size n grows, the term s / √n in the denominator shrinks because √n increases, assuming s is fixed or not growing too fast. This makes the whole fraction larger, so the test statistic t increases (becomes more positive).

A larger positive t-statistic in a right-tailed test corresponds to more extreme evidence against the null hypothesis in the direction of the alternative. Consequently, the p-value, which is the probability of observing such a statistic or more extreme under H0, decreases as n increases.

Putting these together, the statement that describes the behavior is: the test statistic becomes larger, and the p-value becomes smaller as the sample size increases.

Note: The provided options list contains a single statement. Since no other choices are present to compare, this analysis focuses on validating that the described behavior aligns with the statistical properties of the t-statistic and p-value in this scenario.

Suppose that for a right-tailed test of significance for a population mean with unknown standard deviation the sample mean exceeds the hypothesized mean and the sample standard deviation remains fixed. What happens to the test statistic and p-values as the sample size increases?Single choice

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