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?

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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.

STAT 1450.02 SP2025 (28132) Checkpoint 20.4

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?

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Similar Questions

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STAT 1450.02 SP2025 (28132) Checkpoint 20.4

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?

View Explanation

Log in for full answers

Similar Questions

Which one is true?

For an upper-tail hypotheses about a population mean with σ known and α=5%, which one is the rejection region?

For a given sample, the P-value for upper tail test is x, and the P-value for two-tailed test is y, then

For a two-tailed hypothesis test with a test statistic value of z = 2.09, the p-value is _____.

For a sample size of 30, changing from using the t distribution to using the standard normal distribution in a hypothesis test _____.

Exhibit 9-5 n = 16 H0: μ ≥ 80 = 75.607 Ha: μ < 80 σ = 8.6 Assume the population is normally distributed. Refer to Exhibit 9-5. The p-value is equal to _____.

Exhibit 9-1 ​ ​ Refer to Exhibit 9-1. If the test is done at a .01 level of significance, the null hypothesis should _____.

What conclusion for a test would correctly detect a difference between the actual parameter and the hypothesized value for the parameter? c08.p089.q0008

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Stylized Writing Assistant

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Making Your Study Simpler

Exhibit 9-1 Refer to Exhibit 9-1. If the test is done at a .01 level of significance, the null hypothesis should _____.