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.

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?

查看解析

登录即可查看完整答案

类似问题

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

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单

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?

查看解析

登录即可查看完整答案

类似问题

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

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单

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