Which combination of factors will increase the chances of rejecting the null hypothesis?

Question

BlackTom AI · Accepted Answer

To evaluate which combination would raise the likelihood of rejecting the null hypothesis, we need to consider how standard error and the alpha level affect test statistics and decision rules.
Option 1: a small standard error and a small alpha level. A smaller standard error increases precision and can help detect effects, but a smaller alpha makes it harder, not easier, to reject the null, because the threshold for significance is stricter. So this pair has opposing effects: one favorable, one unfavorable.
Option 2: a large standard error and a small alpha level. A large standard error reduces the test statistic's magnitude and makes it harder to achieve significance, and a small alpha further tightens the criterion. Both factors work against rejecting the null, making this the least favorable combination.
Option 3: a small standard error and a large alpha level. Here, the precision is high (small SE), which helps detect true effects, while a large alpha level lowers the bar for declaring significance, increasing the chance of rejection. These factors reinforce each other toward rejecting the null.
Option 4: a large standard error and a large alpha level. The large standard error weakens the signal by broadening the estimate, while a large alpha eases significance criteria. The net effect is mixed: the looser alpha helps, but the imprecision generally undermines ability to detect effects, so this is not as favorable as option 3.
In summary, the combination that both tightens estimation error and relaxes the significance threshold aligns to maximize the chance of rejecting the null, whereas the other options mix opposing influences or introduce weakening factors.

SOCI_V 328 202 2024W2 In-class Knowledge Demonstration #3

Which combination of factors will increase the chances of rejecting the null hypothesis?

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SOCI_V 328 202 2024W2 In-class Knowledge Demonstration #3

Which combination of factors will increase the chances of rejecting the null hypothesis?

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

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 _____.