If the p-value associated with the observed t-statistic for the independent variable in a simple linear regression is less than .05, the critical value of t in the t-distribution:

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The question asks about the relationship between the p-value of the observed t-statistic in a simple linear regression and the corresponding critical value of t.
Option: 'Will be smaller than the observed t-statistic.'
To reason this out, remember that a p-value less than 0.05 means the observed t-statistic falls in the rejection region for a two-tailed test at alpha = 0.05 (or in one-tailed if specified, but commonly two-tailed is assumed). In such cases, the critical t value, t_crit, is the boundary that separates non-rejection from rejection: |t_obs| > t_crit. Therefore, the magnitude of the critical value is indeed smaller than the magnitude of the observed t-statistic.
Let’s contrast with the intuitive alternative: if p < 0.05, you are deeper into the tail than the cutoff, implying the cutoff threshold (the critical value) lies closer to zero than the observed statistic, not larger. This supports the statement that the critical value is smaller in magnitude than the observed t-statistic.
If we imagined a scenario where p were larger than 0.05, the observed t would not exceed the critical boundary, and the inequality |t_obs| > t_crit would not hold; but that is not the current situation. Thus, the claim in the option aligns with the standard decision rule for hypothesis testing using the t-distribution.
In sum, the observed t-statistic surpasses the critical t value in magnitude when the p-value is below 0.05, making the critical value smaller than the observed t-statistic.

PSYC20009_2025_SM2 Quiz for Simple Linear Regression: Part 3B 简单线性回归小测：第 3B 部分

If the p-value associated with the observed t-statistic for the independent variable in a simple linear regression is less than .05, the critical value of t in the t-distribution:

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PSYC20009_2025_SM2 Quiz for Simple Linear Regression: Part 3B 简单线性回归小测：第 3B 部分

If the p-value associated with the observed t-statistic for the independent variable in a simple linear regression is less than .05, the critical value of t in the t-distribution:

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 _____.