It is more difficult to reject the null hypothesis if the significance level is 0.05 compared to 0.10, which means we are less likely to make a Type 1 Error when the null hypothesis is true.

Question

BlackTom AI · Accepted Answer

Observation of the claim requires unpacking two linked ideas about significance level and error types.
Option True: The statement notes that with alpha = 0.05 it is harder to reject H0 than with alpha = 0.10. Since a smaller significance level sets a stricter criterion for rejection, it indeed becomes more difficult to declare significance, hence harder to reject H0. The second part correctly links this to Type I error: a Type I error occurs when we incorrectly reject a true null hypothesis, and its probability is controlled by alpha. Therefore, using alpha = 0.05 yields a smaller chance of a Type I error than alpha = 0.10. In short, lowering the significance level reduces the likelihood of a false positive while making rejection less likely overall.
Option False: If someone argued that a smaller alpha makes it easier to reject H0, that would be incorrect because the decision threshold becomes more stringent, not looser. The claim that lowering alpha increases Type I error would also be wrong, since it decreases the Type I error probability. Thus this option misstates the impact of a smaller significance level on both rejection likelihood and Type I error rate.
Option True is consistent with statistical theory: decreasing alpha tightens the criterion for significance, making rejection less frequent but protecting against false positives. Option False contradicts the fundamental relationship between alpha, decision rules, and Type I error.
Option True covers the core idea that a smaller significance level reduces Type I error risk, while increasing the difficulty of rejecting the null hypothesis; both pieces align with standard hypothesis-testing logic.

FA25_QTM_100_3 5.26: Which is higher?

It is more difficult to reject the null hypothesis if the significance level is 0.05 compared to 0.10, which means we are less likely to make a Type 1 Error when the null hypothesis is true.

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FA25_QTM_100_3 5.26: Which is higher?

It is more difficult to reject the null hypothesis if the significance level is 0.05 compared to 0.10, which means we are less likely to make a Type 1 Error when the null hypothesis is true.

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

More Practical Tools for International Students

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Stylized Writing Assistant

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Past Exam Questions by School

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