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

Question

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

BlackTom AI · Accepted Answer

Consider the context: a hypothesis test with n = 30, comparing using the t distribution (df = n-1 = 29) versus the standard normal (z). 
Option 1: 'will result in the rejection region being larger.' This is correct because the z distribution has lighter tails and smaller critical values for the same alpha level than the t distribution with 29 degrees of freedom. Consequently, the cutoff in z is closer to 0, making it easier to reject the null hypothesis and enlarging the rejection region. 
Option 2: 'will result in the rejection region being smaller.' This would be true if the critical value under z were larger than under t, which is not the case here; z provides a smaller cutoff, not a larger one. 
Option 3: 'would have no effect on the rejection region.' In hypothesis testing, switching distributions changes the sampling distribution of the test statistic, and therefore changes the critical value and the rejection region. So this option ignores the impact of using a different distribution. 
Option 4: 'will result in the rejection region of lower-tail test being smaller.' This statement misunderstands tail behavior: for the same two-tailed test (or a standard setup), moving from t to z affects both tails symmetrically, and the overall rejection region size increases, not specifically shrinking only the lower tail. Hence this option mischaracterizes how the cutoff changes between t and z and misstates tail-specific effects.

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

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MGS*2150*W07 final- Requires Respondus LockDown Browser

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

查看解析

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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 _____.

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

Which of the following statements descrbes best the characteristics of the one-tailed and two-tailed tests in statistical hypothesis testing?

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MGS2150W07 final- Requires Respondus LockDown Browser

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