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.

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

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