Hypothesis Testing: Rejecting Null Hypotheses at Different Significance Levels

Which of the following sample information enables us to reject the null hypothesis at a = 0.05 and at a=0.10?

a. 52n. 130

b. X118; 329

c. +0.41; n = 48

d. P0.41; n = 406

Answer:

Options c and d provide the necessary sample information to perform hypothesis testing and determine whether to reject the null hypothesis at a significance level of 0.05 and 0.10.

To determine whether we can reject the null hypothesis at a significance level of 0.05 and 0.10, we need to compare the given sample information to the critical values from the appropriate table (z table or table).

Let's analyze each option:

Option a: 52n. 130 - This option does not provide enough information to calculate a test statistic or compare it to critical values. We cannot determine whether to reject the null hypothesis based on this information.

Option b: X118; 329 - This option also does not provide enough information to perform hypothesis testing. We cannot determine whether to reject the null hypothesis based on this information.

Option c: +0.41; n = 48 - This option provides a sample proportion (+0.41) and sample size (n = 48). With this information, we can calculate a test statistic (z-score) and compare it to the critical values from the appropriate table. However, we need the sample proportion in decimal form, so we convert +0.41 to 0.41.

Option d: P0.41; n = 406 - This option provides a sample proportion (P0.41) and sample size (n = 406). Similar to option c, we can calculate a test statistic (z-score) and compare it to the critical values.

Based on the given options, only options c and d provide the necessary information to perform hypothesis testing. We can calculate the test statistic (z-score) for each option and compare it to the critical values from the appropriate table to determine whether to reject the null hypothesis at a significance level of 0.05 and 0.10.