In December 2001, 38% of adults with children under the age of 18 reported that their family ate dinner together seven nights a week. In a recent poll, 403 of 1122 adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Has the proportion of families with children under the age of 18 who eat dinner seven nights a week decreased?

a) The actual proportion of families with children under the age of 18 who eat dinner together seven nights a week is 0.35. A researcher tests the hypothesis at a 0.10 level of significance and determined that the power of this test is 0.7794. Would the power of the test increase, decrease, or stay the same if the level of significance was changed to 0.01? Find the new power of the test or merely explain why.

This is a left-tailed test.

b) The actual proportion of families with children under the age of 18 who eat dinner together seven nights a week is 0.35. A researcher tests the hypothesis at a 0.10 level of significance and determined that the power of this test is 0.7794. Would the power of the test increase, decrease, or stay the same if the actual proportion was 0.32 instead? Find the new power of the test or merely explain why.