In a recent Super Bowl, a TV network predicted that 43 % of the audience would express an interest in seeing one of its forthcoming television shows. The network ran commercials for these shows during the Super Bowl. The day after the Super Bowl, and Advertising Group sampled 92 people who saw the commercials and found that 44 of them said they would watch one of the television shows. Suppose you have the following null and alternative hypotheses for a test you are running:

H0:p=0.53H0:p=0.53
Ha:p≠0.53Ha:p≠0.53

a. Calculate the test statistic, rounded to 3 decimal places

A well-known brokerage firm executive claimed that at least 36 % of investors are currently confident of meeting their investment goals. An XYZ Investor Optimism Survey, conducted over a two week period, found that out of 80 randomly selected people, 30 of them said they are confident of meeting their goals.

Suppose you have the following null and alternative hypotheses for a test you are running:

H0:p=0.36H0:p=0.36
Ha:p≠0.36Ha:p≠0.36

b. Calculate the test statistic, rounded to 3 decimal places