1. Question: Steve listens to his favorite streaming music service when he works out. He wonders whether the service's algorithm does a good job of finding random songs that he will like more often than not. To test this, he listens to 50 songs chosen by the service at random and finds that he likes 32 of them.

Use Excel to test whether Steve will like a randomly selected song more often than not, and then draw a conclusion in the context of the problem. Use α=0.05.

2. Question: A magazine regularly tested products and gave the reviews to its customers. In one of its reviews, it tested two types of batteries and claimed that the batteries from Company A outperformed the batteries from Company B. A representative from Company B asked for the exact data from the study. The author of the article told the representative from Company B that in 200 tests, a battery from Company A outperformed a battery from Company B in 108 of the tests. Company B decided to sue the magazine, claiming that the results were not significantly different from 50% and that the magazine was slandering its good name.
3. Question: A candidate in an election lost by 5.8% of the vote. The candidate sued the state and said that more than 5.8% of the ballots were defective and not counted by the voting machine, so a full recount would need to be done. His opponent wanted to ask for the case to be dismissed, so she had a government official from the state randomly select 500 ballots and count how many were defective. The official found 45 defective ballots.

Use Excel to test if the candidate's claim is true and that more than 5.8% of the ballots were defective. Identify the p-value, rounding to three decimal places.

4. Question: Dmitry suspected that his friend is using a weighted die for board games. To test his theory, he wants to see whether the proportion of odd numbers is different from 50%. He rolled the die 40 times and got an odd number 14 times.
5. Question: Dmitry suspects that his friend is using a weighted die for board games. To test his theory, he wants to see whether the proportion of odd numbers is different from 50%. He rolled the die 40 times and got an odd number 14 times.

Dmitry conducts a one-proportion hypothesis test at the 5% significance level, to test whether the true proportion of odds is different from 50%.

1. H0:p=0.5; Ha:p≠0.5, which is a two-tailed test.
2. Use Excel to test whether the true proportion of odds is different from 50%. Identify the test statistic, z, and p-value from the Excel output, rounding to three decimal places.