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# (Solved) MATH225 Week 7 Assignment Construct Hypothesis Test for Proportions – Excel

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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 toÂ 50Â songs chosen by the service at random and finds that he likesÂ 32Â 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. UseÂ Î±=0.05.

Select the correct answer below:

• Reject the null hypothesis. There is sufficient evidence to conclude that Steve will like a randomly selected song more often than not.
• Reject the null hypothesis. There is insufficient evidence to conclude that Steve will like a randomly selected song more often than not.
• Fail to reject the null hypothesis. There is sufficient evidence to conclude that Steve will like a randomly selected song more often than not.
• Fail to reject the null hypothesis. There is insufficient evidence to conclude that Steve will like a randomly selected song more often than not.

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 articleÂ told the representative from Company B that inÂ 200Â tests, a battery from Company A outperformed a battery from Company B inÂ 108Â of the tests. Company B decided to sueÂ the magazine, claiming thatÂ the results were not significantly different fromÂ 50%Â and that the magazine was slandering its good name.

UseÂ Excel to test whether the true proportion of times that Company A’s batteries outperformed Company B’s batteries is different fromÂ 0.5.Â Identify the p-value, rounding to three decimal places.

Question

A candidate in an election lost byÂ 5.8%Â of the vote. The candidate sued the state and said that more thanÂ 5.8%Â 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 askÂ for the case to be dismissed, so sheÂ had a governmentÂ official from the state randomly selectÂ 500Â ballots and countÂ how many were defective. The officialÂ foundÂ 45Â defective ballots.

Use Excel to test if theÂ candidate’sÂ claim is true and that more thanÂ 5.8%Â of the ballots were defective.Â Identify the p-value, rounding to three decimal places.

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 fromÂ 50%. He rolled the dieÂ 40Â times and got an odd numberÂ 14Â times.

Dmitry conducts a one-proportionÂ hypothesis testÂ at theÂ 5%Â significance level, to test whether the true proportion of odds is differentÂ fromÂ 50%.

(a) Â Which answer choice shows the correct null and alternative hypotheses for this test?

Select the correct answer below:

• H0:p=0.35;Â Ha:p>0.35, which is a right-tailed test.
• H0:p=0.5;Â Ha:p<0.5, which is a left-tailed test.
• H0:p=0.35;Â Ha:pâ‰ 0.35, which is a two-tailed test.
• H0:p=0.5;Â Ha:pâ‰ 0.5, which is a two-tailed test.

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.

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