MATH 225N Week 7 Hypothesis Testing Question and Answers(Chamberlain College of Nursing)

1. Steve listens to his favorite streaming music service when he works out.He wonders whether the servicealgorithm does a good job of finding random songs that he will like more often than not.To test this, helistens 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 than not and then draw a conclusion inthe context of a problem.Use α = 0.05.Typeequationhere.Ho:p =≤0.5(50%)p = 0.5Ha:p = > 0.5 (strictly¿>≠)P-value = 0.02 which is <α=0.05we reject Ho and support the HaHypothesis Test for p populationproportionLevel ofSignificance0.05(decimal)Proportion underH0.5000(decimal)0n50Number ofSuccesses32Sample Proportion0.StDev0.SE0.Test Statistic (z)1.One-Sided p-value0.Two-Sided p-value0.Right-Tailed (>)1.-Left-Tailed (<)1.Two-Tailed (≠)±1.Answer:Reject the null hypothesis.There is sufficient evidence to prove that Steve will like a random selectedsong more often than not.1.A magazine regularly tested products and gave the reviews to its customers.In one of itsreviews, it tested 2 types of batteries and claimed that the batteries from company Aoutperformed batteries from company B in 108 of the tests.There were 200 tests.CompanyB decided to sue the magazine, claiming that the results were not significantly different from50% and that the magazine was slandering its good name. Use Excel to test whether the true proportion of times that Company A's batteries outperformed Company B'sbatteries is different from 0.5.Identify the p=value rounding it to 3 decimal places.Ho:p = 0.5Ha≠0.5(two tailed test)n = 200(α isnot givensoleaveit0.05)Hypothesis Test for ppopulation proportionLevel ofSignificance0.05Proportion underH0.50000n200Number ofSuccesses108SampleProportion0.StDev0.SE0.Test Statistic (z)1.One-Sided p-value0.Two-Sided p-value0.Right-Tailed (>)1.-Left-Tailed (<)1.Two-Tailed (≠)±1.Answer:0.258 (because it is a two tailed test).We are not rejecting the null hypothesis and we do not haveevidence to support the alternative hypothesis.2.A candidate in an election lost by 5.8% of the vote.The candidate sued the state and said thatmore than 5.8% of the ballots were defective and not counted by the voting machine, so a fullrecount would need to be done.His opponent wanted to ask for the case to be dismissed, soshe had a government official from the state randomly select 500 ballots and count how manywere defective. The official found 21 defective ballots.Use Excel to test if the candidates claim is true and that < 5.8% of the ballots were defective.Identify thep=value rounding to 3 decimal places.≥0.058¿0.058Ho:p =Ha(one tailed test)n = 500(α isnot given soleaveit0.05)Hypothesis Test for p populationproportionLevel ofSignificance0.05(decimal)Proportion underH0.0580(decimal)0n500Number ofSuccesses21