Mathematics > EXAM > Week 7 Hypothesis Testing Questions and Answers | high grade A+ (All)

Week 7 Hypothesis Testing Questions and Answers | high grade A+

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Week 7 Hypothesis Testing Q & A 1. Steve listens to his favorite streaming music service when he works out. He wonders whether the service 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 than not and then draw a conclusion in the context of a problem. Use α = 0.05. Type equation here . Ho: p = ≤ 0.5 (50%) p = 0.5 Ha: p = > 0.5 (strictly ¿≠ ) P-value = 0.02 which is < α=0.05 we reject Ho and support the Ha Hypothesis Test for p population proportion Level of Significance 0.05 (decimal ) Proportion under H0 0.5000 (decimal ) n 50 Number of Successes 32 Sample Proportion 0.64000 0 StDev 0.50000 0 SE 0.07071 1 Test Statistic (z) 1.97989 9 One-Sided p-value 0.02385 2 Two-Sided p-value 0.04770 4 Right-Tailed (>) 1.644854 Left-Tailed (<) -1.644854 Two-Tailed (≠) ± 1.959964 Answer: Reject the null hypothesis. There is sufficient evidence to prove that Steve will like a random selected song more often than not. 2. A magazine regularly tested products and gave the reviews to its customers. In one of its reviews, it tested 2 types of batteries and claimed that the batteries from company A outperformed batteries from company B in 108 of the tests. There were 200 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. Use Excel to test whether the true proportion of times that Company A’s batteries outperformed Company B’s batteries is different from 0.5. Identify the p=value rounding it to 3 decimal places. Ho: p = 0.5 Ha ≠ 0.5 (two tailed test) n = 200 (α is not given soleave it 0.05) Hypothesis Test for p population proportion Level of Significance 0.05 Proportion under H0 0.5000 n 200 Number of Successes 108 Sample Proportion 0.540000 StDev 0.500000 SE 0.035355 Test Statistic (z) 1.131371 One-Sided p-value 0.129238 Two-Sided p-value 0.258476 Right-Tailed (>) 1.644854 Left-Tailed (<) - 1.644854 Two-Tailed (≠) ± 1.959964 Answer: 0.258 (because it is a two tailed test). We are not rejecting the null hypothesis and we do not have evidence to support the alternative hypothesis.

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