Question 10. Suppose the Miami Marlins hit an average of 2 home runs per game. W
ID: 3324996 • Letter: Q
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Question 10. Suppose the Miami Marlins hit an average of 2 home runs per game. What is the probability that in a particular game, the Marlins hit at least one home run? Note that e 0.1353. a) 0.865 b) 0.594 c) 0.271 d) 0.135 e) 0.406 Question 11. You conduct a two-sided hypothesis test Ho: +0,H: #0 based on a sample of measurements. You compute the test statistic z and obtain -2.24, which of the following is true? 25 I) The resulting p-value is 0.025 You can reject a value of -o with 97.5% confidence. You would reject the null hypothesis (Ho) for a001. III) a) None of the Above b) I only c) Il only d) I and Il only e) All of the Above Question 12. You conduct a one-sided hypothesis test Ho·h20; HxHc0 based on a sample of 25 measurements. You compute the test statistic z and obtain z -2.24. Which of the following is true? I) The resulting p-value is 0.025 You can reject any value of 20 with at least 97.5% confidence You would reject the null hypothesis (Ho) for =0.01. Ill)Explanation / Answer
10) P(x > 2) = 1 - P(x < 2)
= 1 - (P( x = 0) + P(x = 1))
= 1 - (e-2 * 20/0! + e-2 * 21/1!)
= 1 - 0.406 = 0.594
11) i)p-value = 2 * P(Z < -2.24)
= 2 * 0.0125 = 0.025
ii) At 97.5% confidence interval the critical value is +/- 2.24
as the test statistic value is equal to the critical value so the null hypothesis is rejected.
ii) For alpha = 0.01, the critical value is +/- 2.58.
As the test statistic value lies between the critical values(-2.58 < -2.24 < 2.58) so the null hypothesis is not rejected.
option-d is the correct answer.
12) i) p - value = P(Z < -2.24) = 0.0125
ii) At 97.5% cinfidence interval the critical value is -2.24. As the test statistic value is equal to the critical value so the null hypothesis is rejected.
iii) At alpha = 0.01, the critical value is -2.58
as the test statistic value is greater than the critical value (-2.24 > -2.58), SO the null hypothesis is not rejected.
option -ii ) is true.
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