4. In a test of the hypothesis Ho: = 10 versus H, : # 10, a sample ofn = 50 observations possessed mean T = 10.8 and standard deviation s= 3.1. (a) Find an interpret the p-value for this test and answer a question regarding the interpretation of the result if a = 0.10. The p-value is (Fill in the blank; round to four decimal places, as needed.) You should find one of the following useful: P(z 2 2.311) = 0.0104 P(z <-0.711) = 0.2385 P(z 2 1.825) 0.0340 P(: < 1.431) 0.9238

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4. In a test of the hypothesis Ho : u = 10 versus H. : 4 # 10, a sample of n =
I = 10.8 and standard deviation s = 3.1.
50 observations possessed mean
(a) Find an interpret the p-value for this test and answer a question regarding the interpretation of the result if
a = 0.10.
The p-value is
(Fill in the blank; round to four decimal places, as needed.)
You should find one of the following useful:
P(z > 2.311) z 0.0104 P(z < -0.711) z 0.2385 P(z > 1.825) z 0.0340 P(z < 1.431) z 0.9238
"There is sufficient evidence to reject Họ for a = 0.10." TRUE or FALSE (Circle the correct answer.)
(b) Use the rejection region approach for part A. Why is this result equivalent to the p-value method? Draw a
picture and/or explain in words.
You should find one of the following useful:
2, 10 1.282
z.0, 1.645
2025 1.96
01 2.326
2005 2.576
Bonus (4 points). Suppose that instead of n = 50 observations, you were only able to attain a sample of n = 15
observations. In this case, compute the test statistic and provide the recipe for computing the p-value. (Hint: This
sample is not large and we do not know o, and so you cannot rely on the z-distribution.)
Transcribed Image Text:4. In a test of the hypothesis Ho : u = 10 versus H. : 4 # 10, a sample of n = I = 10.8 and standard deviation s = 3.1. 50 observations possessed mean (a) Find an interpret the p-value for this test and answer a question regarding the interpretation of the result if a = 0.10. The p-value is (Fill in the blank; round to four decimal places, as needed.) You should find one of the following useful: P(z > 2.311) z 0.0104 P(z < -0.711) z 0.2385 P(z > 1.825) z 0.0340 P(z < 1.431) z 0.9238 "There is sufficient evidence to reject Họ for a = 0.10." TRUE or FALSE (Circle the correct answer.) (b) Use the rejection region approach for part A. Why is this result equivalent to the p-value method? Draw a picture and/or explain in words. You should find one of the following useful: 2, 10 1.282 z.0, 1.645 2025 1.96 01 2.326 2005 2.576 Bonus (4 points). Suppose that instead of n = 50 observations, you were only able to attain a sample of n = 15 observations. In this case, compute the test statistic and provide the recipe for computing the p-value. (Hint: This sample is not large and we do not know o, and so you cannot rely on the z-distribution.)
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