Nick plans to obtain a random sample of 50 college students and measure the size

Question

Nick plans to obtain a random sample of 50 college students and measure the size of their left ears (top to bottom in cm). Nick will compute the average ear size (X) and use it to test the null hypothesis that college students have the same average ear size as Joe at 5.10 cm versus the alternative that the average is larger than 5.10 cm, with significance level 0.025.

Part 1: Even before collecting his sample, Nick knows:

a. he has a 97.5% chance of rejecting the null hypothesis, if it is false.

b. he has a 2.5% chance of rejecting the null hypothesis, if it is false.

c. he has a 2.5% chance of rejecting the null hypothesis, whether or not it is false.

d. he has a 2.5% chance of rejecting the null hypothesis, if it is not false

e. he has a 97.5% chance of rejecting the null hypothesis, if it is not false

Part 2. Assume that the p-value is 0.02 and Type 1 error is 0.025. What is the correct conclusion

(a) There is no statistical evidence at the 0.025 significant level to conclude that the average ear size of all college students is larger than 5.10 cm.

(b) There is no statistical evidence at the 0.025 significant level to conclude that the average ear size of all college students is 5.10 cm.

(c) There is statistical evidence at the 0.02 significant level to conclude that the average ear size of all college students is larger than 5.10 cm.

(d) There is statistical evidence at the 0.025 significant level to conclude that the average ear size of all college students is 5.10 cm.

(e) There is statistical evidence at the 0.025 significant level to conclude that the average ear size of all college students is larger than 5.10 cm.

Part 3: Assume that the p-value is 0.02(P rob > t = 0.02, P rob < t = 0.98 and P rob > |t| = 0.04). Suppose now Nick is interested to build confidence interval of the average ear size of all college students. Which is the largest confidence interval which will not contain 5.10 cm?

(a) 1%

(b) 80%

(c) 90%

(d) 95%

(e) 97%

Explanation / Answer

part 1) d. he has a 2.5% chance of rejecting the null hypothesis, if it is not false

Part 2) (e) There is statistical evidence at the 0.025 significant level to conclude that the average ear size of all college students is larger than 5.10 cm.

Part 3:

(d) 95%

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