The following data came from a distribution that is known to be normal with a st

Question

The following data came from a distribution that is known to be normal with a standard deviation of 1.8: 17.2, 16.9, 16.1, 19.8, 16.7 The sample mean was 17.34 and the sample standard deviation was 1.4728 The hypothesis H_0: mu lessthanorequalto 16.8 versus H_A: mu > 16.8 was tested by 3 different students using three different methods. They obtained the following three p-values: .1562, .22917, .2511 What were the three methods and which gave which p-value Which method would be the most appropriate? Why

Explanation / Answer

Sample SD, S = 1.4728

Population SD, S' = 1.8

Sample size, n = 5

First we calculate the test statistic using z-test.

z-score = (17.34-16.8)/(1.8/50.5) = 0.670

The p-score using z-table is: 0.2511

So 0.2511 is obtained using z-test.

Next we calculate the test statistic using t-test.

t-score = (17.34-16.8)/(1.4728/50.5) = 0.819

The p-score using t-table and 3 degress of freedom is: 0.229

So 0.229 is obtained using t-test.

(b)

The method of z-test is more appropriate here because the population stadard deviation is known to us. t-test is used only when population SD is not known and it is approximated by sample SD. But here z-test is preferred.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.