Question

2. A researcher would like to determine if the average height of MLB players is greater than the population mean of adult male Americans, 69.3 inches. He takes a sample of 6 MLB players and calculates x ̄ = 72.5in and s = 3.27in. He decides to conduct this study with a hypothesis test at the 5% level of significance. Assume that heights of MLB players follow a normal distribution.

1. (a) State the hypotheses for this test.

2. (b) Which is more appropriate here – a z-test, or a t-test?

3. (c) Calculate the test statistic for this test.

4. (d) Find the P-value for this test. If you cannot find an exact P-value, use your table to find an appropriate range for the P-value.

5. (e) Make a fully-worded conclusion for this test.

Answer 1

2)

This is the right tailed test .

The null and alternative hypothesis is

H₀ :   = 69.3

H_a : > 69.3

Test statistic = t

= ( - ) / s / n

= (72.5 - 69.3) / 3.27 / 6

Test statistic = 2.40

df = 5

P-value = 0.0308

= 0.05

P-value <

Reject the null hypothesis .

There is sufficient evidence to conclude that the  average height of MLB players is greater than the population mean of adult male Americans, 69.3 inches.