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.
(a) State the hypotheses for this test.
(b) Which is more appropriate here – a z-test, or a t-test?
(c) Calculate the test statistic for this test.
(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.
(e) Make a fully-worded conclusion for this test.
2)
This is the right tailed test .
The null and alternative hypothesis is
H_{0} : = 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.
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