Question 129839: How tall are college hockey players? The average height has been 68.3 inches. A random sample of 14 hockey players gave a mean height of 69.1 inches. We may assume that x has a normal distribution with σ = 0.9 inch. Does this indicate that the population mean height is different from 68.3 inches? Use 5% level of significance.
a) State the null and the alternate hypothesis.
b) Identify the sampling distribution to be used: the standard normal distribution or the Student's t distribution. Find the critical value(s).
c) Compute the z or t value of the sample test statistic.
d) Find the P value or an interval containing the P value for the sample test statistic.
e) Based on your answers to a through d, decide whether or not to reject the null hypothesis at the given significance level. Explain your conclusion in the context of the problem.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! How tall are college hockey players? The average height has been 68.3 inches. A random sample of 14 hockey players gave a mean height of 69.1 inches. We may assume that x has a normal distribution with σ = 0.9 inch. Does this indicate that the population mean height is different from 68.3 inches? Use 5% level of significance.
a) State the null and the alternate hypothesis.
Ho: mu = 68.3
Ha: mu is not equal to 68.3 (2-tailed test)
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b) Identify the sampling distribution to be used: the standard normal distribution or the Student's t distribution. Find the critical value(s).
t-distribution; Critical value = +-1.96 for alpha = 5% on two-tail test.
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c) Compute the z or t value of the sample test statistic.
t(69.1) = (69.1-68.3)/[0.9/sqrt(14)] = 0.8*sqrt(14)/0.9 = 3.3259...
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d) Find the P value or an interval containing the P value for the sample test statistic.
p-value = 2*P(3.3259
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e) Based on your answers to a through d, decide whether or not to reject the null hypothesis at the given significance level. Explain your conclusion in the context of the problem.
Since p-value is less than 5% and since the test statistic is in the
rejection region we Reject Ho. The test indicates there is significant
statistical evidence that the mean height of hockey players is not 68.3.
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Cheers,
Stan H.
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