A local tennis player pro-shop strings tennis rackets at the tension (pounds per

Question

A local tennis player pro-shop strings tennis rackets at the tension (pounds per square inch) requested by the customer. Recently a customer made a claim that the pro-shop consistently strings rackets at Lower tensions, on average, than requested. To support this claim, the customer asked the pro shop to string 13 new rackets at 59 psi. Upon receiving the rackets, the customer measured the tension of each and calculated the following summary statistics. Sample statistic mean (x_)= 57 psi, s= 2.4 psi. In order to conduct the test, the customer selected a significance level of alpha = .05. Interpret this value.
A) the smallest value of alpha that guy can use and still reject is H0 is .05 B). The probability of making a type 2 error is .95 C). There is a 5% chance that the sample will be biased D) the probability of concluding that the true mean is less than 59 psi when in fact it is equal to 59 psi us only .05 A local tennis player pro-shop strings tennis rackets at the tension (pounds per square inch) requested by the customer. Recently a customer made a claim that the pro-shop consistently strings rackets at Lower tensions, on average, than requested. To support this claim, the customer asked the pro shop to string 13 new rackets at 59 psi. Upon receiving the rackets, the customer measured the tension of each and calculated the following summary statistics. Sample statistic mean (x_)= 57 psi, s= 2.4 psi. In order to conduct the test, the customer selected a significance level of alpha = .05. Interpret this value.
A) the smallest value of alpha that guy can use and still reject is H0 is .05 B). The probability of making a type 2 error is .95 C). There is a 5% chance that the sample will be biased D) the probability of concluding that the true mean is less than 59 psi when in fact it is equal to 59 psi us only .05 A local tennis player pro-shop strings tennis rackets at the tension (pounds per square inch) requested by the customer. Recently a customer made a claim that the pro-shop consistently strings rackets at Lower tensions, on average, than requested. To support this claim, the customer asked the pro shop to string 13 new rackets at 59 psi. Upon receiving the rackets, the customer measured the tension of each and calculated the following summary statistics. Sample statistic mean (x_)= 57 psi, s= 2.4 psi. In order to conduct the test, the customer selected a significance level of alpha = .05. Interpret this value.
A) the smallest value of alpha that guy can use and still reject is H0 is .05 B). The probability of making a type 2 error is .95 C). There is a 5% chance that the sample will be biased D) the probability of concluding that the true mean is less than 59 psi when in fact it is equal to 59 psi us only .05

Explanation / Answer

Using Minitab:

One-Sample Z

Test of = 59 vs < 59
The assumed standard deviation = 2.4

N    Mean SE Mean 95% Upper Bound      Z      P
13 57.000    0.666           58.095             -3.00 0.001

P-value <0.05 we reject null hypothesis.

B. The probability of concluding that the true mean is less than 59 psi when in fact it is equal to 59 psi is only .05

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