# A manufacturer produces plastic golf tees, The injector molder produces golf tees that are designed to have an average height of 63 mm.

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A manufacturer produces plastic golf tees. The injector molder produces golf tees that are designed to have an average height of 63 mm. To determine if this specification is met, random samples are taken from the production floor. One sample is contained in the table below.

Data: 62.53 62.18 66.30 59.06 60.11 61.77 60.17 63.04 62.25 66.95 60.75 65.99

a. Determine if the process is not producing the tees to specification. Use a significance level of 0.02.
b. If the hypothesis test determines the specification is not being met, the production process will be shut down while causes and remedies are determined. At times this occurs even though the process is functioning to specification. What type of statistical error would this be?

a. State the appropriate null and alternative hypotheses. Choose the correct answer below.

Determine the critical value(s) for a = 0.02.

State the conclusion. Test that the items produced have a mean of 63 mm,

Hypothesis

H0:  mu  = 63 mm

Ha: mu != 63 mm

The sample values give a mean of  = 62.59

Standard deviation = 2.582

Because the population standard deviation is not given use the t-statistic.

t  = (x_bar   - mu)/(s/sqrt(n))

t = (62.5 9 - 63)/(2.582/sqrt(12)) =  -0.671

The p-value for a t-test can be obtained using Excel,  with 11 degrees of freedom. =T.DIST(-0.671,11,TRUE)  =  0.2580

2 tailed p value = 0.2580 * 2 =  0.516.

p = 0.516

Fail to reject the null hypothesis, this means that the specification are met.