Question

A manufacturer produces plastic golf tees. The injector molder produces golf tees that are designed to have an average height of mm. To determine if this specification is met, random samples are taken from the production floor. One sample is contained in the table below. 70 Click the icon to view the data table. 2 a. Determine if the process is not producing the tees to specification. Use a significance level of 0.01. 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. A. H0 : μ = 70 HA : μ ≠ 70 B. H0 : μ > 70 HA : μ ≤ 70 C. H0 : μ ≥ 70 HA : μ < 70 D. H0 : μ ≠ 70 HA : μ = 70 E. H0 : μ < 70 HA : μ ≥ 70 F. H0 : μ ≤ 70 HA : μ > 70 Determine the critical value(s) for α = 0.01. (1) = (Use a comma to separate answers as needed. Round to four decimal places as needed.) Calculate the test statistic. t = (Round to four decimal places as needed.) State the conclusion. Choose the correct answer below. A. the null hypothesis. There sufficient evidence that the golf tees do not have an average height of mm. Do not reject is not 70 B. the null hypothesis. There sufficient evidence that the golf tees do not have an average height of mm. Reject is not 70 C. the null hypothesis. There sufficient evidence that the golf tees do not have an average height of mm. Do not reject is 70 D. the null hypothesis. There sufficient evidence that the golf tees do not have an average height of mm. Reject is 70 b. If the hypothesis test determines the specification is not being met, the production process will be shut down. If this occurs even though the process is functioning to specification, what type of statistical error would this be? Type II error Type I error 70.85 70.34 69.94 69.22 70.29 69.91 69.31 72.44 69.54 70.12 71.66 69.86 70.66 70.82 70.16 70.16 70.77 71.21 71.11 69.76 71.35 70.22 71.26 69.22 ± tα / 2 tα − tα

Answer 1

Following table shows the output of descriptive statistics generated by excel:

Descriptive statistics
	X
count	24
mean	70.4242
sample standard deviation	0.8137
sample variance	0.6621
minimum	69.22
maximum	72.44
range	3.22

The critical values are: -2.8073, 2.8073

The test statistics is t = 2.5287

C. the null hypothesis. There is not sufficient evidence that the golf tees do not have an average height of mm. Do not reject mu is 70

If this occurs even though the process is functioning to specification, what type of statistical error would this be?

Ans: Since we reject the true null hypothesis in this case so type I is possible.