# 1. The tensile strength of a fiber used in manufacturing cloth is of interest to the purchaser

August 30, 2017

Question
1. The tensile strength of a fiber used in manufacturing cloth is of interest to the purchaser. Previous experience indicates that the standard deviationof tensile strength is 2 psi. A random sample of eight fiber specimens isselected, and the average tensile strength is found to be 127 psi.

(a) Test the hypothesis that the mean tensile strength equals 125 psi versusthe alternative that the mean exceeds 25 psi. Use ? = 0.05.

(b) What is the P-value for this test?

(c) Discuss why a one-sided alternative was chosen in part (a).

(d) Construct a 95% lower confidence interval on the mean tensile strength.

2. A machine is used to fill containers with a liquid product. Fill volume canbe assumed to be normally distributed. A random sample of 10 containersis selected, and the contents (oz) are as follows: 12.03, 12.01, 12.04, 12.02,12.05, 11.98, 11.96, 12.02, 12.05, and 11.99.

(a) Suppose that the manufacturer wants to be sure that the mean netcontents exceeds 12 oz. What conclusions can be drawn from the data(use ? = 0.05)?

(b) Construct a two-sided 95% confidence interval on the mean fill volume.

(c) Does the assumption of normality seem appropriate for the fill volumedata?

(d) If the true mean fill volume is 12.05 oz, approximately how many sampleswould be required to reject the null hypothesis with a probability of at least 0.90?

3. The diameters of aluminum alloy rods produced on an extrusion machineare known to have a standard deviation of 0.0001 in. A random sample of25 rods has an average diameter of 0.5046 in.

(a) Test the hypothesis that mean rod diameter is 0.5025 in. Assume atwo-sided alternative and use ? = 0.05.

(b) Find the P-value for this test.

(c) Construct a two-sided 95% confidence interval on the mean rod diameter.

4. The output voltage of a power supply is assumed to be normally distributed.Sixteen observations are taken at random on voltage are as follows: 10.35,79.30, 10.00, 9.96, 11.65, 12.00, 11.25, 9.58, 11.54, 9.95, 10.28, 8.37, 10.44,9.25, 9.38, and 10.85.

(a) Test the hypothesis that the mean voltage equals 12 V against the twosidedalternative using ? = 0.05.

(b) Construct a two-sided 95% confidence interval on µ.

(c) Test the hypothesis that ?2 = 1 using ? = 0.05.

(d) Construct a 95% two-sided confidence interval on ?.

(e) Construct a 95% upper confidence bound on ?.

(f) Does the assumption of normality seem reasonable for the output voltage?Provide evidence in support of your response.

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