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# A random sample of 500 connecting rod pins contains 59 nonconforming units. Estimate the process fraction

nonconforming.

(a) Test the hypothesis that the true fraction defective in this process is 0.08. Use alpha = 0.03. (b) Construct a 97% upper confidence interval on the true process fraction nonconforming.

A random sample of 200 printed circuit boards contains 18 defective or nonconforming units. Estimate the process fraction nonconforming. Test the hypothesis that the true fraction nonconforming in this process is 0.10. Use alpha = 0.10. Construct a 90% two-sided confidence interval on the true fraction nonconforming in the production process.

The diameters of aluminum alloy rods produced on an extrusion machine are known to have a standard deviation of 0.0001 in. A random sample of 25 rods has an average diameter of 0.5046 in.

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

Construct a 95% two-sided confidence interval on the mean rod diameter

Please answer the above questions and give explanation and also draw a graph for each question whether it is rejected or accepted the null hypothesis . so, that I learn from your knowledge. please, post a correct answer without including wrong data. Thank You!

In any canning process, a manufacturer will lose money if the cans contain either significantly more or
significantly less than is claimed on the label. Accordingly, canners pay close attention to the amount of
their product being dispensed by the can-filling machines. Consider a company that produces a fast-drying
rubber cement in 32-ounce aluminum cans. A quality control inspector is interested in testing whether the
variance of the amount of rubber cement dispensed into the cans is more than .3. If so, the dispensing
machine is in need of adjustment. Since inspection of the canning process requires that the dispensing
machines be shut down, and shutdowns for any lengthy period of time cost the company thousands of
dollars in lost revenue, the inspector is able to obtain a random sample of only 10 cans for testing. After
measuring the weights of their contents, the inspector computes the following summary statistics:
x = 31.55 ounces
\$ = . 48 ounce
a. Does the sample evidence indicate that the dispensing machines are in need of adjustment? Test at
significance level a = .05.
b. What assumption is necessary for the hypothesis test of part a to be valid?

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