# Determine sample size from Control Chart values

Below are the X-bar and R values for five samples. If the lower control limit for the X-bar chart is 8.34, what is the sample size?

See attachment for values.

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#### Solution Summary

Calculate the sample size is detailed on back-solving for the size-specific anti-biasing constant in an attached Excel file.

Hypothesis Testing

9. Consider the following hypothesis test:

Ho:u > 20

Ho:u < 20

A sample of 50 provided a sample mean of 19.4. The population standard deviation is 2.

a. Compute the value of the test statistic.

b. What is the p-value?

c. Using a = .05, what is your conclusion?

d. What is the rejection rule using the critical value? What is your conclusion?

Please see the attached file.

9. Consider the following hypothesis test:

Ho:u > 20

Ho:u < 20

A sample of 50 provided a sample mean of 19.4. The population standard deviation is 2.

a. Compute the value of the test statistic.

b. What is the p-value?

c. Using a = .05, what is your conclusion?

d. What is the rejection rule using the critical value? What is your conclusion?

23. Consider the following hypothesis test:

Ho:u < 12

Ho:u > 12

A sample of 25 provided a sample mean xbar=14 and a sample standard deviation s = 4.32

a. Compute the value of the test statistic.

b. Use the t distribution table to compute a range for the p-value.

c. At a = .05, what is your conclusion?

d. What is the rejection rule using the critical value? What is your conclusion?

25. Consider the following hypothesis test:

Ho:u > 45

Ho:u < 45

A sample of 36 is used. Identify the p-value and state your conclusion for each of the following sample results. Use a = .01.

a. xbar = 44 and s = 5.2

b. xbar = 43 and s = 4.6

c. xbar = 46 and s = 5.0

29. The cost of a one-carat VS2 clarity, H color diamond from Diamond Source USA is $5600. A Midwestern jeweler makes calls to contacts in the diamond district of New York City to see whether the mean price of diamonds there differs from $5600.

a. Formulate hypotheses that can be use to determine whether the mean price in New York City differs from $5600.

b. There was a sample of 25 New York City contacts. What is the p-value?

c. At a = .05, can the null hypothesis be rejected? What is your conclusion?

d. Repeat the preceding hypothesis test using the critical value approach.

Ch. 18

1. A process that is in control has a mean of u = 12.5 and a standard deviation of o = .8

a. Construct an x chart if samples of size 4 are to be used.

b. Repeat part (a) for samples of size 8 and 16.

c. What happens to the limits of the control chart as the sample size is increased? Discuss why this change is reasonable.

3. Twenty-five samples of 100 items each were inspected when a process was considered to be operating satisfactorily. In the 25 samples, 135 items were found to be defective.

a. What is an estimate of the proportion defective when the process is in control?

b. What is the standard error of the proportion if sample sizes of size 100 will be used for statistical process control?

c. Compute the upper and lower limits for the control chart.

9. An automotive industry supplier produces pistons for several models of automobiles.

20 samples, each consisting of 200 pistons, were selected when the process was

known to be operating in conrol. The numbers of defective pistons found in the

samples follow.

8 10 6 4 5 7 8 12 8 15

14 10 10 7 5 8 6 10 4 8

a. What is an estimate of the proportion defective for the piston manufacturing process when it is in control?

b. Construct a p chart for the manufacturing process, assuming each sample has 200 pistons.

c. With the results of part (b), what conclusion should be drawn if a sample of 200 has 20 defective pistons?

d. Compute the upper and lower control limits for an np chart.

e. Answer part (c) using the results of part (d).