Question

Many cardiac patients wear an implanted pacemaker to control their heartbeats. There is a plastic connector module mounted on the top of the pacemaker. Engineers have designed the connector module with a tolerance to ensure that the pacemaker functions correctly. Assume that the thickness of the module made by a certain manufacturing company is normally distributed and known to have a population standard deviation of 0.0015 inch. The engineer took a random sample of 20 modules was measured, and the average depth is measured to be 0.310 inch. Use this information and answer the following questions.

Question a:  In order to find a confidence interval for the average thickness of the module made by this company, which distribution table would you use?

Group of answer choices

Z - table

t - table

Either table will provide the same answer

Not enough information to tell

Question b: Why did you select the table in Question a to find a confidence interval for the average thickness of the module made by this company? (select all that apply)

Group of answer choices

The population standard deviation of the thickness of the module is known.

The sample standard deviation (20 samples) of the thickness of the module is known.

The thickness of the module is normally distributed.

The distribution of the thickness of the module is unknown.

The sample size is less than 30.

Question c: Find the lower bound of a 98% confidence interval for the average thickness of all connector modules produced by this company. (Use 4 decimal places)

Question d: You would like find a 95% confidence interval for the average thickness of all connector modules produced by this company instead of the 98% confidence interval you calculated above. What would happen to the width of the confidence interval as compared to that of Question c?

Group of answer choices

The width of the confidence interval will increase.

The width of the confidence interval will decrease.

The width of the confidence interval will stay the same.

There is not enough information to tell.

Question e:  The engineer decided to sample an addition 10 modules, and then calculate the 98% confidence interval for the average thickness of all connector modules produced by this company. What would happen to the width of the confidence interval as compared to that of Question c?

Group of answer choices

The width of the confidence interval will increase.

The width of the confidence interval will decrease.

The width of the confidence interval will stay the same.

There is not enough information to tell.

Question f:  With a follow up study, the company determined that the standard deviation of the module thickness is actually 0.0020 inch instead of the original 0.0015 inch. What would the margin of error change in comparing to that of Question c?

Group of answer choices

The width of the confidence interval will increase.

The width of the confidence interval will decrease.

The width of the confidence interval will stay the same.

There is not enough information to tell.

Answer 1

Solution:-

a)  In order to find a confidence interval for the average thickness of the module made by this company, we should use Z - table.

b)

The population standard deviation of the thickness of the module is known. The thickness of the module is normally distributed.

c) 98% confidence interval for the average thickness of all connector modules produced by this company is

d) The width of the confidence interval will decrease.

As the confidence level decreases the width of confidence interval decreases.

e)  The width of the confidence interval will decrease.

As the sample size increases the width of confidence interval decreases.

f) The width of the confidence interval will increase.

As the standard deviation increases the width of confidence interval increases..