Below you are given ages that were obtained by taking a random ...

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Below you are given ages that were obtained by taking a random sample of 6 undergraduate instructors at a university. Assume the population has a normal distribution. 40 42 43 39 37 39
 a. What is the point estimate of ?
  b. Determine the standard deviation.
  c. Construct a 90 confidence interval for the average age of undergraduate instructors.
  d. Construct a 99 confidence interval for the average age of undergraduate instructors.
  e. Discuss why the 90 and 99 confidence intervals are different.

Question 2

Brakes Shop, Inc, is a franchise that specializes in repairing brake systems of automobiles. The company purchases brake shoes from a national supplier. Currently, lots of 1,000 brake shoes are purchased, and each shoe is inspected before being installed on an automobile. The company has decided instead of 100 inspection to adopt an acceptance sampling plan.
 a. Explain what is meant by the acceptance sampling plan.
  b. If the company decides to adopt an acceptance sampling plan, what kinds of risks are there?
  c. The quality control department of the company has decided to select a sample of 10 shoes and inspect them for defects. Furthermore, it has been decided that if the sample contains no defective parts, the entire lot will be accepted. If there are 50 defective shoes in a shipment, what is the probability that the entire lot will be accepted?
  d. What is the probability of accepting the lot if there are 100 defective units in the lot?

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Answer to Question 1

a. 40 years
b. 2.19 (rounded)
c. 38.20 to 41.80 years (rounded)
d. 36.39 to 43.61 years (rounded)
e. As the level of confidence increases, the confidence interval gets wider.

Answer to Question 2

a.
The acceptance sampling plan refers to a statistical quality control procedure for accepting or rejecting a given lot based on the results of the sample. The plan requires the establishment of a sample size (n) and an acceptance criterion (c), where c represents the maximum number of defective units that can be found in the sample and still consider the lot as acceptable.
b.
Under the acceptance sampling plan, two types of risks are involved. First, the company could reject a good quality lot based on the sample information. This risk is known as the Producer's Risk (Type I error), since the items will be returned to the producer even though they are good. Next, it is possible for the company to accept a bad quality lot based on the sample information. This latter risk is known as the Consumer's Risk (Type II error), since these bad items could eventually be passed on to consumers.
c. 0.5987
d. .3487

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Gracias!

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Excellent