Question

Repair time (X) for an oil change at a car dealership has a population mean of...

Repair time (X) for an oil change at a car dealership has a population mean of 50 min and a population standard deviation of 7 min. Questions A and B must be done using a pencil and paper.

a.) If a random sample of 50 oil changes is selected. Set up a 99% confidence interval estimate for an oil change.

b.) If a random sample of 75 oil changes is selected. Set up a 95% confidence interval estimate for an oil change.

Homework Answers

Answer #1

a)

sample mean, xbar = 50
sample standard deviation, σ = 7
sample size, n = 50


Given CI level is 99%, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, Zc = Z(α/2) = 2.58


ME = zc * σ/sqrt(n)
ME = 2.58 * 7/sqrt(50)
ME = 2.55

CI = (xbar - Zc * s/sqrt(n) , xbar + Zc * s/sqrt(n))
CI = (50 - 2.58 * 7/sqrt(50) , 50 + 2.58 * 7/sqrt(50))
CI = (47.4459 , 52.5541)

b)

sample mean, xbar = 50
sample standard deviation, σ = 7
sample size, n = 75


Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96


ME = zc * σ/sqrt(n)
ME = 1.96 * 7/sqrt(75)
ME = 1.58

CI = (xbar - Zc * s/sqrt(n) , xbar + Zc * s/sqrt(n))
CI = (50 - 1.96 * 7/sqrt(75) , 50 + 1.96 * 7/sqrt(75))
CI = (48.4158 , 51.5842)


Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Questions A and B must be done using a pencil and paper. A.) Assume that a...
Questions A and B must be done using a pencil and paper. A.) Assume that a sample of 16 tires is randomly chosen with a mean of 63531.9 and a standard deviation of 3811.7 to test a new compound. set up a 95% confidence interval estimate for the new tire compound. B.) Set up a 99% confidence interval estimate for the tire compound.
The manager of the service department of a local car dealership has noted that the service...
The manager of the service department of a local car dealership has noted that the service times of a sample of 15 new automobiles have a sample variance of S2 = 16. A 95% confidence interval estimate for the population variance of service times for all their new automobiles is: A 95% confidence interval estimate for the population standard deviation of service times for all their new automobiles is:
In a random sample of 35 refrigerators, the mean repair cost was $29.00  and the population standard...
In a random sample of 35 refrigerators, the mean repair cost was $29.00  and the population standard deviation is $15.90 . Construct a 95% confidence interval for the population mean repair cost. Interpret the results. 95%  confidence interval is________ ?   (Round to two decimal places as needed.) Interpret your results. Choose the correct answer below. A. With 95 % confidence, it can be said that the confidence interval contains the sample mean repair cost. B. With 95 % confidence, it can be...
7. If I have a population of an unknown mean and unknown standard deviation, what is...
7. If I have a population of an unknown mean and unknown standard deviation, what is the 95% confidence interval estimate of the mean if a. A random sample of size 25 gives a mean of 50 and a standard deviation of 12 b. A random sample of size 16 gives a mean of 50 and a standard deviation of 12 8. The average cost per night of a hotel room in New York City is $325. Assume this estimate...
Sketching required. 7. ​A car dealership would like to estimate the mean mpg of its new...
Sketching required. 7. ​A car dealership would like to estimate the mean mpg of its new model car with 90% confidence. The population is normally distributed; however we are taking a sample of 25 cars with a sample mean of 96.52 and a sample standard deviation of 10.70. Calculate a 90% confidence interval for the population mean using this sample data. Answers Point Estimate Standard Error Margin of Error Alpha Critical Value Confidence Interval
The manager of the service department of a local car dealership has noted that the service...
The manager of the service department of a local car dealership has noted that the service times of a sample of 30 new automobiles has a standard deviation of 7 minutes. A 99% confidence interval estimate for the standard deviation of the service times for all their new automobiles is 16.047 to 45.722 4.778 to 8.066 22.93 to 96.31 27.1520 to 108.299
To estimate mean oil consumption in a population of 10,000 houses. You draw a representative sample...
To estimate mean oil consumption in a population of 10,000 houses. You draw a representative sample of 100 houses from this population. Calculate the mean of the sample (120.6 thermounits) and provide a 95% two-sided confidence interval (118.4 $ µ $ 122.8)... 1- What is the interpretation of this confidence interval? 2- There are several ways to control the width of the confidence intervals. Please name the ways you can change the width of this confidence interval 3- Assume the...
In a random sample of four mobile​ devices, the mean repair cost was ​$85.00 and the...
In a random sample of four mobile​ devices, the mean repair cost was ​$85.00 and the standard deviation was ​$12.00. Assume the population is normally distributed and use a​ t-distribution to find the margin of error and construct a 95​% confidence interval for the population mean. Interpret the results. The 95​% confidence interval for the population mean mu is ​( ​,​). ​(Round to two decimal places as​ needed.) The margin of error is ​$ nothing. ​(Round to two decimal places...
The shape of the distribution of the time required to get an oil change at a...
The shape of the distribution of the time required to get an oil change at a 20​-minute ​oil-change facility is unknown.​ However, records indicate that the mean time is 21.4 minutes​, and the standard deviation is 3.7 minutes. Complete parts ​(a) through ​(c). ​(a) To compute probabilities regarding the sample mean using the normal​ model, what size sample would be​ required? ​(b) What is the probability that a random sample of nequals35 oil changes results in a sample mean time...
Construct a 95% confidence interval for the population mean,Assume the population has a normal distribution, A...
Construct a 95% confidence interval for the population mean,Assume the population has a normal distribution, A random sample of 16 fluorescent light bulbs has a mean life of 645 hours with a standard devastion of 31 hours. From the above question calculate the 99% confidence interval for n = 16. then, Letting n= 100, calculate the 95% and 99% confidence intervals (a) What happend to the interval width from 95% to 99% (b) what happend to the interval width from...