Question

Student's t Distribution CI (PLEASE SHOW EXCEL FUNCTIONS) The manager of The Cheesecake Factory in Boston...

Student's t Distribution CI (PLEASE SHOW EXCEL FUNCTIONS)

The manager of The Cheesecake Factory in Boston would like to know the mean number of customers served on weekdays. She believes that the number of customers served follows a Normal distribution. She reports that on six randomly selected weekdays an average of 158.3 customers were served with a sample standard deviation of 52.2.

(EXCEL FUNCTIONS)

a. Calculate the standard error of the sample mean. (EXCEL FUNCTIONS)
b. Find the t-critical value for a 99% confidence interval with a sample size of 6. (EXCEL FUNCTIONS)
c. Calculate a 99% confidence interval of the mean. (EXCEL FUNCTIONS)
d. Interpret the confidence interval in the context of the problem. (EXCEL FUNCTIONS)

Homework Answers

✔ Recommended Answer
Answer #1

excel function are in bold:

a)

std error 'sx=s/√n=52.2/sqrt(6)= 21.3106

b)

for 99% CI; and 5 df, value of t=tinv(1-0.99,6-1) =4.032

c)

margin of error E=t*std error    =4.032*21.3106 = 85.924
lower bound=sample mean-E =158.3-85.924 = 72.376
Upper bound=sample mean+E =158.3+85.924 = 244.224
from above 99% confidence interval for population mean =(72.38,244.22)

d)

above interval gives 99% confidence to contain true value of population mean
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Similar Questions
The manager of The Cheesecake Factory in Boston reports that on six randomly selected weekdays, the...
The manager of The Cheesecake Factory in Boston reports that on six randomly selected weekdays, the number of customers served was 230, 235, 65, 185, 120, and 245. She believes that the number of customers served on weekdays follows a normal distribution. Construct the 99% confidence interval for the average number of customers served on weekdays. (You may find it useful to reference the t table. Round intermediate calculations to at least 4 decimal places, "sample mean" and "sample standard...
The manager of The Cheesecake Factory in Boston reports that on six randomly selected weekdays, the...
The manager of The Cheesecake Factory in Boston reports that on six randomly selected weekdays, the number of customers served was 165, 135, 95, 145, 125, and 265. She believes that the number of customers served on weekdays follows a normal distribution. Construct the 90% confidence interval for the average number of customers served on weekdays. (You may find it useful to reference the t table. Round intermediate calculations to at least 4 decimal places, "sample mean" and "sample standard...
Normal Distribution CI IQ tests are designed to yield results that are approximately Normally distributed. Researchers...
Normal Distribution CI IQ tests are designed to yield results that are approximately Normally distributed. Researchers think believe that the standard deviation, σ, is 15. A reporter is interested in estimating the average IQ of employees in a large high-tech firm in California. She gathers the IQ information on 22 employees of this firm and recoreds the sample mean IQ as 106. Let X represent a random variable describing a person's IQ: X~N(µ, 15). a. Find the standard error of...
A hair salon in Cambridge, Massachusetts, reports that on seven randomly selected weekdays, the number of...
A hair salon in Cambridge, Massachusetts, reports that on seven randomly selected weekdays, the number of customers who visited the salon were 72, 55, 49, 35, 39, 23, and 77. It can be assumed that weekday customer visits follow a normal distribution. [You may find it useful to reference the t table.] a. Construct the 90% confidence interval for the average number of customers who visit the salon on weekdays. (Round intermediate calculations to at least 4 decimal places, "sample...
a. Use the Student's t distribution to find tc for a 0.99 confidence level when the...
a. Use the Student's t distribution to find tc for a 0.99 confidence level when the sample is 8. (Round your answer to three decimal places.) b. Use the Student's t distribution to find tc for a 0.90 confidence level when the sample is 8. (Round your answer to three decimal places.) c. Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Round your answer to four decimal places.) The area to...
done not using excel The manufacturer of Boston and Vermont asphalt shingles provides its customers with...
done not using excel The manufacturer of Boston and Vermont asphalt shingles provides its customers with a 20-year warranty on most of its products. To determine whether a shingle will last the entire warranty period, accelerated-life testing is conducted at the manufacturing plant. Accelerated-life testing exposes the shingle to the stresses it would be subject to in a lifetime of normal use via a laboratory experiment that takes only a few minutes to conduct. In this test, a shingle is...
**** PLEASE SHOW HOW TO SOLVE IN EXCEL NOT HANDWRITTEN*** The average cost per night of...
**** PLEASE SHOW HOW TO SOLVE IN EXCEL NOT HANDWRITTEN*** The average cost per night of a hotel room in New York City is $325. Assume this estimate is based on a sample of 100 hotels and that the sample standard deviation is $75. What is the 95% confidence interval estimate of the population mean? What is the 99% confidence interval estimate of the population mean?
For the standard normal distribution, compute Z0.69. Use Excel and round the answer to two decimal...
For the standard normal distribution, compute Z0.69. Use Excel and round the answer to two decimal places. Consider the following test performed with the level of significance 0.01: A random sample of size 28 is obtained from a normally distributed population. The population standard deviation is equal to 3.6. The sample mean happened to be 24. For this hypothesis test, what will be the critical value (the relevant z-alpha)?  Round the answer to three decimal places. A probability distribution of all...
Chapter 6, Section 2-CI, Exercise 083 Use the t-distribution to find a confidence interval for a...
Chapter 6, Section 2-CI, Exercise 083 Use the t-distribution to find a confidence interval for a mean u given the relevant sample results. Give the best point estimate for u, the margin of error, and the confidence interval. Assume the results come from a random sample from a population that is approximately normally distributed. A 90% confidence interval for u using the sample results i = 3.2, s = 0.2, and n = 100 Round your answer for the point...
Use the standard normal distribution or the​ t-distribution to construct a 99​% confidence interval for the...
Use the standard normal distribution or the​ t-distribution to construct a 99​% confidence interval for the population mean. Justify your decision. If neither distribution can be​ used, explain why. Interpret the results. In a random sample of 13 mortgage​ institutions, the mean interest rate was 3.59​% and the standard deviation was 0.42​%. Assume the interest rates are normally distributed. Select the correct choice below​ and, if​ necessary, fill in any answer boxes to complete your choice. A. The 99​% confidence...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT