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Confidence interval for mean

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1. A simple random sample of 40 items resulted in a sample mean of 25. The population standard deviation is = 5.
a. What is the standard error of the mean, _
x ?
b. At 95% confidence, what is the margin error

3. A simple random sample of 60 items resulted in a sample mean of 80. The population standard deviation is = 15.
a. Compute the 95% confidence interval for the population mean.
b. Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean.
c. What is the effect of a larger sample size on the interval estimate?

9. Please see attachment GPA
A study was conducted of students admitted to the top graduate business schools. The data contained in the CD file named GPA show the undergraduate grade point average for students and is consistent with the findings reported. Using the past years' data, the population standard deviation can be assumed know with = .28. What is the 95% confidence interval estimate of the mean undergraduate grade point average for students admitted to the top graduate business schools?

11. For a t distribution with 16 degrees of freedom, find the area, or probability, in each region.
a. To the right of 2.120
b. To the left of 1.337
c. To the left of -1.746
d. To the right of 2.583
e. Between -2.120 and 2.120
f. Between -1.746 and 1.746

17. please see excel file Miami
The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of 50 business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of 50 business travelers follow.
Develop a 95% confidence interval estimate of the population mean rating for Miami.

19. A National Retail Foundation survey found households intended to spend an average of $649 during the December holiday season. Assume that the survey included 600 households and that the sample standard deviation was $175.
a. With 95% confidence, what is the margin of error?
b. What is the 95% confidence interval estimate of the population mean?
c. The prior year, the population mean expenditure per household was $632. Discuss the change in holiday season expenditures over the on-year period.

21. Complaints about rising prescription drug prices caused the U.S. Congress to consider laws that would force pharmaceutical companies to offer prescription discounts to senior citizens without drug benefits. The House Government Reform Committee provided data on the prescription cost for some of the most widely used drugs. Assume the following data show a sample of the prescription cost in dollars for Zocor, a drug used to lower cholesterol.

110 112 115 99 100 98 104 126
Given a normal population, what is the 95% confidence interval estimate of the population mean cost for a prescription of Zocor?

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The solution contains answers to various problems related to confidence interval, margin of error, z score and standard error of mean.

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Confidence Intervals, Samples, and Unknown Variance

Let (X1, X2,..., Xn) be a sample, where each Xi is a random variable of normal distribution with mean mu and variance sigma². Let us suppose that n = 20, and sigma² = 9. An experiment has yielded the results (X1, X2,..., X20), and we have calculated that the empirical mean x20 = 2.09.

1) Give a confidence interval with level of confidence 90% for mu.

2) How big would the sample have to be for the interval to be half as long?

3) Let us now suppose the variance is not known. Knowing that counting from i=1 to 20 (xi - x20)² = 14.6, give a confidence interval with level of confidence 90% for the value of mu.

4) We now suppose we know mu is known and is equal to 2. Give a confidence interval with a confidence level of 90% for the value of sigma².

5) Same question if we do not know the value of mu.

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