1. Suppose a sample of n = 50 items is drawn from a population of manufactured products and the weight, X, of each item is recorded. Prior experience has shown that the weight has a probability distribution with m= 6 ounces and standard deviation= 2.5 ounces. Which of the following is true about the sampling distribution of the sample mean if a sample of size 15 is selected?
a) The mean of the sampling distribution is 6 ounces.
b) The standard deviation of the sampling distribution is 2.5 ounces.
c) The shape of the sample distribution is approximately normal.
d) All of the above are correct.

2. A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. If the dean wanted to estimate the proportion of all students receiving financial aid to within 3% with 99% reliability, how many students would need to be sampled?

a) n = 1,844
b) n = 1,784
c) n = 1,503
d) n = 1,435

3. An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average income of $15,000. What sample size would the economist need to use for a 95% confidence interval if the width of the interval should not be more than $100?
a) n = 1537
b) n = 385
c) n = 40
d) n = 20

I need detail explanation.

Thanks.

Solution Summary

Answers to the questions with an explanation for each have been provided.

In order to determine the fuel efficiency for the Subaru Impreza the following information was gathered:
a) A random sample of 12 Imprezas were driven yielding the following miles per gallon (mpg).
25.1 24.6 22.5 27.8 26.1 21.0 23.9 28.4 24.4 23.5 26.2 20.7
Create a 95% confidence interval estimate

11. Product filling weights for a cereal manufacturer are normally distributed with a mean of 350 grams, a variance of 225 grams and a standard deviation of 15 grams.
a) Develop the control limits that would be used on the company's x-bar control charts of samples of sizes 10, 20, 30.
b) What happens to the control limits a

Suppose that, for a samplesize n = -100 measurements, we find that x = 50. Assuming that the standard deviation equals 2, calculate confidenceintervals for the population mean with the following confidence levels:
a) 95% b) 99% c) 97% d) 80% e) 99.73% f) 92%

Question: A sample of 119 golfers showed that their average score on a particular golf course was 93.54 with a standard deviation of 6.16.
Answer each of the following (show all work and state the final answer to at least two decimal places):
(A) Find the 98% confidence interval of the mean score for all 119 golfers.
(B)

A recent study indicated that 29% of the 100 women over age 55 in the study were widows.
a. How large a sample must one take to be 90% confident that the estimate is within 0.05 of the true proportion of women over ages 55 who are widows?
b. If no estimate of the sample proportion is available how large should the sample

The owner of Limp Pines Resort wanted to know the average age of its clients. A random sample of 25 tourists is taken. It shows a mean age of 46 years with a standard deviation of 5 years. The width of a 98 percent CI for the true mean client age is approximately ____ years. In a samplesize calculation for a mean, if the confid

2. Each of the following is a confidence interval for μ = true average (i.e., population mean) resonance frequency (Hz) for all tennis rackets of a certain type:
(114.4. 115.6) (114.1,115.9)
a. What is the value of the sample mean resonance frequency?
b. Both intervals were calculated from the same sample data. The confi

1) Eight chemical elements do not have isotopes (different forms of the same element having the same atomic number but different atomic weights). A random sample of 30 of the elements that do have isotopes showed a mean number of 19.63 isotopes per element and the population a standard deviation of 18.73.
Estimate the true

Why are estimations andconfidenceintervals important?
Do confidenceintervalsand estimation play a role in the selection of samplesize?
Please explain your answer.