I am currently studying probability and am having a bit of trouble with the following questions. Can you help me? If you can, thank you very much. The questions are:

1.) An office manager wishes to estimate the mean time required to handle customer complaints. A sample of 38 complaints shows a mean time of 28.7 minutes with a standard deviation of 12 minutes.

a) Construct a 90% confidence interval for the true mean time required to handle customer complaints.
b) How large a sample should be taken, if the manager wishes to estimate the mean time to handle a complaint to within +/- one minute? Assume that the confidence interval is to be 90%.

2.) A hospital claims that the average length of stay is 5 days. A study of the length of stay for a random sample of 25 patients found the mean stay to be 6.2 days with a standard deviation of 1.2 days. Do these data present sufficient evidence to support the hospital's claim? Use a 0.05 significance level.

3.) A survey was conducted to determine the proportion of registered nurses in a particular state that are actively employed. A random sample of 400 nurses selected from the state registry showed 274 actively employed. Find a 95% confidence interval estimate for the true proportion of registered nurses actively employed in the state.
Thanks.

Solution Preview

1. In part b of the first question, the 90% confidence limits are given by:

Suppose that 55 percent of the people in a population of 500,000 support your candidate. If you conduct a poll of 1,000 people, what is the interval that has a 95 percent chance of containing the results of your poll?
Suppose you have 60 red marbles and 40 blue marbles in a box. If you pick out 10 marbles without replacemen

Suppose that, for a sample size 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%

1. Why are confidenceintervals useful?
2. You and a colleague conducted a study on grocery totals for shoppers in the State of Michigan. Your estimated grocery totals at CI 95%: ($78, $98). In writing the report, your colleague stated: "There is a 95% chance that the true value of µ will fall between $78 and $98.
a.

ConfidenceIntervals for the Mean (Large Samples)
Find the critical value zc necessary to form a confidence interval at the given level of confidence. (References: definition for level of confidence
a. 95%=
b. 75%=

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

What is the probability of P(-1.4 < Z < 0.6)?
In a standard normal distribution, what is the area which lies between Z = -1.72 and
Z = 2.53?
Use the following information to conduct the confidenceintervals specified to estimate μ.
95% confidence; X ̅=25, σ^2= 12.25, and n=60.
30% confidence; X ̅=119.6,

7.11 A simple random sample of n = 300 full-time
employees is selected from a company list containing the
names of all, N = 5,000 full-time employees in order to
evaluate job satisfaction.
a. Give an example of possible coverage error.
b. Give an example of possible nonresponse error.
c. Give an example of possible samplin