Confidence interval for mean and standard deviation

3. in an effort to estimate the annual income for new graduates, data were collected from 500 new graduates over a one -year period. assume a population standard deviation of $500.

a) if the sample mean is $15,000, what is the 95% confidence interval for the population mean?

b) if the sample mean is $15,000, what is the 98% confidence interval for the population mean?

c) discuss what happens to the width of the confidence interval as confidence level is increased. does this seem reasonable? explain.

d) if the data were collected for a sample of 25 rather than 500, develop a 95% confidence interval for the population mean (assuming the population has a normal probability distribution).

e) discuss what happens to the width of the confidence interval as the sample size decreases. does this seem reasonable? explain.

Solution Summary

The solution provides step by step method for the calculation of confidence interval for mean . Formula for the calculation and Interpretations of the results are also included.

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The body mass index (BMI) for a sample of men and a sample of women are given below. Assume the samples are simple random samples obtained from populations with normal distributions.
[Please refer to the attachment for the data].
Construct an 80% confidenceinterval estimate of the standard deviation of BMIs for men.

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2. If each of the following is decreased but everything else remains the same, will a confidenceinterval become wider, will it become narrower, or wil

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a. 0.7 < o < 2.3
b. 0.9 < o < 1.5
c. 0.8 < o < 2.1
d. 0.8 < o < 1.9

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In a recent study of 51 eighth graders, the mean number of hours per week that they watched television 21.9. assume the standard deviation =5.8 hours.
If possible, find the 97% confidenceinterval of the mean. Interpret the meaning of this interval.
If the standard deviation is doubled to 11.6, what will be the effect on

Which of the following is not needed to be known to calculate a confidenceinterval?
a. standard deviation
b. sample size
c. mean
d. degree of confidence

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