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# Confidence interval for mean

Please see attached. If you can help me with the details of the nine attached questions...with detailed formulas and solutions, I really would appreciate it.

1. Of 139 adults selected randomly from one town, 30 of them smoke.

a. Construct a 99% confidence interval for the true percentage of all adults in the town that smoke.
b. Construct a 95% confidence interval for the true percentage of all adults in the town that smoke.

2. The speeds (in mph) of the cars passing a certain checkpoint are measured by radar. The results for a random sample are shown below.

44.4 41.8 42.9 40.7 43.5 40.1 44.6 41.9
44.4 42.0 43.5 41.9 40.7 43.5 41.8

a. Find x-bar and s for this data set.
b. Construct a 90 percent confidence interval for the mean speed of cars passing this checkpoint. You may assume the speeds are normally distributed.

3. A random sample of the duration of 50 telephone calls handled by a local telephone company had a mean of 11.6 min and a standard deviation of 3.8 minutes. Find a 95% confidence interval for the true mean duration of calls handled by the company.

4. A parcel service selected a random sample of 17 packages in order to estimate the mean weight of all packages received by the service. The sample had a mean weight of 15.3 pounds and a standard deviation of 1.9 pounds. Find the 95% confidence interval for the true mean weight of all packages received by the parcel service. You may assume package weights are normally distributed.

5. When obtaining a confidence interval for a population mean in the case of a finite population of size N and a sample size n which is greater than 0.05N, the margin of error is multiplied by the following finite population correction factor:

a. Find the 95% confidence interval for the mean of 200 weights if a sample of 33 of those weights yields a mean of 147.7 pounds and a standard deviation of 26.7 pounds.
b. Assume the sample of 33 weights is selected from a population of 2000 weights. Would you use the same technique as in part a? Why or why not? (Base your decision and explanation on the criteria for using this correction factor that is given above.)

#### Solution Summary

The solution gives step by step procedure for the calculation of descriptive statistics and confidence interval.

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