Solve the below:
Q1. 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.
Q2. 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.
Q3. 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.
Q4. 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.
Q5. 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:
√(N-n/N-1)
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?