Project #30335 - Statistics Assignment

1. We intend to estimate the average driving time of a group of commuters.  From a previous study, we believe that the average time is 42 minutes with a standard deviation of 12 minutes.  We want our 99 percent confidence interval to have a margin of error of no more than plus or minus 3 minutes.  What is the smallest sample size that we should consider?

2. A hotel chain wants to estimate the average number of rooms rented daily in each month.  The population of rooms rented daily is assumed to be normally distributed with a standard deviation of 24 rooms for each.  During January, a sample of 36 days has a sample mean of 48 rooms.  Compute confidence interval estimates for the population mean with a 97.5% confidence levels.

3. Forty students are enrolled in and Economics class.  After the first examination a random sample of 5 papers was selected with grades of 60, 75, 80, 70, and 90.  Calculate a 92.5% confidence interval estimate for the population mean.

4. Suppose a brewery has a filling machine that fills 12 ounce bottles of beer.  It is known that the amount of beer poured by this filling machine follows a normal distribution with a mean of 12.44 ounces and a standard deviation of 0.06 ounces.  Find the probability that a sample of 36 of the bottles has a mean that: a) exceeds 12.46 ounces   b) is between 12.42 and 12.46 ounces   c) is less than 12.45 ounces

5.  A sample of 50 days last winter yielded an occupancy rate of 60%.  Find the 4% confidence interval estimate for the true occupancy rate last winter.

6. A local radio station wantes to estimate the proportion of people in a target market who have a favorable impression of its morning show.  THe marketing department wishes to estimate this proportion within .03 of the true population value with a confidence level of 92.5%.  The best estimate for this population proportion is between .42 and .48.  How many people should be sampled?

7. A 90% confidence interval for the mean percentage of airline reservations being cancelled on the day of the flight is (1.3%, 5%).  What is the point estimator of the mean percentage of reservations that are cancelled on the day of the flight?

8. A retired statistician was interested in determining the average cost of a $200,000.00 term life insurance policy for a 60-year-old male non-smoker.  He randomly sampled 65 subjects (60-year-old male non-smokers) and constructed the following 95 percent confidence interval for the mean cost of the term life insurance: ($850.00, $1,050.00).  What value of alpha was used to create this confidence interval?

9. A marketing research company is estimating which of two soft drinks college students prefer.  A random sample of 157 college students produced the following confidence interval for the proportion of college students who prefer drink .344-.494.  Is this a large enough sample for this analysis to work?

10.  A random sample of 50 employees of a large company was asked the question, "Do you participate in the company's stock purchase plan?"  The answer are shown below:

yes-32  no-18

What is the point estimate for the population proportion of employees who participate in the company's stock purchase plan?

11. The following information gives the number of days absent from work last year for a population of 5 workers at a small factory.

Worker 'A' absent 5 days, Worker 'B; absent 7 days, Worker 'C' absent 1 day, Worker 'D' absent 4 days, Worker 'E' absent 8 days.

a. Derive the sampling distribution for the sample mean for samples of size 2.

b. Calculate the mean , variance, and standard error of the sampling distribution of the sample mean that you derived.

c. Show that the mean of the sampling distribution that you derived equals the population mean.

Subject Mathematics
Due By (Pacific Time) 5/7 11pm
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