# Basic statistics and hypothesis testing using Minitab

Please see the attachment.

Instructions:

? Follow the directions for each problem.

? Use Minitab for all the calculations.

? The data set is available in contents page of D2L in the Final Exam module called fall 2009.MTW.

? Label each printout of your Minitab session according to the problem and part of that problem.

? Use a separate sheet for each problem. Staple the sheets together in order with a coversheet that has your name and discussion section.

? Answer all the questions thoroughly, hand in both the answers to the questions and the Minitab printouts. You can cut and paste the Minitab output into Word if so desired.

? If there are any questions do not hesitate to ask your TA or instructor.

? This is to be your own work.

? Total possible points 50.

Problem 1: (10 points) The data is in the worksheet fall 2009.MTW. This worksheet contains the list Price, number of bedrooms (Bed), number of bathrooms (Bath), size (Sq Feet) and City that the house is in (Milwaukee or Madison) from a simple random sample of houses that are for sale.

a) What is the population? Be specific.

b) Construct a histogram of the square feet of these houses. Under binning tab for editing X-axis, use the cutpoint as the interval type, and use 10 classes (number of intervals) What "shape" is this histogram?

c) Give the mean, standard deviation, median, Q1 and Q3 for the square feet from this sample.

Problem 2: (5 points) Use the worksheet fall 2009.MTW. We want to estimate the mean list price of a home for sale.

a) Estimate the mean list price of all houses that are for sale in Milwaukee and Madison. Use a 99% confidence interval.

b) Interpret the 99% confidence interval found in part a.

Problem 3: (20 points) Again use the worksheet fall 2009.MTW. Is the mean list price for houses in Milwaukee less than the mean list price of houses in Madison? To answer this question we will construct a confidence interval and hypothesis test.

a) Find the sample mean list price for the houses that are for sale in Milwaukee and Madison separately. Hint: We want to determine the sample mean by the categorical variable City.

b) Create a boxplot of the list price by city. Give any similarities or differences to the list price between the two cities.

c) Determine a 98% confidence for the difference in the mean list price of homes for sale in Milwaukee and homes for sale in Madison. Use city as the subscript.

d) Let Madison be population 1 and Milwaukee be population 2. Test if mean list price for houses in Madison is greater than the mean list price of houses in Milwaukee. Give the null and alternative hypothesis, p-value, decision of the test and conclusion. Use a =0.05.

Problem 4: (15 points) Use the worksheet fall 2009.MTW. In most real estate markets the price of the home is directly related to the size of the house. We want to use the size of a house to predict the price of a home.

a) Give a scatterplot of price (y-axis) and square feet (x-axis). Describe the relationship between price and size by describing the form, direction and scatter of this scatterplot.

b) Determine the correlation between list price and size (sq feet).

c) Determine the simple linear regression line to predict list price by size (sq feet) of a house.

d) Using the regression equation, predict the list price of a home that has a size of 2,400 sq. feet.

e) What percent of variation in list price can be explained by this regression equation?

https://brainmass.com/statistics/hypothesis-testing/basic-statistics-and-hypothesis-testing-using-minitab-287163

#### Solution Summary

The solution provides step by step method for the calculation of Basic statistics and hypothesis testing using Minitab . Formula for the calculation and Interpretations of the results are also included.

10 problems on Confidence Intervals solved using MINITAB

1. An environmental group at a local college is conducting independent tests to determine the distance a particular make of automobile will travel while consuming only 1 gallon of gas. A sample of five cars is tested and a mean of 28.2 miles is obtained. Assuming that the standard deviation is 2.7 miles, find the 95% confidence interval for the mean distance traveled by all such cars using 1 gallon of gas.

[26.16 30.24]

[20.70 35.70]

[24.85 31.55]

[26.70 29.70]

[25.83 30.57]

2. A random sample of size 30 from a normal population yields a mean of 32.8 with a population standard deviation of 4.51. Construct a 95 percent confidence interval for the mean.

[23.96 41.64]

[32.04 33.56]

[31.45 34.15]

[31.19 34.41]

3. In a manufacturing process a random sample of 36 bolts manufactured has a mean length of 3 inches with a standard deviation of .3 inches. What is the 99% confidence interval for the true mean length of the bolt?

2.902 to 3.098

2.884 to 3.117

2.865 to 3.136

2.228 to 3.772

2.465 to 3.205

4. A federal bank examiner is interested in estimating the mean outstanding defaulted loans balance of all defaulted loans over the last three years. A random sample of 20 defaulted loans yielded a mean of $67,918 with a standard deviation of $16,552.40. Calculate a 90% confidence interval for the mean balance of defaulted loans over the past three years.

[66,487 69,349]

[39,299 96,537]

[57,329 78,507]

[61,829 74,007]

[61,519 74,317]

5. Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to estimate its average number of unoccupied seats per flight over the past year. 225 flight records are randomly selected and the number of unoccupied seats is noted with a sample mean of 11.6 seats and a standard deviation of 4.1 seats. How many flights should we select if we wish to estimate margin of error to within 2 seats and be 95% confident?

130

65

33

17

12

6. The coffee/soup machine at the local bus station is supposed to fill cups with 6 ounces of soup. Ten cups of soup are brought with results of a mean of 5.93 ounces and a standard deviation of 0.13 ounces. How large a sample of soups would we need to be 95% confident that the sample mean is within 0.03 ounces of the population mean?

97

96

73

62

10

7. Recently, a case of food poisoning was traced to a particular restaurant chain. The source was identified and corrective actions were taken to make sure that the food poisoning would not reoccur. Despite the response from the restaurant chain, many consumers refused to visit the restaurant for some time after the event. A survey was conducted three months after the food poisoning occurred with a sample of 319 patrons contacted. Of the 319 contacted, 29 indicated that they would not go back to the restaurant because of the potential for food poisoning Construct a 95% confidence interval for the true proportion of the market who still refuse to visit any of the restaurants in the chain three months after the event.

[.059 .122]

[.090 .091]

[.000 .196]

[.240 .339]

[.118 .244]

8. The Ohio Department of Agriculture tested 203 fuel samples across the state in 1999 for accuracy of the reported octane level. For premium grade, 14 out of 105 samples failed (they didn't meet ASTM specification and the FTC Octane posting rule). Find a 99% confidence interval for the true population proportion of premium grade fuel-quality failures.

[.045 .221]

[.068 .198]

[.023 .115]

[.048 .219]

[.100 .276]

9. Recently, a case of food poisoning was traced to a particular restaurant chain. The source was identified and corrective actions were taken to make sure that the food poisoning would not reoccur. Despite the response from the restaurant chain, many consumers refused to visit the restaurant for some time after the event. A survey was conducted three months after the food poisoning occurred with a sample of 319 patrons contacted. Of the 319 contacted, 29 indicated that they would not go back to the restaurant because of the potential for food poisoning. What sample size would be needed in order to be 99% confident that the sample proportion is within .02 of the true proportion of customers who refuse to go back to the restaurant?

14

38

129

1,371

1,777

10. The Ohio Department of Agriculture tested 203 fuel samples across the state in 1999 for accuracy of the reported octane level. For premium grade, 14 out of 105 samples failed (they didn't meet ASTM specification and the FTC Octane posting rule). How many samples would be needed to create a 99% confidence interval that is within 0.02 of the true proportion of premium grade fuel-quality failures?

4148

2838

1913

744

54