Maths Assignment Fall 2015

| August 30, 2017

Question

Read questions and follow all directions carefully. Show work in a clear and logical format. Use examples from the posted lecture notes as a guide for expected answer format. No credit will be given for illegible work or answers. Round all answers to the hundredths place. You may use technology for computational purposes and when doing so do not also need to show work by hand for that particular calculation. If you are using technology, it would be beneficial to indicate which functions are being used and what values were entered. No partial credit will be given for wrong answers that do not have any supportive work.

1. According to the manufacturer of M&M’s, 13% of the plain M&M’s in a bag should be brown, 14% yellow, 13% red, 24% blue, 20% orange, and 16% green. A student randomly selected a bag of plain M&M’s and counted the number of each color yielding the data in the following table. Test whether plain M&M’s follow the stated distribution at a 0.05 level of significance. You may perform the test using either the Classical Approach or the P-Value Approach. SHOW ALL SIX STEPS OF THE TEST CLEARLY!

Color

Frequency

Brown

61

Yellow

64

Red

54

Blue

61

Orange

96

Green

64

2. The following data represent the smoking status by level of education for residents of the United States 18 years old or older from a random sample of 936 residents. Test whether smoking status and level of education are independent using a 1% level of significance. You may perform the test using either the Classical Approach or the P-Value Approach. SHOW ALL SIX STEPS OF THE TEST CLEARLY!

Smoking

Status

Years of Education

Current

Former

Never

Less than 12

178

88

208

12

137

69

143

13 – 15

44

25

44

3. An environmentalist wanted to determine if the mean acidity (as measured by pH level) of rain differed between Alaska, Florida, and Texas. A random sample of six rain dates at each of the three locations yielded the following data.

a) Test the hypothesis that at least one of the mean acidity levels is different than the others using a 5% level of significance. You may perform the test using either the Classical Approach or the P-Value Approach. SHOW ALL SIX STEPS OF THE TEST CLEARLY!

Alaska

Florida

Texas

5.41

4.87

5.46

5.39

5.18

6.29

4.90

4.40

5.57

5.14

5.12

5.15

4.80

4.89

5.45

5.24

5.06

5.30

b) Use Tukey’s test to determine which pairwise means differ using a familywise error rate of 5%. Test all possible combinations.

4. An economist wants to determine the relationship between one’s FICO credit score (x) and the interest rate of a 36-month auto loan (y). A random sample of six auto loans yielded the following data.

Credit Score (x)

Interest Rate Percent (y)

545

18.982

595

17.967

640

12.218

675

8.612

705

6.680

750

5.150

a) Construct the least-squares regression line for the relationship between credit score and auto loan interest rate. Write your answer in the proper form and using appropriate notation.

b) Test the hypothesis that there is a negative linear relationship between credit score and auto loan interest rate. Use a 5% level of significance. You may perform the test using either the Classical Approach or the P-Value Approach. SHOW ALL SIX STEPS OF THE TEST CLEARLY!

c) Construct and interpret a 95% confidence interval for the slope of the true least-squares regression line.

d) Construct and interpret a 95% confidence interval for the mean auto loan interest rate for a FICO credit score of 600.

e) Construct and interpret a 95% prediction interval for the predicte

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