Statistics / Mr. Hansen
4/19/2004


Check one:

                 Name: __________________________________
c Regular time (36 minutes)
c Extended time (54 minutes)

CFU on Chapters 13 and 14

Instructions and Scoring.

  • Show all work and answers on separate sheets.
  • Show as much work as time provides. Justify all steps except for algebraic simplification or area calculations. For full credit, you should show the details of s.e. and m.o.e. calculations to the extent possible.
  • You will not earn full credit for a correct answer without adequate justification, or a correct answer without correct notation.

 

 

 

 

1.

A women’s group has contracted with an independent research organization to gather evidence to support the notion that all men are slobs. To this end, they have analyzed the following data regarding education level and likelihood that men wash their hands after using the bathroom:

 

 

 

Education level

% of hand washers

 

 

 

below H.S.
H.S. diploma
some college
college graduate
some graduate sch.
postgraduate degree

44%
38%
36%
58%
48%
50%

 

 

 

 

(a)

Formulate a test for independence between education level and percentage of hand washing. Assume that the men used were a random sample and that there were 50 in each group. Raise your hand before you start punching buttons on your calculator.

 

 

(b)

Show the work for the calculation for the expected entry in the fourth row and first column.

 

 

(c)

Carry out the test, showing all steps and writing a conclusion.

 

2.

Researchers are interested in the relationship between time remaining to graduation and seniors’ happiness level, on a scale from 1 to 10. On a random sample of school days, the following data were gathered:

 

 

 

Time Left (Days)

Form VI Happiness Level

 

 

 

90
80
70
60
45
40
30
20
10
5

1
3.4
5
4.8
5.9
6.5
7.2
7
9.92
9.998

 

 

 

 

(a)

Describe the relationship between the variables, using words that indicate the context of the problem. Provide at least one diagram and at least one piece of quantitative evidence to support your claim.

 

 

(b)

Using time remaining as a predictor of happiness level, compute the slope of the line of best fit.

 

 

(c)

Interpret your answer to part (b) in the context of the problem, using words such as “time remaining” and “happiness level.” Your answer should make sense to someone who has studied little or no statistics.

 

 

(d)

Compute a 90% confidence interval for the slope requested in part (b).

 

 

(e)

Perform a significance test for the proposition that the true linear correlation coefficient is nonzero. Show all steps.