Statistics / Mr. Hansen
4/20/2004


Check one:

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

Test 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.

The owner of a bakery claims that her loaves have weight that is normally distributed with mean 16.2 oz. and s.d. 0.8 oz.

 

 

(a)

Assuming that this is true, fill in the following chart for an SRS of 250 loaves. Give all answers to 3 decimal places, and verify that the percentages add to 100% except for possible rounding errors.

 

 

 

Weight

% expected (probability)

Number of loaves expected

 

less than 15 oz.
15.0 to 15.5 oz.
15.5 to 16 oz.
16 to 16.5 oz.
16.5 to 17 oz.
more than 17 oz.

______ %
______ %
______ %
______ %
______ %
______ %

______
______
______
______
______
______

 

 

(b)

What do the expected number of loaves add up to?

 

 

(c)

Here are some observations for the SRS of 250 loaves.

 

 

 

 

Weight

Observed frequency

 

 

less than 15 oz.
15.0 to 15.5 oz.
15.5 to 16 oz.
16 to 16.5 oz.
16.5 to 17 oz.
more than 17 oz.

8%
12%
20%
26%
20%
14%

 

 

 

 

 

Conduct a goodness-of-fit test, showing all steps. Is there evidence to refute the baker’s initial claim?

 

2.

Researchers are interested in the relationship between GPA and time spent playing video games for students at Bali High School. Specifically, they wish to know whether video gaming time can be used as a predictor of GPA. The following data came from an SRS of students:

 

 

 

 

GPA

Video Gaming Time (Hrs./Wk.)

 

 

 

2.4
2.6
2.6
2.85
3.0
3.3
3.45
3.7
3.9

6
5
7.5
9
9.5
8
10.2
10.4
11

 

 

 

 

 

(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 video game time as a predictor of GPA, state the line of best fit as a mathematical model in which variables are defined.

 

 

(c)

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

 

 

(d)

Compute a 95% confidence interval for the slope of the linear regression model.

 

 

(e)

Perform a significance test for the proposition that the true slope is positive. Show all steps.