Statistics

profiled-mac 71

 

1.  (10 points) A random pool of 1200 loan applicants, attending four-year public or private colleges and universities was analyzed.  The sample of applicants carried an average credit card balance of $3173.  The median balance was $1645 so this distribution is skewed but because our sample size is quite large, we can rely on the central limit theorem to assure us that the confidence interval based on the normal distribution.  Assume the standard deviation for the population is $3500.  Compute a 95% confidence interval for the true mean credit card balance among all undergraduate loan applicants.

 

2. (5 points)  A dual-energy X-ray absorptiometry (DXA) scanner is used measure bone mineral density for people who may be at risk for osteoporosis.  To ensure its accuracy, the company uses an object called a “phantom” that has known mineral density μ=1.4 grams per square centimeter.  Once installed, the company scans the phantom 10 times and compares the sample mean reading with the theoretical mean μ using a significance test.  State the null and alternative hypotheses for this test.

 

3.  (10 points) Compute the test statistic and P-value.  Ho: μ=25 base on a random sample of n=36.  Assume σ=5.

a) If Xbar (mean) = 27, what is the test statistic z?

b) What is the P-value if Ha: μ > 25?

c) What is the P-value if Ha: μ≠25?   

 

4.  (10 points) A driver recorded the mpg by dividing the miles driven by the number of gallons at each fill-up.  The following data are the differences between the computer’s and the driver’s calculations for a random sample of 20 records.  The driver wants to determine if these calculations are different.  Assume the standard deviation of a difference to be σ= 3.0. 

5.0

6.5

-0.6

1.7

3.7

4.5

8.0

2.2

4.9

3.0

4.4

0.1

3.0

1.1

1.1

5.0

2.1

3.7

-0.6

-4.2

a) State the appropriate Ho and Ha to test.

b) Calculate the test.  Give the P-value, and then interpret the result in plain language.

 

5.  (10 points) According to data from the Tobacco Institute testing Laboratory, Camel Lights king size cigarettes contain an average of 0.9 milligrams of nicotine.  An advocacy group commissions an independent test to see if the mean nicotine content is higher than the industry laboratory claims.

a) State the appropriate Ho and Ha.

b) Suppose that the test statistic is z=1.83.  Is the result significant at the 5% level?

c) Is the result significant at the 1% level?

 

 

 

 

 

 

 

6. (15 points)   You want to compare the daily number hits for two different MySpace page designs that advertise your band.  You assign the next 30 days to either design A or design B, 15 days to each.

a) Would you use a one-sided or two-sided significance test for this study?  Explain your choice.

b) If you use a table to fine the critical value, what are the degrees of freedom using the second approximation?

c)  If you perform the significance test using α=0.05, how large (positive or negative) must the t statistic be to reject the null hypothesis that the two designs result in the same average hits?

d) If the t statistic =2.45, what p-value would you report? 

e)  What would you conclude using α=0.05?

 

7.  (20 points) The “misery is not miserly” phenomenon refers to a person’s spending judgment going haywire when sad.  In a recent study, 31 young adults were given $10 and randomly assigned to either a sad or neutral group.  The participants in the sad group watched sad movie and those in the neutral group watched a video on the Great Barrier Reef.  After the video, each participant was offered the chance to trade $0.50 increments of the $10 for an insulated water bottle.  Data is listed below.

Group

Price

Group

Price

S

1.00

N

0.00

S

2.50

N

1.00

S

3.00

N

2.00

S

4.00

N

0.00

S

1.00

N

0.00

S

1.50

N

0.00

S

4.00

N

1.00

S

1.00

N

2.00

S

1.50

N

0.00

S

3.50

N

0.00

S

0.50

N

0.50

S

3.00

N

1.00

S

1.50

N

0.00

S

2.00

N

0.50

S

0.00

 

 

S

3.50

 

S

2.50

 

 

a) Make a table with sample size, mean, and

standard deviation for each of the two groups.

b) State the appropriate null and alternative

hypothesis for comparing these two groups.

c) Perform the significance test at the α = 0.05

level, making sure to report the test statistic,

degrees of freedom, and p-value.  What is your

conclusion?

d) construct a 95% confidence interval for the

mean difference in purchase price between the

two groups.

 

8. (20 points) As part of the study on ongoing fright symptoms due to exposure to horror movies at a young age, the following table was presented to describe the lasting impact these movies have had during bedtime and waking life: 

 

Bedtime

Waking

Count

Yes

Yes

36

Yes

No

33

No

Yes

33

No

No

17

a. What percent of the students have lasting waking-life symptoms?

b. What percent if the students have both waking-life and bedtime symptoms?

 

c. Test whether there is an association between waking-life and bedtime symptoms.  State the null and alternative hypotheses, the Χ2 statistic, and the p-value.

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