statistics 3230632 2
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1. (10 points) A random pool of 1200 loan applicants, attending fouryear 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 dualenergy Xray 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 Pvalue. H_{o}: 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 Pvalue if H_{a}: μ > 25?
c) What is the Pvalue if H_{a}: μ≠25?
4. (10 points) A driver recorded the mpg by dividing the miles driven by the number of gallons at each fillup. 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 H_{o }and H_{a} to test.
b) Calculate the test. Give the Pvalue, 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 H_{o} and H_{a}.
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 onesided or twosided 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 pvalue 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 pvalue. 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 wakinglife symptoms?
b. What percent if the students have both wakinglife and bedtime symptoms?
c. Test whether there is an association between wakinglife and bedtime symptoms. State the null and alternative hypotheses, the Χ^{2} statistic, and the pvalue.
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