Download Read and Classify the Following Problems

Math 12
Read and Classify the Following Problems:
What are you being asked for, what distribution will you use?
1. The Chetah and Lundra are two new sports cars. A random sample of 30 Cheetahs showed
average first-year maintenance costs to be $1578 with a standard deviation of $180. For the
Lundra, a random sample of 32 vehicles showed average first-year maintenance costs to be $1612
with a standard deviation of $185. Test the claim that there is no difference in the average firstyear maintenance costs for these two sports cars. Use α = 0.05.
2. A national restaurant guide has published an article stating that the mean cost of dinner out for a
party of two adults is $47.50 including the tip. A random sample of 20 parties of two adults
dining out had a mean bill x = $52.50 with a sample standard deviation s = $8.25. Does this data
indicate that the figure quoted in the restaurant guide is too low? Use a 1% significance level.
3. According to one newspaper article, 47% of the households receiving magazine sweepstakes
solicitations in the mail do not respond to them. An intensive TV campaign was aired for two
weeks prior to the mailing of the Fantastic Fantasy Sweepstakes offering. In a random sample of
300 households it was found that 153 responded to the sweepstakes mailing. Is this evidence that
the level of response to Fantastic Fantasy Sweepstakes was higher than 47%? Use α = 0.05.
4. Ralph Smith took a random sample of 400 homes in El Paso and found that the homes received
an average of 18.6 pieces of junk mail per week with a standard deviation of 5.2 pieces. Fine a
95% confidence interval for the mean number of pieces of junk mail received per week by El
Paso families.
5. A wildlife biologist is studying a population of fish in a lake. The biologist captured, tagged, and
released fish. One year later the biologist returned and captured 32 fish, of which 8 were tagged.
The following year the biologist captured 40 fish, of which 8 were tagged.
a) Test to see if the proportion of tagged fish in the lake is decreasing. Use a 5%
significance level.
b) If the proportion of tagged fish in the lake is decreasing, what could that be telling
you about the population of fish in the lake?
6. In a study regarding public opinion about national policy, a random sample of 40 people showed
that 25 agreed with national policy. How many more people should be included in the sample to
be 90% sure that the sample estimate is within 8 percentage points of the population proportion,
p?
Math 12
7. Entrance into Lanthrop Medical School is highly competitive, and the school administers its own
entrance exam. The admission board is considering having its applicants take a blood test to
determine if any applicant has taken a stimulant before the exam. One member of the board
suggested that they conduct an experiment to determine if a stimulant of a specified strength has
any effect on test performance. The board took a random sample of 5 applicants and had them
take the test. One week later, they called the 5 applicants back, gave them a stimulant of specified
strength and had them take an equivalent test. Here are the scores. The highest possible score is
500 points.
Applicant
Score AFTER stimulant
Score BEFORE stimulant
1
430
420
2
450
430
3
285
290
4
390
400
5
400
390
Using a 5% level of significance, test the hypothesis that applicants did better after taking the
stimulant.