Practice Midterm

Key to this Practice Midterm

Problem 1  Please answer the following True or False

To view a plethora of these problems, please go to the link below and check "Probability" and "Confidence Intervals and Z".

http://www.ltcconline.net/greenl/java/Statistics/TrueFalse/statsTrueFalse.html

Problem 2  Five percent of all university students are math majors. 

A.  If 80 randomly selected college students are surveyed, what is the exact probability that at least 6 of them will be math majors.

B.  Could you have used the normal distribution to approximate the binomial distribution for part A.

Problem 3

Your tire company's snow and mud tires have an average lifetime of 80,000 miles with a standard deviation of 10,000 miles.  Answer the following assuming the distribution is normal.

A.  If the current guarantee for the tires is 65,000 miles, about what percentage of the tires will wear out before the guarantee expires?

B.  You want to reconsider the guarantee so that about 98% last past the guarantee period.  What should you set as the guarantee period on your tires?

Problem 4

The Lake Tahoe Visitor's Authority has determined that 65% of the tourists who come to the Lake Tahoe area to go snowboarding are from the Bay area.  The Boarder Motel has all of its 35 rooms booked during this weekend.

A.  Use the normal distribution to estimate the probability that between 20 and 25 of the rooms host bay area visitors?

B.  Why is your estimate valid?

Problem 5

 Explain what the difference is between a sampling distribution and the distribution of a sample.

Problem 6

It is known that the mean number of houses a Trick-Or-Treater visits is 46 and the standard deviation is 8.  

A.  Assuming that the distribution is approximately normal, what is the probability that your seven year old neighbor will visit fewer than 42 houses on Halloween?

B.  25 children were randomly selected and observed.  What is the probability that their mean number of visits is between 48 and 55?

Problem 7

Do you favor allowing pilots to carry a gun in the cockpit?  74% of Americans are in favor of allowing pilots to carry a gun in the cockpit. 

A.  80 passengers board a plane heading toward New York.  What is the probability that the greater than 75% of them favor allowing the pilot to carry a gun?  Use the normal approximation to work this problem out.

B.  Is the normal approximation valid?  Explain.

Problem 8

The manager of Wasabi restaurant tallied the number of customers that he received over a 50 day period.  He found that the mean number per day for this period was 45 with a standard deviation of 8. 

A.  Construct a 95% confidence interval for the true mean. 

B.  Write a sentence that explains your findings.

C.  Explain what it means in the context of this study to be 95% confident.

D.  Was it necessary to make any assumptions about the underlying distribution of the population?  Explain.

Problem 9

Thirteen black bears in the Sierra Nevada Mountains were captured and released for a research project.  Their mean weight was found to be 320 pounds with a standard deviation of 23 pounds.  

A.  Determine a 95% confidence interval for the mean weight of black bears in the Sierra Nevada Mountains.

B.  Write a sentence that explains your findings.

C.  Explain what it means in the context of this study to be 95% confident.

D.  Was it necessary to make any assumptions about the underlying distribution of the population?  Explain.

Problem 10

A psychologist is doing research on blindly following orders.  200 volunteers were ordered to push a button that would inflict 50 volts of electricity into a laboratory animal.  35 of them refused to push the button.

A.  Construct a 90% confidence interval for the true proportion of people who will refuse to zap the animal.

B.  Write a sentence that explains your findings.

C.  Explain what it means in the context of this study to be 90% confident.

D.  Was it necessary to make any assumptions about the underlying distribution of the population?  Explain.

Problem 11

Nationally, 2% of the population carry a venereal disease.  You are interested in constructing a 95% confidence interval for the proprotion of carriers in the Tahoe Basin.  How many people will you need to test if you want a margin of error of  1%?

Problem 12

Your burger joint just sent out a coupon for fifty cent burgers.  Your research has shown that 20% of coupon bearing customers just purchase a burger resulting a a loss to your restaurant of $0.25, 30% of coupon bearing customers also purchase fries with their burger resulting in a profit of $.50, and the rest opt for the full meal of a burger fries and a drink resulting in a profit of $1.50. 

A.  Write down a probability distribution table for the indicated distribution.

B.  Find the expected value and standard deviation.

C.  Use  a complete sentence to interpret the expected value in the context of the question.

Problem 13

Thirteen males and fourteen females participated in a study of leg strength.  Right leg strength (in Newtons) was recorded for each participant resulting in the table below.  Is there a difference between strength in men and women?  Use a 5% level of significance.  Give the P-value and interpret what it means.  State any assumptions needed.

Problem 14

A study was done to see if Caucasians have a lower pass rate than Latinos in their statistics class.  192 Caucasians and 83 Latinos were considered.  135 of the Caucasians and 65 of the Latinos passed the course. 

A.  Conduct the appropriate hypothesis test and state your conclusion in the context of the problem using a 0.05 level of significance.

 B.  Find the appropriate 95% confidence interval and explain in a complete sentence what it means.

Problem 15

A biologist measured the muscle masses in grams of eight laboratory rats before and after putting them on a high protein diet to see if the mean muscle mass increases with high protein diet.  The results are shown in the table below.  Assume normal distributions.

Before	4	6	2	3	4	5	3	2
After	5	8	3	3	5	4	5	4

A.  What can be concluded at the 0.05 level of significance?

B.  Construct and interpret the appropriate 95% confidence interval.

Problem 16

The fifteen year survival rate for prostrate cancer is 76%.  A medical researcher has developed a new technique to treat prostrate cancer and has conducted a study on 250 randomly selected men with prostrate cancer who had this new very painful treatment.   Fifteen years after the treatment 210 of these men were still alive.  The researcher wants so find out of the treatment increases the survival rate.

A.  State the Null and Alternative Hypotheses.

B.  State the repercussions of a Type I error in the context of this study.

C.  State the repercussions of a Type II error in the context of this study.

D.  Sketch the Rejection Region with a level of significance of 0.05.

E.  Calculate the test statistic and P-value

F.  Use a complete sentence to state your results using a level of significance of 0.05 in the context of the question.

G.  The level of significance of 5% represents a probability.  State what this represents in the context of the study.

H.  The P-Value that you obtained represents a probability.  State what this represents in the context of the study.

Problem 17

Suppose the mean number of nights that Americans stay in hotels and motels per year is 7.9 and the standard deviation is 3.1.  A researcher wants to see if this number is different for people who live in South Lake Tahoe.  She surveys 12 randomly selected South Lake Tahoe residents.  Assume the underlying distribution is approximately normal.  The results of the survey are shown below:

   0, 2, 4, 5, 5, 7, 7, 8, 8, 9, 10, 14

Perform the relevant hypothesis test using a level of significance of 0.05 and state your conclusion in the context of the survey.

Problem 18

A study was done to determine if the average student get less than the average recommended daily amount of sleep of 8 hours.  The 35 randomly selected students surveyed received an average of 7.6 hours of sleep and their standard deviation was 1.7 hours.  Conduct the relevant hypothesis test using a level of significance of 0.10 and state your conclusion in the context of the survey.

Problem 19  

Twenty students were asked how far they travelled each day to get to the college.  Nineteen of the students all traveled between 0 and 7 miles, but one student lived in Sacramento and traveled 100 miles each day. 

A.  Which of the following would be changed significantly if the student from Sacramento had not been surveyed:  mean, median, mode, standard deviation, variance?

B.  Suppose that the student from Sacramento had not been surveyed and that the mean was calculated to be 3.2 and the standard deviation was 0.9.  Use a sentence or two to interpret the standard deviation  in the context of the study.