Math 201 Practice Final

Please work out each of the given problems. Credit will be based on the steps that you show towards the final answer.  Show your work. 

Printable Key

Problem 1

Match the following hypotheses and estimates with the appropriate test statistic or confidence interval.  Explain your reasoning.

i)  A confidence interval for a population mean.

ii)  A confidence interval for a population proportion.

iii)  A confidence interval for the difference between two independent population means

iv)  A confidence interval for the difference between two population proportions.

v)  A confidence interval for paired differences (dependent samples).

vi)  A confidence interval for the value of y given a value of x using a regression line.

vii)  A hypothesis test for a population mean.

viii)  A hypothesis test for a population proportion.

ix)  A hypothesis test for the difference between two independent population means

x)  A hypothesis test for the difference between two population proportions.

xi)  A hypothesis test for paired differences (dependent samples).

xii)  Chi squared test for goodness of fit.

xiii)  Chi squared test for independence.

xiv)  Chi squared test for homogeneity

xv) 1-Way ANOVA

A.  Are automobile prices higher in South Lake Tahoe then in Sacramento.  Fifty Subaru Legacy's from the South Tahoe dealership and fifty from the Sacramento dealership were sold last month and recorded

B.  Does the color of the paper used for a final exam influence performance? 200 students were randomly given the same test on blue, red, and white paper.  The number of  A's, B's, C's, D's and F's for each color were tabulated.

C.  Is honey a better medicine for small wounds than conventional salves?  Currently 9% of the wounds that are treated with conventional salves end up infected.  150 wounds in a study group were treated with honey.

D.  How much of the food that you buy ends up being thrown out?  A refrigerator was monitored that had 45 perishable items.

E.  How long can you expect to live if your cholesterol level is 230?  Data has been taken from 45,000 people with varying levels of cholesterol.

F.  How much better has the NASDAQ done than the Dow Jones Industrial Average this year?  The daily point gains and losses have been charted since January 2.

G.  What are the low and high estimates for the number of Kokanee salmon that will run in Trout Creek this fall?  Data has been collected over the last forty years.

For additional practice go to:

http://www.ltcconline.net/greenl/java/Statistics/catStatProb/categorizingStatProblemsJavaScript.html

Problem 2  Answer the following True or False.  For practice on this go to the following link and make sure all categories are checked.

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

Problem 3  Your business is being investigated about unfair promotion practices with regard to race.  Your policy is to promote 20% of your employees.  Your current staff consists of 200 Caucasians, 45 Hispanics, 30 African Americans, and 25 classified as other.  Below is a table that shows the number of employees that were promoted last year.

what can be concluded at the 5% level?

Problem 4  A certain model of car comes in a two-door version, a four door version, and a hatchback version.  Each version can be equipped with either an automatic transmission or a manual transmission.  The accompanying table gives the relevant proportions.

A customer who has purchased one of these cars is randomly selected.

A.  What is the probability that the customer purchased a car with an automatic transmission?  A four-door car?

B.  Given that the customer purchased a four door car, what is the probability that it has an automatic transmission?

C. Given that the customer did not purchase a hatchback, what is the probability that the car has a manual transmission?

D.  If 8 cars were sold, where is the probability that exactly 6 of them were two doors with automatic transmission?

Problem 5  You want to construct a confidence interval for the percent of registered voters who are planning on voting for the latest environmental bill.  You want to have a margin of error of  0.03.  

A.  How many registered voters should you survey (use a  =  0.05)?

B.  Suppose that you conducted this survey (as in part A) and found that 52% of the respondents intended to vote for the latest environmental bill. Construct the appropriate 90% confidence interval.  Interpret this interval.  How would the Sierra Club respond to this confidence interval?

Problem 6  Data was collected to study the effect of alcohol on reaction time.  Forty participants were given various amounts of alcohol and then took a test to see how many milliseconds it took to press a button upon seeing headlights.  The scatter diagram is shown below.

A.  Given an approximate equation of the regression line.  Interpret the slope and the y-intercept.

Solution

B.  Give an approximation of the correlation coefficient.  Explain using a complete sentence why you chose this number.

Solution

Problem 7

Twenty-five students took the first midterm exam.  The number of minutes that they each took are shown below.

35, 45, 48, 50, 50, 52, 60, 61, 64, 70, 72, 75, 78, 78, 81, 83, 84, 87, 88, 88, 89, 90, 90, 90, 90

A.  Construct a stem and leaf diagram for this data.

B.  Construct a histogram for this data using 5 classes.

C. You took one hour to complete the exam.  What is your percentile?

D.  What is the mode?

E.  If the student who took 35 minutes for the exam is disregarded, would the standard deviation decrease, increase, or stay the same.  Explain.

Problem 8

A researcher is interested in finding out if there is a difference between the mean weights of female Freshmen, Sophomores, Juniors, and Seniors at the university level.  The table below shows the results of a survey that was taken.  What can be concluded at the 0.05 level of significance?  What assumptions must be made in order to conduct this hypothesis test?

 Problem 9

A study was done to see if men are more likely than women to purchase at least one item when they go to the mall.  92 of the 120 men in the study purchased an item and 174 of the 260 women in the study purchased an item. 

A.  Conduct the appropriate hypothesis test and state your conclusion using a complete sentence using a level of significance of 0.10.

B.  The P-Value represents a probability.  Interpret this probability in the context of the problem.

C.  The level of significance represents a probability.  Interpret this probability in the context of the problem.

D.  Was it appropriate to use the normal distribution for your calculations?  Explain.

Problem 10

You decide to conduct a study asking 500 college students how many times a month they use the cafeteria. 

A.  Is the variable quantitative or qualitative?

B.  Describe how you would select your participants if you wanted to use the method of cluster sampling.

C.  Suppose you know that the distribution is approximately normal and the mean was 12.1 and the standard deviation was 3.5.  What does the Empirical rule tell you about one standard deviation from the mean?