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 independence.

xiii)  Chi squared test for goodness of fit.

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

Solution

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.

Solution

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.

Solution

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

Solution

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.

Solution

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.

Solution

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.

Solution

Problem 2  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, 50 Hispanics, 30 African Americans, and 20 classified as other.  Below is a table that shows the number of employees that were promoted last year.

 Caucasian Hispanic African American Other 50 6 3 1

what can be concluded at the 5% level?

Solution

Problem 3  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.

 TD FD HB A 0.32 0.27 0.18 M 0.08 0.04 0.11

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?

Solution

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

Solution

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

Solution

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

Solution

Problem 4  You want to construct a confidence interval for the percent of registered voters who are planning on voting for George Bush for president for his second term.  You want to have a margin of error of 0.03.

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

Solution

B.  Suppose that you conducted this survey (as in part A) and found that 52% of the respondents intended to vote for George Bush. Construct the appropriate 90% confidence interval.  Interpret this interval.  How would the Bush campaign react to this confidence interval?

Solution

Problem 5  For the following please answer true or false.  If true explain why.  If false explain why or provide a counter example.

A.  To provide a confidence interval for a population proportion, if the sample size is 18, it is appropriate to use a t-statistic since the z-statistic is used only for large samples.

Solution

B.  For a large sample, of the mean, the median, and the standard deviation, only two of these will be highly affected by an addition of an extreme outlier.

Solution

C.  No matter how the population data is distributed, the distribution of all possible samples of size 500 will be approximately normal with approximately the same mean and standard deviation as the population mean and standard deviation.

Solution

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.

Solution

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

Solution

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

Solution

D.  What is the mode?

Solution

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

Solution

Problem 8

A study was done to see the relationship between the type of town and the quality of service.  An index was used with 100 meaning average service and larger numbers above average.  The table below displays the results of the survey.

 Police Fire Department Libraries Schools Urban 110 115 140 82 Rural 132 128 130 84 Suburban 95 102 118 92
1. List the factors and the number of levels of each factor.
Solution

2. Assume that there is no interaction between the factors.  Determine if there is a difference in population mean index based on town type.  Use a level of significance of 0.05.  Make sure you state the null and alternative hypothesis and state your conclusions using a complete sentence in the context of the question.
Solution

3. Determine if there is a difference in population mean index bases on public service.  Use a level of significance of 0.05.Make sure you state the null and alternative hypothesis and state your conclusions using a complete sentence in the context of the question.
Solution

 Treatment Variation Block Variation Within Variation Total Variation Treatment Statistic Its P-Value Block Statistic Its P-Value