Math 201 Practice Midterm 3

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

Go to the link below and practice the True or False applet.  Be sure to check "Hypothesis Testing", "Regression Analysis", "Chi-Square", and "ANOVA".

http://www.ltcconline.net/greenl/java/Statistics/TrueFalse/statTrueFalseWithChoices2.html

 

Problem 2

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.

Gender n x s
Male 13 2127 513
Female 14 1643 446

Solution

Problem 3

Is one ski resort better than another?  Data was collected to determine whether the ski resort that was visited had a bearing on how much enjoyment the skier had.  The following table shows the data that was collected.  What can you conclude at the 5% level?  

Bored Had an OK time Had a Great Time The Best Experience Ever
Heavenly 7 25 42 4
Sierra-at-Tahoe 5 20 30 1
Kirkwood 9 12 30 15

Solution

Problem 4

You are the owner of an automobile dealership and have done research on the relationship between the cost of the clothes (x) that a potential buyer wears and the price of the car (y) that the person will buy.  The data below gives the data that you have collected.

Clothes ($) 35 45 60 80 95 120 140 150
Car (in $1000) 15 18 14 22 25 33 30 75

 

A.  Find the equation of the regression line.

B.  A man walks into your dealership sporting a $100 outfit.  What is your prediction for the price of the car that this man will buy?

C.  Interpret the slope in the context of the study.

D.  Interpret the y-intercept if applicable.  If not, explain why it does not have meaning.

E.  Find the correlation.

F.  Find r2 and give its interpretation in terms of explained variation in the the context of the question.

G.  Conduct the appropriate hypothesis test to see if there is a correlation and interpret your results using a complete sentence.

H.  What assumptions are needed for the test from part G?

 

 

Problem 5

You are the owner of the Tahoe Inn Motel and are interested in how the price per room is related to the number of units that are occupied.  Below is the StatCrunch readout produced from motels throughout the Tahoe area.  

A.  What is the equation of the regression line?  Interpret the slope of the regression line for this study.  Interpret the y-intercept.

B.  Use your regression line to provide a point estimate for the number of units occupied when the price per room is $100.

C.  Construct a possible scatter plot for this data and explain using a complete sentence or two your reasoning in constructing the scatter plot the way you did it.


Simple linear regression results:
Dependent Variable: Units
Independent Variable: Price

Sample size: 26
Correlation coefficient: -0.69
Estimate of sigma: 20.581867

 

Parameter Estimate Std. Err. DF T-Stat P-Value
Intercept 91.39109 6.9450126 24 13.159241 <0.0001
Slope -0.5198245 0.111319035 24 -4.669682 <0.0001


 

Problem 6

You are interested in seeing whether the soil quality in the Tahoe Basin has changed since 1970.  Soil samples were taken then and this year.  The table below shows the results of this study.

Good Fair Poor Very Poor
1970 45 80 36 50
This Year 30 40 60 75

What can be concluded at the 0.05 level of significance?

 

Problem 7

The percent of community college students in California by their main goals is given in the table below
Goal Transfer Job Skills Personal development Improve Basic Skills Certification
Percent 48 23 12 8 9

A study was done to see if this distribution is different at LTCC.  The table below shows the finding of this study.
Goal Transfer Job Skills Personal development Improve Basic Skills Certification
# of Students 72 40 25 20 15

What can be concluded at the 0.05 level of significance? 

 

Problem 8

A researcher is interested in determining whether there is a difference between the mean amount of money spent on textbooks in the fall at the three California public university systems.  Ten students from UC campuses, 8 students from Cal State campuses and 14 students from community colleges were surveyed.  Below is the StatCrunch readout for this survey.

Analysis of Variance results:
Data stored in separate columns.
Column means
 

Column n Mean Std. Error
UC 10 234.9 23.159088
Cal State 8 201.75 11.846865
Comm Col 12 183.16667 13.26983


ANOVA table
 

Source df SS MS F-Stat P-value
Treatments 2 14740.9 7370.45 2.5071433 0.1003
Error 27 79374.07 2939.7803    
Total 29 94114.97      

 

 

 

 

A.  What assumptions have we made about the data to apply a single-factor ANOVA test?

 

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

Problem 9

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 10

A biologist measured the muscle masses in grams of ten 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.
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.