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

A study was done to determine whether LTCC transfer students had a lower retention rate from the retention rate of the average US student retention rate of 71%.  Of the 121 LTCC transfer students tracked, 84 eventually received their bachelor's degree.  What can you conclude with a level of significance of 5%?  Give the P-value and interpret what it means.

Solution

Problem 2

Thirteen males and fourteen females participated in a study of grip and 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.

 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 average customer comes in wearing a \$120 outfit.  45 different respondents participated in the study.  You have found that the equation of the regression line is

y  =  8000 + 50x

and that Se  =  1000 and  SSx  =  12,000

A.  A man walks into your dealership sporting a \$200 outfit.  What is your prediction for the price of the car that this man will buy?

Solution

B.  Find a 95% confidence interval for the price of the car that the man will buy.

Solution

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 Webcrunch 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.

Solution

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

Solution

C.  What is the correlation coefficient?  Interpret this coefficient.

Solution

D.  Construct a possible scatterplot for this data and explain using a complete sentence or two your reasoning in constructing the scatterplot 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

Solution

Problem 6

Do students do better on exams if they meditate for the hour just before the exam.  At a large university the average score on the first exam is 82%38 students volunteered to go through an hour of meditation before their first exam.  The meditators averaged 84% on the exam with a standard deviation of 5%.  What can you conclude at a .05 level?  give the P-value and interpret what it means.

Solution

Problem 7

A medical researcher is concerned that a new medication has a side effect of raising the variance of the salt content in the blood.  For 25 days the blood salinity of a patient who was not on the medication was tested.  She calculated the variance as 0.06 percent.  Then the patient began taking the medication and the blood salinity was tested for the next 13 days.  The variance over these 13 days was found to be 0.15 percent.  Use a level of significance of 0.05 to test the claim that the variance of the blood salinity is greater while on medication.

Solution

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?

Solution

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

Solution