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Math


Question 1: Specific Motors of Detroit has developed a new Automobile known as the M car

Question 1:

Specific Motors of Detroit has developed a new Automobile known as the M car. 24 M cars and 28 J cars (from Japan) were road tested to compare miles-per-gallon (mpg) performance. Sample 1(M-Cars) Sample 2 (J Cars)

Sample 1(M-Cars)

Sample 2 (J Cars)

n1 = 24

n2= 28

X1 = 29.8

X2 = 27.3

S1 = 2.56 S2 = 1.81

Calculate a 90% confidence interval for the difference between mpg performance of the 2 car models.

A.) The manager claims that there is no difference in the mpg performance of M and J cars.

B.) Write out the null and alternative hypothesis to test the manager’s claim.

C.) Calculate the test statistic.

D.) Calculate the p-value.

E.) At a 5% level of significance do you accept or reject Ho.

Question 2:

Twenty undergraduate students are discussing the number of hours they need to study statistics for the final exam. They have three different plans. The entries in the table for the different plans are:

Plan 1

Plan 2

Plan 3

   

7.5

     
 

4.5

 
     

The resulting ANOVA table is shown below:

Its urgent 1

Test the hypothesis that the mean of the 3 plans are the same, at 5% level of significance. State the null and alternative hypotheses.

Question 3:

Suppose that Vancouver School Board wants to examine the effect of new curriculum on three different discitis: Vancouver, Richmond and Delta. It collects a sample of students’ marks in the National Beard Exam of three different schools from each district.

Using the hypothetical data provided below, test whether the mean of students’ marks for each district is the same.

Use α=5%.

Table ANOVA.1

Vancouver district

Richmond district

Delta district

643

469

484

702

525

402

655

427

456

 

666.67 473.67 447.33

 

S: 31.18 49.17 41.68

  1. State the null and alternative hypotheses.

  2. Calculate the appropriate test statistic

  3. Obtain the Critical Value

Question 4:

A university administrator wants to investigate if there is any relationship between international student’s IELTS exam score (X) and the number of admitted students at university (Y). A sample of 16 students is randomly selected and the results are summarized in the ANOVA table below:

ANOVA

       

 

df

SS

MS

F

Regression

1

372.707

372.707

42.927

Residual

15

130.234

8.682

 

Total

16

502.941

 

 

         

 

Coefficients

Standard Error

t Stat

P-value

Intercept

45.623

3.630

12.569

0.000

Price

0.107

0.016

6.552

0.000

  1. What is the estimated regression equation that relates the number of admitted students at university (Y) to the exam score in IELTS (X)?

  2. What is the estimated number of admitted students if a student got a score of 8.0 in IELTS?

  3. Is the regression relationship significant? Use the p-value approach and 2% level of significance

  4. Compute the coefficient of determination between the exam score in accounting and the exam score in mathematics. Interpret the result in the context of the problem.

 

 

 

Question 6:

Obtain regression equation of Y on X and estimate Y when X=60 from the following:

   

55

43

45

65

43

60

65

75

70

65

55

53

40

35

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