Question

The next three questions are based on the following data on the closing price at year’s end in Euros of the DAX Stock Index. year 1994 1995 1996 1997 closing price 2100.98 2280.81 2844.09 4125.54

11. Find ˆm. A. ≈ 506.4 B. ≈ 663.7 C. ≈ 792.4 D. ≈ 914.9 E. other value

12. Find the coefficent of determination.

A. ≈ .877 B. ≈ .899 C. ≈ .936 D. ≈ .948 E. other value

13. Find a 90% confidence interval for the slope of the regression line.

A. [150.4, 1177] B. [250.07, 1077.33] C. [332.17, 995.23] D. [375.76, 951.64] E. other value

14. Suppose you randomly ask 500 people and 270 of them say chocolate is their favorite ice cream flavor. Perform a one-sided significance test of the hypothesis that half the population favors chocolate. How sure can you be that a majority of the population favor chocolate?

A. ≈ .9633 B. ≈ .9266 C. ≈ .0734 D. ≈ .0367 E. other value

15. Suppose your friend claims that students in a large lecture got an average test score of 85%. You randomly ask 20 students from that lecture and record an average test score of ¯x = 80% and a sample standard deviation of s = 10%, perform an appropriate one-sided significance test of your friend’s claim. How sure can you be based on the sample that your friend’s claim is false?

A. ≈ .9429 B. ≈ .9875 C. ≈ .9969 D. ≈ .9999 E. other value

Answer 1

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
1	2100.98	2.2500	542984.7656	1105.313
2	2280.81	0.2500	310299.1320	278.523
3	2844.09	0.2500	38.8752	3.118
4	4125.54	2.2500	1658132.6592	1931.528

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	10.00	11351.42	5.00	2511455.43	3318.48
mean	2.50	2837.86	SSxx	SSyy	SSxy

11)

sample size ,   n =   4          
here, x̅ = Σx / n=   2.500   ,     ȳ = Σy/n =   2837.855  
  
SSxx =    Σ(x-x̅)² =    5.0000          
SSxy=   Σ(x-x̅)(y-ȳ) =   3318.5          
                  
estimated slope , ß1 = SSxy/SSxx =   3318.5   /   5.000   =   663.7

12) R² =    (SSxy)²/(SSx.SSy) =    0.877

13) confidence interval for slope                  
α=   0.1              
t critical value=   t α/2 =    2.920   [excel function: =t.inv.2t(α/2,df) ]      
estimated std error of slope = Se/√Sxx =    393.06077   /√   5.00   =   175.782
                  
margin of error ,E= t*std error =    2.920   *   175.782   =   513.281
estimated slope , ß^ =    663.6960              
                  
                  
lower confidence limit = estimated slope - margin of error =   663.6960   -   513.281   =   150.4148
upper confidence limit=estimated slope + margin of error =   663.6960   +   513.281   =   1176.9772

A. [150.4, 1177]

14)

Ho :   p =    0.5  
H1 :   p >   0.5   (Right tail test)
          
Level of Significance,   α =    0.05  
Number of Items of Interest,   x =   270  
Sample Size,   n =    500  
          
Sample Proportion ,    p̂ = x/n =    0.5400  
          
Standard Error ,    SE = √( p(1-p)/n ) =    0.02236  
Z Test Statistic = ( p̂-p)/SE =    (0.54-0.5)/0.0224=   1.78885  
          

          
p-Value   =   0.0367    [Excel function =NORMSDIST(-z)