Question

1.Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.

x

86

70

80

76

70

67

y

57

43

46

50

50

41

Given that Se ≈ 4.075, a ≈ 16.319, b ≈ 0.435, and x bar≈ 74.833 , ∑x = 449, ∑y = 287, ∑x2 = 33,861, and ∑y2 = 13,895, find a 99% confidence interval for y when x = 72.

Select one:

a. between 25.3 and 66.8

b. between 25.6 and 66.6

c. between 25.8 and 66.3

d. between 27.0 and 65.1

e. between 24.9 and 67.2

2.Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.

x

65

80

68

64

69

71

y

43

49

51

47

42

52

Given that Se ≈ 4.306, a ≈ 17.085, b ≈ 0.417, and x bar≈ 69.5 , ∑x = 417, ∑y = 284, ∑x2 = 29,147, and ∑y2 = 13,528, find a 98% confidence interval for y around 53.4 when x = 87.

Select one:

a. between 26.4 and 77.3

b. between 25.1 and 78.6

c. between 24.6 and 79.1

d. between 21.3 and 82.5

e. between 23.8 and 79.9

3.Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.

x

81

65

78

87

70

81

y

46

48

54

51

44

51

Given that Se ≈ 3.668, a ≈ 16.331, b ≈ 0.436, and x bar≈ 77 , use a 5% level of significance to find the P-Value for the test that claims β is greater than zero.

Select one:

a. 0.1 <  P-Value < 0.2

b. 0.005 <  P-Value < 0.01

c. P-Value < 0.005

d. 0.2 <  P-Value < 0.25

e. P-Value > 0.25

Answer 1

1)

X Value   72
Confidence Level   99%
  

Sample Size , n=   6
Degrees of Freedom,df=n-2 =   4
critical t Value = 4.604 [using t-table]
X̅ =    74.833

SSxx =    Σx² - (Σx)²/n =   260.8333333

Σ(x-x̅)² =Sxx   260.833
Standard Error of the Estimate,Se=   4.075
h Statistic = (1/n+(X-X̅)^2/Sxx) =    0.197
Predicted Y (YHat) = 46.075

margin of error,E=t*Se*√(1+h-stat) =    20.5308
Prediction Interval Lower Limit=Ŷ -E =   25.6
Prediction Interval Upper Limit=Ŷ +E =   66.6
so, answer is b) between 25.6 and 66.6

2)

X Value   87
Confidence Level   98%
  
Intermediate Calculations  
Sample Size , n=   6
Degrees of Freedom,df=n-2 =   4
critical t Value   3.747
X̅ =    69.500
Σ(x-x̅)² =Sxx   165.500
Standard Error of the Estimate,Se=   4.306
h Statistic = (1/n+(X-X̅)^2/Sxx) =    2.017
Predicted Y (YHat)   51.880

margin of error,E=t*Se*√(1+h-stat) =    28.0241
Prediction Interval Lower Limit=Ŷ -E =   23.8560
Prediction Interval Upper Limit=Ŷ +E =   79.90428492

so, answer is option e)

3)

SSxx =    Σx² - (Σx)²/n =   326
slope hypothesis test
Ho:   ß1=   0          
H1:   ß1 >   0          
n=   6              
alpha=   0.05              
estimated std error of slope =Se(ß1) =                s/√Sxx =    0.2031
                  
t stat =    ß1 /Se(ß1) =        1.0267   
                  
0.1 <  P-Value < 0.2   

decision :    p-value>α , do not reject Ho  

option a)