Question

Question 12 parts are based on the random sample below which is obtained to test the following hypothesis about the population mean.

74 88 89 67 89 81 86 83 78 76 73 82 90 77 85 89 81 81 87 81 76 89 68 83 80 75 83 88 87 67 80 90 78 67 76 69 82 87 74 80 70 82 89 72 80 88 74 72 75 78 80 70 84 82 82 72 86 73 73 87 77 89 90 72 78 90 89 67 69 71 75 88 73 78 74 72 84 88 72 77 70 71 78 67 70 72 83 69 88 69 87 83 69 82 85 75 71 70 82 77 78 67 79 75

Test the hypothesis that the mean is less than 80. I already calculated the estimated mean as 78.61 and the estimated variance of the mean as 50.066.

12a) The value of the test statistic is (if negative use the absolute value):

a 1.58

b 1.84

c 1.92

d 2.00

12b) Given α = 0.05, the critical value for the test is,

a 2.363

b 1.983

c 1.660

d 1.290

12c) The approximate p-value for the test is,

a 0.054

b 0.038

c 0.023

d 0.018

12d) Based on the p-value in the previous question,

a Reject H₀ at α = 0.10; do not reject H₀ at α = 0.05

b Reject H₀ at α = 0.05; do not reject H₀ at α = 0.01

c Reject H₀ at α = 0.01; do not reject H₀ at α = 0.05

d reject H₀ at α = 0.05; reject H₀ at α = 0.01

Answer 1

Null hypothesis  

           
              
Alternative hypothesis     

       
              
We have for given sample,              
Population mean for given sample=80
Sample mean=78.61      
Sample standard deviation s=7.076  
Sample size =n=   104      
              
Degree of freedom = n-1 =103  
              
              
              
t test statistic formula is              


=-2.003          

t critical value for left tailed test with degree of freedom =n-1 = 103 and   is =-1.66

P value is =0.023 .......................y using Excel command TDIST(-2.003,103,1)

12 a) Option d) 2.00

12 b) Option c) 1.660

12 c) Option c) 0.023

12 d) b Reject H₀ at α = 0.05; do not reject H₀ at α = 0.01