Question

1. Toyota has been manufacturing small automobiles that have averaged 50 miles per gallon of gasoline in highway driving. The company has developed a more efficient engine for its small cars and now advertises that its new small cars average more than 50 miles per gallon in highway driving. An independent testing service road-tested 36 of the automobiles. The sample showed an average of 51.5 miles per gallon. The population standard deviation is 6 miles per gallon.

1. With a 0.025 level of significance, test to determine whether or not the manufacturer's advertising campaign is legitimate.

1. Use critical value approach

2. Use p value approach

3. State a type 1 error for this problem

4. State a type 2 error for this problem

1. Toyota has been manufacturing small automobiles that have averaged 50 miles per gallon of gasoline in highway driving. The company has developed a more efficient engine for its small cars and now advertises that its new small cars average more than 50 miles per gallon in highway driving. An independent testing service road-tested 36 of the automobiles. The sample showed an average of 51.5 miles per gallon. The population standard deviation is 6 miles per gallon.

1. With a 0.025 level of significance, test to determine whether or not the manufacturer's advertising campaign is legitimate.

1. Use critical value approach

2. Use p value approach

3. State a type 1 error for this problem

4. State a type 2 error for this problem

Answer 1

a)

Ho :   µ =   50                  
Ha :   µ >   50       (Right tail test)          
                          
Level of Significance ,    α =    0.025                  
population std dev ,    σ =    6.0000                  
Sample Size ,   n =    36                  
Sample Mean,    x̅ =   51.5000                  
                          
'   '   '                  
                          
Standard Error , SE = σ/√n =   6.0000   / √    36   =   1.0000      
Z-test statistic= (x̅ - µ )/SE = (   51.500   -   50   ) /    1.0000   =   1.500
                          
critical z value, z* =       1.960   [Excel formula =NORMSINV(α/no. of tails) ]              

since, test stat < critical value, fail to reject Ho

b)

p-Value   =   0.0668
Decision:   p-value>α, Do not reject null hypothesis   

c)

Type I error is conlcuding that  manufacturer's advertising campaign is legitimate. while in actual it is not

d) Type II error is ocnluding that  manufacturer's advertising campaign is not legitimate. while in actual, it is legitimate