Question

Exercise 9-56

A shopping centre wants to examine the amount of space required for parking. Studies indicated that 68% of staff and shoppers use public transportation. A survey of 1,002 was taken, and 663 responded that they used public transportation.

a. State the null hypothesis and the alternate hypothesis. Round the final answers to 2 decimal places.

H₀: p =           

H₁: p ≠           

b. State the decision rule for 0.10 significance level. (Negative answer should be indicated by a minus sign. Round the final answers to 2 decimal places.)

Reject H₀ if z > or z < .

c. Compute the value of the test statistic. (Negative answer should be indicated by a minus sign. Round the final answer to 2 decimal places.)

Value of the test statistic           

d. At the 0.10 significance level, is it reasonable to conclude that the survey results indicate a change?

H₀. There is evidence to indicate that the results have changed.

Answer 1

a. State the null hypothesis and the alternate hypothesis.

Ho :   p =    0.68
H1 :   p ╪   0.68

b. State the decision rule for 0.10 significance level. (Negative answer should be indicated by a minus sign. Round the final answers to 2 decimal places.)

Level of Significance,   α =    0.10

critical z value =    ±    1.65 [excel formula =NORMSINV(α/2)]          

Reject H0 if z > 1.65 or z < -1.65

c. Compute the value of the test statistic. (Negative answer should be indicated by a minus sign. Round the final answer to 2 decimal places.)

Number of Items of Interest,   x =   663                  
Sample Size,   n =    1002                  
                          
Sample Proportion ,    p̂ = x/n =    0.6617                  
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.0147                  
Z Test Statistic = ( p̂-p)/SE = (   0.6617   -   0.68   ) /   0.0147   =   -1.24

d. At the 0.10 significance level, is it reasonable to conclude that the survey results indicate a change?

Decision:   | Z-stat | < | critical value |, so, Do not Reject Ho     
There is not enough evidence to conclude that survey results indicate a change.

Please revert in case of any doubt.

Please upvote. Thanks in advance