Question

A shopping centre wants to examine the amount of space required for parking. Studies indicated that 52% of staff and shoppers use public transportation. A survey of 1,002 was taken, and 482 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?

(Click to select)  Do not reject  Reject  H₀. There is  (Click to select)  enough / not enough evidence to indicate that the results have changed.

Answer 1

Solution:

Given:  52% of staff and shoppers use public transportation

that is: p = 0.52

Sample size = n = 1002

x = Number of people used public transportation = 482

Part a. State the null hypothesis and the alternate hypothesis.

H₀: p = 0.52

H₁: p ≠ 0.52

Part b. State the decision rule for 0.10 significance level.

Since this is two tailed test , find  

Look in z table for Area = 0.0500 and find corresponding z value.

Area 0.0500 is in between 0.0495 and 0.0505 and both the area are at same distance from 0.0500

Thus we look for both area and find both z values

Thus Area 0.0495 corresponds to -1.65 and 0.0505 corresponds to -1.64

Thus average of both z values is : ( -1.64+ - 1.65) / 2 = -1.645

Thus Z = -1.645 = -1.65

Since this is two tailed test , there are two z critical values = (-1.65 , 1.65)

Thus  the decision rule for 0.10 significance level is:

Reject H0 if :

z < -1.65

z > 1.65

Part c. Compute the value of the test statistic.

where

thus

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

Since   < z critical value = -1.65 , we reject null hypothesis H0.

Thus:

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