Question

A shopping centre wants to examine the amount of space required for parking. Studies indicated that 66% of staff and shoppers use public transportation. A survey of 1,002 was taken, and 680 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

a)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.66
Alternative Hypothesis, Ha: p ≠ 0.66

b)

Rejection Region
This is two tailed test, for α = 0.1
Critical value of z are -1.64 and 1.64.
Hence reject H0 if z < -1.64 or z > 1.64

c)

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.6786 - 0.66)/sqrt(0.66*(1-0.66)/1002)
z = 1.24

d)

Do not reject H0. There is not enough evidence to indicate that the results have changed