A shopping centre wants to examine the amount of space required for parking. Stu

Question

A shopping centre wants to examine the amount of space required for parking. Studies indicated that 50% of staff and shoppers use public transportation. A survey of 1002 was taken, and 483 responded that they used public transportation.

a. State the null hypothesis and the alternate hypothesis.
H0: p =
H1: p

b. State the decision rule for 0.05 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.)

d. At the 0.05 significance level, is it reasonable to conclude that the survey results indicate a change?

(Reject/ Accept) H0. There is (Not enough/ Enough) evidence to indicate that the results have changed.

Explanation / Answer

sample proportion = 483/1002 = 0.48

Null Hypothesis = population proportion of people that use public transportation = 0.50

SE = sqrt[0.52 x 0.48/1002] = 0.0157

test-statistic

z = (0.50 - 0.48)/0.0157 = 1.26

Let, Z be a standard normal variable. P(Z < 1.26) = 0.1038
So, p-value = 0.207 > 0.05

So, at 5% significance level, we don't have enough evidence to accept the null hypothesis.

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