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. At 5% level of significance, is it reasonable to conclude that the survey results indicate a change?

Answer 1

We accept H₀ data from the survey is not enough to claim that 50% of the proportion indicated in previous studies have change

Explanation:

To get conclusions about the survey we need to develop a hypothesis test of proportion

According to previous studies, (p₀ ) 50 % of staff and customers use public transportation, and we got from a survey 0f 1002 people 483 responded they also use then p = 483/1002 then

n sample size is 1002 and p = 0,482 (48,2 % )

Test Hypothesis

Null hypothesis H₀ p = p₀

Alternative hypothesis Hₐ p < p₀

CI = 95 % α = 5 % α = 0,05 and from z-table we find z score for that value z(c) = - 1,64

z(s) = ( p - p₀ ) / √ (p₀*q₀)/ n p₀ = q₀ = 0,5

z(s) = - 0,018* 31,65 / 0,5

z(s) = - 1,1394

To compare

z(s) and z(c) -1,1394 > 1,64

Then z(s) is inside the acceptance region. We accept H₀ , because we don´t have enough evidence to claim that the survey results indicate a change in

the original proportion