Question

The policy of the Suburban Transit Authority is to add a bus route if more than 55% of the potential commuters indicate they would use the particular route. A sample of 70 commuters revealed that 42 would use a proposed route from Bowman Park to the downtown area. Does the Bowman-to-downtown route meet the STA criterion? Use the 0.05 significance level.

a. What is the decision rule? (Round the final answer to 3 decimal places.)

Reject H₀: p ≤ 0.55 and accept H₁: p > 0.55 when the test statistic is              (Click to select)   greater than   less than   equal to   .

b. Compute the value of the test statistic. (Round the final answer to 3 decimal places.)

Value of the test statistic            

c. What is your decision regarding H₀?

H₀ is              (Click to select)   rejected   not rejected  .

Answer 1

H0: p = 0.55

Ha: p > 0.55

Sample proportion = 42 / 70 = 0.60

a)

Decision rule = Reject H0 when test statistics > 1.645.

b)

Test statistics

z = - p / sqrt( p ( 1 - p) / n)

= 0.60 - 0.55 / sqrt( 0.55 * 0.45 / 70)

= 0.841

This is test statistics value.

c)

Since test statistics falls in non-rejection region that is below 1.645, we do not have sufficient

evidence to reject H0.

H0 is not rejected.