Question

Past experience at Crowder Travel Agency indicated that 44 percent of those people who want the agency to plan a vacation for them, wanted to go to Europe. A sample of 1,200 travelers was selected at random from agency files and 558 of those wanted to travel to Europe. At a 5% significance level, has there been a shift upwards in the proportion of people wanting to travel to Europe? (Round final all statistics and answer to four decimal places) [8 points]

b) Does your answer change if the significance level is changed to 1%? [1 point]

Answer 1

Step 1:

Ho : p = 0.44

Ha: p > 0.44

Step 2: Test statistics

x = 558

n = 1200

z = 1.745

Step 3:

= 0.05

Critical Value of Z (Right Tailed): 1.65

As z stat (1.745) falls in the rejection region, we reject the Null hypothesis.

Hence we have sufficient evidence to believe that the proportion of people who plan a vacation to Europe has increased from 0.44 (i.e. 44%)

(b)

= 0.01

Critical Value of Z (Right Tailed): 2.33

As z stat does not fall in the rejection region we fail to reject the Null hypothesis.

Yes the answer changes at 1% significance level.