Question

A survey of 1375 people who took trips revealed that 125 of them included a visit to a theme park. Based on those survery results, a management consultant claims that less than 10 % of trips include a theme park visit. Test this claim using the α=0.01 significance level. The test statistic is The critical value is

Answer 1

Given that ,

The sample size is N = 1375, the number of favorable cases is X = 125, and the sample proportion is ,

and the significance level is

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: p = 0.10

Ha: p < 0.10

This corresponds to a left-tailed test, for which a z-test for one population proportion needs to be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.01, and the critical value for a left-tailed test is zc = -2.33.

The rejection region for this left-tailed test is R = {z: z < -2.33}

(3) Test Statistics

The z-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that , it is then concluded that the null hypothesis is not rejected.

(5) Conclusion

There is not enough evidence to claim that the population proportion p is less than p0, at the significance level.