Question

A survey of 1565 people who took trips revealed that 135 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

The conclusion is :  

A. There is sufficient evidence to support the claim that less than 10 % of trips include a theme park visit.

B. There is not sufficient evidence to support the claim that less than 10 % of trips include a theme park visit

Answer 1

Null hypothesis:-

Alternate hypothesis:-

we have sample proportion = (135/1565) = 0.09

Population proportion = 10/100 = 0.10

Sample size n = 1565

we have to use significance level of 0.01 or 99% confidence level

Z critical value of 99% confidence level is -2.33 for left tailed hypothesis

Calculation for the test statistic

Formula for the calculation of z statistic is given as

z =

where we have

setting the values, we get

z =

So, the test statistic is -1.32

Since the calculated test statistic is less not less than the z critical score, thus we failed to reject the null hypothesis and we can conclude that we have insufficient evidence to support the claim.

SO, option B is correct for conclusion