A study reveals that 65% of homeowners in Omaha own a lawn mower. To test this claim, you form a sample of 500 homeowners in Omaha, of which, 68% owned a lawnmower. Is there enough evidence to reject the claim using a level of significance of 5%?

There is no enough evidence to reject the claim using a level of significance of 5%

Step-by-step explanation:

Let p be the true proportion of homeowners in Omaha who own a lawnmower. We want to test  

vs (two-tailed alternative).

We have a large sample of size n = 500 and a point estimate for p is . The test statistic is given by

where is the standard error of when is true. The observed value is = 1.4064 which comes from a standard normal distribution. Because we want to use a level of significance of 5%, our rejection region is RR={z | z < -1.96 or z > 1.96} where -1.96 and 1.96 are the 2.5th and 97.5th quantiles respectively. Because 1.4064 does not belong to RR, we fail to reject the null hypothesis.