A survey was conducted in a large city to investigate public opinion on banning the use of trans fats in restaurant cooking. A random sample of 230 city residents with school-age children was selected, and another random sample of 341 city residents without school-age children was also selected. Of those with school-age children, 94 opposed the banning of trans fats, and of those without school-age children, 147 opposed the banning of trans fats. An appropriate hypothesis test was conducted to investigate whether there was a difference between the two groups of residents in their opposition to the banning of trans fats. Is there convincing statistical evidence of a difference between the two population proportions at the significance level of 0.05

There is no enough evidence to claim that there is a difference between the two population proportions.

Step-by-step explanation:

We have to perform an hypothesis testing for a difference between two population proportions.

The null hypothesis will state that both proportions are the same, and the alternative hypothesis will state that they differ. This would be than a two-side hypothesis test.

We can write this as:

The significance level for this test is 0.05.

The sample of city residents with school-age children has a sample size n1=230 and a sample proportion p1=0.41

The sample of city residents without school-age children has a sample size n2=341 and a sample proportion p2=0.51

The weighted p, needed to calculate the standard error, is the weighted average of both sample proportions:

The standard error of the difference of proportions can now be calculated as:

The test statistic z is:

The P-value for this two side test and this value of the z-statistic is:

The P-value is bigger than the significance level, so the effect is not significant. The null hypothesis failed to be rejected.

There is no enough evidence to claim that there is a difference between the two population proportions.

good luck!

cutie~