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In: Statistics and Probability

The USDA is concerned that most farmers are older Americans. In 2000, it was reported that...

The USDA is concerned that most farmers are older Americans. In 2000, it was reported that 25% of all US farmers were over the age of 65. In 2020, a random sample of 350 US farmers was taken and it was found that 98 were over the age of 65. The USDA claims that the proportion of all farmers who are over the age of 65 is now greater than 25%. Does this provide evidence to support the USDA’s claim at the 5% significance level? Run a hypothesis test. Be sure state Ho and Ha, the test statistic and p-value, whether you reject Ho or not and your conclusion in terms of the claim.

Solutions

Expert Solution

Let p denote the proportion of farmers over the age of 65 in the population.

So to test

vs

Now from the sample the favourable outcomes are 98 out of 350

So

The test statistic is given by

  

Now the p value is given by

P(z>1.29) where z follows standard normal

So as the p value is greater than 0.05 at 5% LOS we accept the null hypothesis.

This means that the proportion of farmers above 65 age is not greater than 0.25.

Thank you !!

orchestra answered 2 years ago
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