Question

For any Hypothesis Test make sure to state Ho, Ha, Test statistic, p-value, whether you reject Ho, and your conclusion in the words of the claim.

For any confidence interval make sure that you interpret the interval in context, in addition to using it for inference.

Round to the thousandths place

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.

Answer 1

Given : n=350 , X=98 ; The estimate of the sample proportion is ,

Hypothesis : Vs  

The test statistic is ,

Teh p-value is ,

p-value=

Decision : Here , p-value = 0.0968 > 0.05

Therefore , fail to reject Ho.

Conclusion : Hence , there is not sufficient evidence to suppot the USDA claims that the proportion of all farmers who are over the age of 65 is now greater than 25%.