Question

Marietta is running for a seat in the Ames City Council. She claims to be supported by over 40% of residents. To examine this claim, you ask 10 randomly chosen residents whether they are supporting Marietta (there is not enough money in City Council elections to conduct a large survey). 8 of the 10 answer that they, indeed, support Marietta. a) What is the null hypothesis about the probability p for any resident to support Marietta, if you want to set up a statistical test of this claim? b) Given the result of your survey, what is the p-value? (you can use the binomial table from Canvas/script). c) Given your answer in part b), can you reject the null hypothesis at the 5%-significance level?

Answer 1

a)

the point estimate of the proportion of residents in support of Marietta is

b) Test statistic =

The P-value for the right-tailed test is P(Z>2.582) = 0.0049

Since the P-value is less than the significance level 0.05, we can reject the null hypothesis.

Hence we have evidence that claims to be supported by over 40% of residents.