Question

A researcher believes that the proportion of a community’s population in favor of a new park is greater than the countywide proportion of 0.65. A survey of 67 people in the community reveals that the estimated proportion of the community in favor of it is equal to 0.76. Use alpha = 0.05. State the null and alternative hypotheses, find the test statistic, compare it with the critical value, make a decision, and find the p-value.

Answer 1

solution:

the given information as follows:

sample size = n = 67

proportion of community in favor = = 0.76

the null and alternative hypothesis:

test statistics:

significance level = 0.05

since it is a right tail test,

critical value of z =

since z = 1.89 > 1.645 , so we reject the null hypothesis

p value = 1 - value of z to the left of 1.89 = 1 - 0.9706 = 0.0294

conclusion : there is sufficient evidence that the researcher's believe is right.