# Hypothesis Testing: Z Test and Difference of Proportions

In the year 2000, the state of Indiana began a $40-million renovation of its state fairgrounds, which included the building of a miniature golf course and a state-of-the-art livestock building. Now, Indiana officials are interested in learning what sorts of people are visiting the new attractions. In a survey done at this year's state fair, it was found that, among a random sample of 67 couples at the fair with their children, 24 had visited the new miniature golf course, and among an independently chosen, random sample of 75 couples at the fair on a date (without children), 40 had visited the miniature golf course. Based on these samples, can we conclude, at the 0.01 level of significance, that the proportion p1 of all couples attending the fair with their children who visited the miniature golf course is different from the proportion p2 of all couples attending the fair on a date who visited the miniature golf course?

Perform a two-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)

The null hypothesis Ho:

The alternate hypothesis H1:

The type of test statistic: Z, t, chi square, or F:

The value of the test statistic: (Round to at least three decimal places):

The p-value (Round to at least three decimal places):

Can we conclude that the proportion of couples visiting the miniture golf course is different between the two groups?

https://brainmass.com/statistics/z-test/hypothesis-testing-z-test-and-difference-of-proportions-244093

#### Solution Preview

Answer

The null hypothesis tested is

H0: The proportion of all couples attending the fair with their children who visited the miniature golf course is not significantly different from the proportion of all couples attending the fair on a date who visited the miniature golf course (P1=P2)

The alternative hypothesis is:

H1: The proportion of all couples attending the fair with their children who visited the miniature golf course is ...

#### Solution Summary

The solution provides step by step method for the calculation of Z test for proportion, Formula for the calculation and interpretations of the results are also included. This solution is provided in an attached Word and Excel file.