Assignment:
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 72 couples at the fair with their children, 41 had visited the new miniature golf course, and among an independently chosen, random sample of 76 couples at the fair on a date (without children), 26 had visited the miniature golf course. Based on these samples, can we conclude, at the 0.01 level of significance, that the proportion of all couples attending the fair with their children who visited the miniature golf course is different from the proportion 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.
- State the null hypothesis:
- State the alternative hypothesis:
- The type of test statistic:
- The value of the test statistic (rounded to three decimal places):
- The P value (rounded to three decimal places):
Can we conclude that the proportion of couples visiting the miniature golf course is different between the two groups?
Provide complete and step by step solution for the question and show calculations and use formulas.