Hypothesis Testing for a Proportion and Confidence Interval

After once again losing the most important football game of the year, a college’s alumni association takes an SRS of 100 alumni. 64 of the 100 favor firing the coach. You wish to test the claim that more than 50% of alumni support firing the coach. Ho: p = 0.50 Ha: p > 0.50 What is the “test statistic” (z-score) for this hypothesis test?

(a)  

A poll from last year found that 73% of local adults wanted more casual dining options in town. You want to calculate a 98% confidence interval with a margin of error of +/- 5%.

The minimum sample size required to do this is at least (a)   people.

A 2015 national poll found that 38% of dog owners say they love their dog more than their spouse. You don’t think this poll can possibly be true and believe the proportion to be much less. You take an SRS of 150 dog owners. 48 admit that they love their dog more than their spouse. Which is the ALTERNATE hypothesis?

A 2015 national poll found that 38% of dog owners say they love their dog more than their spouse.

You don’t think this poll can possibly be true and believe the proportion to be much less. You take an SRS of 130 dog owners. 39 admit that they love their dog more than their spouse.

What is the p-value?

You are testing Ho: p = 0.55 against Ha: p > 0.55. After calculating the test statistic, you get z = 1.86 ...

Which is the correct p-value?

Which is true about a 98% confidence interval for a population proportion based on a given sample?

We have calculated a confidence interval based on a sample of size n = 100. Now we want to get a better estimate with a margin of error that is only one-fourth as large. How large does our new sample need to be?

The manager of an orchard expects about 70% of his apples to exceed the weight requirement for “Grade A” designation. At least how many apples must he sample to be 90% confident of estimating the true proportion within ±4%?

A statistics professor wants to see if more than 80% of her students enjoyed taking her class. At the end of the term, she takes a random sample of students from her large class and asks, in an anonymous survey, if the students enjoyed taking her class. Which set of hypotheses should she test?

Suppose that a manufacturer is testing one of its machines to make sure that the machine is producing more than 97% good parts (Ho : p = 0.97 and Ha : p > 0.97). The test results in a P-value of 0.122. Unknown to the manufacturer, the machine is actually producing 99% good parts. What probably happens as a result of the testing?