Bob, an organic fruit grower, ran a blind taste test to see if people could tell the difference between organically grown fruit and non-organically grown fruit. He randomly selected a sample of 250 people, and gave each person a piece of each type of fruit. He asked them to identify which was the organically grown fruit, and 147 people correctly did so. Use these results to help answer the questions below.

1

Let p be the population proportion of people who can correctly identify the organic fruit.

Return again to our hypotheses in Q25. Remember that 147 out of 250 correctly identified the organic fruit. What is the value of the test statistic?

a.

2.78

b.

5.57

c.

-2.83

d.

2.83

2

Let p be the population proportion of people who can correctly identify the organic fruit.

Return again to our hypotheses in Q25. Remember that 147 out of 250 correctly identified the organic fruit. What is the 99% confidence interval for p?

a.

(0.527, 0.649)

b.

(0.516, 0.660)

c.

(0.526, 0.650)

d.

(0.508, 0.668)

3

Let p be the population proportion of people who can correctly identify the organic fruit.

Suppose a different sample was taken, where n = 500 and 294 people correctly identified the organically grown fruit. Then a 99% confidence interval for p was calculated using just this new sample. How would the width of the new confidence interval compare to the width of the confidence interval in Q31?

a.

Both would have the same width.

b.

Not enough information to tell.

c.

New confidence interval would have smaller width.

d.

New confidence interval would have greater width.

4

Let p be the population proportion of people who can correctly identify the organic fruit.

Assume the p-value for the test in Q25 was correctly calculated at 0.02 and so Bob reasons that since p< 0.05 we can reject H₀ at the 5% level of significance and so conclude that more than 50% of people prefer organic fruit. Which of the following reasons best explains why Bob is wrong?

a

We did not collect the right data to answer questions about who prefers organic fruit.

b.

He shouldn't say that he rejects H₀, but rather than he fails to reject H₁.

c.

This is clearly a type I error and Bob should report it.

d.

The central limit theorem doesn't apply here, so we can't trust the p-value and so Bob shouldn't make such conclusions.