06.07

A student performs a test of H₀: p = 0.5 versus H_a: p

The student should have stated the data prove H_ais true.

The student should have stated the data prove H₀is true.

The p-value should be compared with the mean, not the hypothesized value of p.

The p-value should be compared with the standard deviation, not the hypothesized value of p.

The p-value should be compared with a significance level such as ? = 0.05, not the hypothesized value of p.

Suppose a candidate is interested in the proportion of the vote her opponent will receive. If she samples voters at random and tests hypotheses regarding p, the population proportion, what should she do to reduce her risk of making a Type I error? (4 points)

I. Increase the number of voters she will sample to 50

II. Decrease the number of voters she will sample to 10

III. Increase the significance level

IV. Decrease the significance level

I only

II only

III only

IV only

I and III only

A female is picked up by the police for stealing jewelry, but she claims she is innocent and this is a case of mistaken identity. The case goes to trial and the judge informs the jury the accused is innocent until she is proved guilty. That is, jurors should find her guilty only if there is overwhelming evidence to reject the assumption of innocence. What risk is involved in the jury making a Type II error? (4 points)

She is guilty, but the jury finds her innocent and she goes free.

She is guilty, and the jury finds her guilty, and she goes to jail.

She is innocent, and the jury finds her innocent, and she goes free.

She is innocent, but the jury finds her guilty, and she goes to jail.

A conclusion cannot be made based on the information given.

A few months before a citywide election, 680 individuals responded to a poll of 1,000 randomly selected registered voters, indicating they favor candidate X for mayor (p?₁= 0.6800). One month before the election, a second poll of 900 registered voters is conducted and 598 individuals respond who indicate they favor candidate X (p?₂= 0.6644). A 90% two-proportion z confidence interval for the true difference between the proportions favoring candidate X in the first and second polls was constructed and found to be (?0.0199, 0.0510). Which of the following is the best interpretation of this interval? (4 points)

There has not been a significant decrease in support for candidate X.

There has been a significant decrease in support for candidate X.

There has been significant change in support for candidate X.

Because zero is included in the confidence interval, candidate X is likely to win a majority of votes in the general election.

Because support for candidate X has not decreased below 50%, this candidate is likely to win a majority of votes in the general election.

Does the amount of shade affect the birth rate of chickens? A study in a local paper reported that, although 52 of 60 shaded (from sunlight) eggs hatched, only 41 of 55 unshaded eggs hatched. Which of the following is the 98% confidence interval for the true difference between the proportions of shielded and unshielded eggs that hatch? (4 points)

O 52 41 93 93 + 60 + 2.326 55 V( 115 115 60 55 O 52 41 93 93 1 + 2.576 + 60 55 V 715 115 60 55 O 52 41 93 93 52 41 60 +2.326 + 55 115 115 60 55 O 52 52 41 41 1 - 1 - 52 60 60 55 55 60 60 55 O 52 52 41 41 1- 1 - 52 41 60 60 55 55 + 2.5761 + 55 60 55