8.4.2 B.

In a survey of

210

males ages 20 to 24,

38%

were neither in school nor working. In a survey of

220

females ages 20 to 24,

45%

were neither in school nor working. These samples are random and independent. At

=0.06,

can you support the claim that the proportion of males ages 20 to 24 who were neither in school nor working is less than the proportion of females ages 20 to 24 who were neither in school nor working? Complete parts(a) through (e) below.

(a) Identify the claim and state

H0

and

Ha.

(b) Find the critical value(s) and identify the rejection region(s).

The critical value(s) is(are)

nothing.

(Use a comma to separate answers as needed. Round to two decimal places as needed.)

Identify the rejection region(s). Choose the correct answer below.

(c) Find the standardized test statistic.

z=

(Round to two decimal places as needed.)

Decide whether to reject or fail to reject the null hypothesis.

Choose the correct answer below.

Fail to reject

H0.

Reject

H0.

Interpret the decision in the context of the original claim.

Choose the correct answer below.

A.

At the

6%

significance level, there is

insufficient

evidence to support the claim.

B.

At the

6%

significance level, there is

sufficient

evidence to reject the claim.

C.

At the

6%

significance level, there is

insufficient

evidence to reject the claim.

D.

At the

6%

significance level, there is

sufficient

evidence to support the claim

Question 2

A nutritionist wants to determine how much time nationally people spend eating and drinking. Suppose for a random sample of

1083

people age 15 or older, the mean amount of time spent eating or drinking per day is

1.08

hours with a standard deviation of

0.75

hour. Complete parts (a) through (d) below.

(a) A histogram of time spent eating and drinking each day is skewed right. Use this result to explain why a large sample size is needed to construct a confidence interval for the mean time spent eating and drinking each day.

A.

The distribution of the sample mean will always be approximately normal.

B.

The distribution of the sample mean will never be approximately normal.

C.

Since the distribution of time spent eating and drinking each day is not normally distributed (skewed right), the sample must be large so that the distribution of the sample mean will be approximately normal.

Your answer is correct.

D.

Since the distribution of time spent eating and drinking each day is normally distributed, the sample must be large so that the distribution of the sample mean will be approximately normal.

(b) There are more than 200 million people nationally age 15 or older. Explain why this, along with the fact that the data were obtained using a random sample, satisfies the requirements for constructing a confidence interval.

A.

The sample size is greater than 5% of the population.

B.

The sample size is less than 5% of the population.

Your answer is correct.

C.

The sample size is less than 10% of the population.

D.

The sample size is greater than 10% of the population.

(c) Determine and interpret a

90%

confidence interval for the mean amount of time Americans age 15 or older spend eating and drinking each day.

Select the correct choice below and fill in the answer boxes, if applicable, in your choice.

(Type integers or decimals rounded to three decimal places as needed. Use ascending order.)

A.

The nutritionist is

90%

confident that the amount of time spent eating or drinking per day for any individual is between

nothing

and

nothing

hours.

B.

There is a

90%

probability that the mean amount of time spent eating or drinking per day is between

nothing

and

nothing

hours.

C.

The nutritionist is

90%

confident that the mean amount of time spent eating or drinking per day is between

nothing

and

nothing

hours.

D.

The requirements for constructing a confidence interval are not satisfied.

Question 3

Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced that the highest bid in excess of $15,000 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $15,000 and $20,000.

(a) 0.4

Suppose you bid $17,000. What is the probability that your bid will be accepted?

(b) 0.6

Suppose you bid $18,000. What is the probability that your bid will be accepted?

(c) 20000

What amount should you bid in dollars to maximize the probability that you get the property?

$

(d)

Suppose you know someone who is willing to pay you $21,000 for the property.

What is the expected profit in dollars if you bid the amount given in part (c)?

$

Find a bid in dollars which produces a greater expected profit than bidding the amount given in part (c). (If an answer does not exist, enter DNE.)

$

Would you consider bidding less than the amount in part (c)? Why or why not?

Yes. There is a bid which gives a greater expected profit than the bid given in part (c), and thus a higher expected profit is possible with a bid smaller than the amount in part (c).No. The bid which maximizes the expected profit is the amount given in part (c), thus it does not make sense to place a smaller bid.

Need D part only

Question 4

According to the National Institute of Allergy and Infectious Diseases, about 4.2% of American adults have a food allergy. A large company plans a lunch reception for its 350 employees. Assume that employees are independent. Let the random variable X be the number of company employees who have a food allergy. (a) What is the distribution of X? (b) What are the mean and standard deviation of the distribution ofX? (c) Using the Normal approximation (with continuity correction), determine the probability that at most 10 of the 350 employees have a food allergy