Question

a. The Institute of Education Sciences measures the high school dropout rate as the percentage of 16-through 24-year-olds who are not enrolled in school and have not earned a high school credential. Last year, the high school dropout rate was 8.1%. A polling company recently took a survey of 1,000 people between the ages of 16 and 24 and found that 6.5% of them are high school dropouts. The polling company would like to determine whether the dropout rate has decreased. At a 5% significance level, the p-value and α are _____________________.

• p-value = 0.0318 and α = 0.025

• p-value = 0.0210 and α = 0.025

• p-value = 0.0210 and α = 0.05

• p-value = 0.0318 and α = 0.05

b. A schoolteacher is worried that the concentration of dangerous, cancer-causing radon gas in her classroom is greater than the safe level of 4pCi/L. The school samples the air for 36 days and finds an average concentration of 4.4pCi/L with a standard deviation of 1pCi/L. The value of the test statistic is ___________.

• z = –2.40

• t₃₅ = –2.40

• t₃₅ = 2.40

• z = 2.40

c. The owner of a large car dealership believes that the financial crisis decreased the number of customers visiting her dealership. The dealership has historically had 800 customers per day. The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750. Assume that the population standard deviation is 350. The value of the test statistic is ____________.

• t₉₉ = –1.429

• t₉₉ = 1.429

• z = 1.429

• z = –1.429

d. The alternative hypothesis typically ___________.

• corresponds to the presumed default state of nature

• states the probability of rejecting the null hypothesis when it is true

• contests the status quo, for which a corrective action may be required

• states the probability of rejecting the null hypothesis when it is false

e. When conducting a hypothesis test concerning the population mean, and the population standard deviation is unknown, the value of the test statistic is calculated as __________.

• tdf=p−−popo(1−po)n√tdf=p−−popo(1−po)n

• z=p−−popo(1−po)n√z=p−−popo(1−po)n

• tdf=x−−μos/n√tdf=x−−μos/n

• z=x−−μoσ/n√

f. When conducting a hypothesis test concerning the population mean, and the population standard deviation is known, the value of the test statistic is calculated as _________.

• z=p−−popo(1−po)n√z=p−−popo(1−po)n

• tdf=x−−μos/n√tdf=x−−μos/n

• z=x−−μoσ/n√z=x−−μoσ/n

• tdf=p−−popo(1−po)n√

Answer 1

A.

Using the P-value approach:

p-value = 0.0318

= 0.05

i.e option D is correct.

B.

• A population that is not normally distributed (assuming n 30; the central limit theorem applies)

                

Putting all the values in the above formula:

z = 2.40

i.e option D is correct.

C.

• A normally distributed population--variances known

                

z = z = –1.429

i.e option D is correct.

D.

corresponds to the presumed default state of nature.

i.e. option A is correct.

E.

• A normally distributed population--variances unknown

                

i.e. option C is correct.

F.

• A normally distributed population--variances known

                

i.e. option C is correct.

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