9.4

1. 11% of all Americans suffer from sleep apnea. A researcher suspects that a lower

percentage of those who live in the inner city have sleep apnea. Of the 322 people from the

inner city surveyed, 29 of them suffered from sleep apnea. What can be concluded at the

level of significance of α = 0.01?

a. For this study, we should use

b. The null and alternative hypotheses would be:

Ho:

(please enter a decimal)

H1:

(Please enter a decimal)

c. The test statistic

places.)

d. The p-value =

e. The p-value is

=

(please show your answer to 3 decimal

(Please show your answer to 4 decimal places.)

α

f. Based on this, we should

g. Thus, the final conclusion is that …

the null hypothesis.

o

The data suggest the populaton proportion is significantly smaller than 11%

at α = 0.01, so there is sufficient evidence to conclude that the population

proportion of inner city residents who have sleep apnea is smaller than 11%

o

The data suggest the population proportion is not significantly smaller than

11% at α = 0.01, so there is sufficient evidence to conclude that the population

proportion of inner city residents who have sleep apnea is equal to 11%.

The data suggest the population proportion is not significantly smaller than

11% at α = 0.01, so there is not sufficient evidence to conclude that the

population proportion of inner city residents who have sleep apnea is smaller

than 11%.

h. Interpret the p-value in the context of the study.

o

o

o

There is a 11% chance of a Type I error

If the sample proportion of inner city residents who have sleep apnea is 9%

and if another 322 inner city residents are surveyed then there would be a

12.64% chance of concluding that fewer than 11% of inner city residents have

sleep apnea.

o

If the population proportion of inner city residents who have sleep apnea is

11% and if another 322 inner city residents are surveyed then there would be a

12.64% chance fewer than 9% of the 322 residents surveyed have sleep apnea.

There is a 12.64% chance that fewer than 11% of all inner city residents

have sleep apnea.

i. Interpret the level of significance in the context of the study.

o

o

There is a 1% chance that the proportion of all inner city residents who

have sleep apnea is smaller than 11%.

o

There is a 1% chance that aliens have secretly taken over the earth and

have cleverly disguised themselves as the presidents of each of the countries

on earth.

o

If the population proportion of inner city residents who have sleep apnea is

smaller than 11% and if another 322 inner city residents are surveyed then

there would be a 1% chance that we would end up falsely concluding that the

proportion of all inner city residents who have sleep apnea is equal to 11%.

o

If the population proportion of inner city residents who have sleep apnea is

11% and if another 322 inner city residents are surveyed then there would be a

1% chance that we would end up falsely concluding that the proportion of all

inner city residents who have sleep apnea is smaller than 11%.

2. The recidivism rate for convicted sex offenders is 11%. A warden suspects that this

percent is different if the sex offender is also a drug addict. Of the 391 convicted sex

offenders who were also drug addicts, 63 of them became repeat offenders. What can be

concluded at the α = 0.10 level of significance?

a. For this study, we should use

b. The null and alternative hypotheses would be:

Ho:

(please enter a decimal)

H1:

(Please enter a decimal)

c. The test statistic

places.)

d. The p-value =

e. The p-value is

=

(please show your answer to 3 decimal

(Please show your answer to 4 decimal places.)

α

f. Based on this, we should

g. Thus, the final conclusion is that …

the null hypothesis.

o

The data suggest the population proportion is not significantly different

from 11% at α = 0.10, so there is statistically significant evidence to conclude

that the population proportion of convicted sex offender drug addicts who

become repeat offenders is equal to 11%.

o

The data suggest the population proportion is not significantly different

from 11% at α = 0.10, so there is statistically insignificant evidence to conclude

that the population proportion of convicted sex offender drug addicts who

become repeat offenders is different from 11%.

The data suggest the populaton proportion is significantly different from

11% at α = 0.10, so there is statistically significant evidence to conclude that

the population proportion of convicted sex offender drug addicts who become

repeat offenders is different from 11%.

h. Interpret the p-value in the context of the study.

o

o

If the population proportion of convicted sex offender drug addicts who

become repeat offenders is 11% and if another 391 convicted sex offender drug

addicts are observed, then there would be a 0.12000000000001% chance that

either more than 16% of the 391 convicted sex offender drug addicts in the

study become repeat offenders or fewer than 6% of the 391 convicted sex

offender drug addicts in the study become repeat offenders.

o

There is a 0.12000000000001% chance that the percent of all convicted sex

offender drug addicts who become repeat offenders differs from 11%.

o

If the sample proportion of convicted sex offender drug addicts who

become repeat offenders is 16% and if another 391 convicted sex offender drug

addicts are observed then there would be a 0.12000000000001% chance that we

would conclude either fewer than 11% of all convicted sex offender drug

addicts become repeat offenders or more than 11% of all convicted sex

offender drug addicts become repeat offenders.

There is a 0.12000000000001% chance of a Type I error.

i. Interpret the level of significance in the context of the study.

o

o

There is a 10% chance that the proportion of all convicted sex offender

drug addicts who become repeat offenders is different from 11%.

o

If the population proportion of convicted sex offender drug addicts who

become repeat offenders is 11% and if another 391 convicted sex offender drug

addicts are observed, then there would be a 10% chance that we would end up

falsely concluding that the proportion of all convicted sex offender drug

addicts who become repeat offenders is different from 11%.

o

If the population proportion of convicted sex offender drug addicts who

become repeat offenders is different from 11% and if another 391 convicted sex

offender drug addicts are observed then there would be a 10% chance that we

would end up falsely concluding that the proportion of all convicted sex

offender drug addicts who become repeat offenders is equal to 11%.

o

There is a 10% chance that Lizard People aka “Reptilians” are running the

world.

3. Only about 16% of all people can wiggle their ears. Is this percent lower for millionaires? Of

the 358 millionaires surveyed, 36 could wiggle their ears. What can be concluded at the α =

0.10 level of significance?

a. For this study, we should use

b. The null and alternative hypotheses would be:

H0:

(please enter a decimal)

H1:

(Please enter a decimal)

c. The test statistic

places.)

d. The p-value =

e. The p-value is

=

(please show your answer to 3 decimal

(Please show your answer to 3 decimal places.)

α

f. Based on this, we should

g. Thus, the final conclusion is that …

the null hypothesis.

o

The data suggest the population proportion is not significantly lower than

16% at α = 0.10, so there is statistically significant evidence to conclude that

the population proportion of millionaires who can wiggle their ears is equal to

16%.

o

The data suggest the populaton proportion is significantly lower than 16%

at α = 0.10, so there is statistically significant evidence to conclude that the

population proportion of millionaires who can wiggle their ears is lower than

16%.

o

The data suggest the population proportion is not significantly lower than

16% at α = 0.10, so there is statistically insignificant evidence to conclude that

the population proportion of millionaires who can wiggle their ears is lower

than 16%.

9.5

1. Suppose a hypothesis test was performed with a level of significance of 0.05. Then if the

null hypothesis is actually true, then there is a 5% chance that the researcher will end up

accepting the alternative hypothesis in error.

•

true

•

false

2. A 2011 survey, by the Bureau of Labor Statistics, reported that 91% of Americans have paid

leave. In January 2012, a random survey of 1000 workers showed that 89% had paid leave.

The resulting p-value is 0.0271; thus, the null hypothesis is rejected. It is concluded that

there has been a decrease in the proportion of people, who have paid leave from 2011 to

January 2012.

What type of error is possible in this situation?

•

type I

•

type II

•

neither

•

both

3. A researcher looks at the mean salaries of male and female electricians and decides based

on the evidence that there is no difference between the two groups. The researcher could

have made a

in drawing this conclusion.

4. A hypothesis test was conducted to investigate whether the population mean age of college

students at Osler city is different from 21.

a) This is a

•

two-tailed test.

•

right-tailed test.

•

left-tailed test.

•

half-way test.

b) Select a correct formulation of the appropriate hypotheses:

•

H0:μ21

H1:μ≤21

•

H0:μ≠21

H1:μ=21

5. Testing:

H0:μ≥46.3

H1:μ1.75

•

z1.41

•

z>1.41

•

z

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