Question

What is your favorite color? A large survey of countries,
including the United States, China, Russia, France, Turkey, Kenya,
and others, indicated that most people prefer the color blue. In
fact, about 24% of the population claim blue as their favorite
color.† Suppose a random sample of *n* = 52 college students
were surveyed and *r* = 10 of them said that blue is their
favorite color. Does this information imply that the color
preference of all college students is different (either way) from
that of the general population? Use *α* = 0.05.

(a) What is the level of significance?

State the null and alternate hypotheses.

*H*_{0}: *p* = 0.24;
*H*_{1}: *p* ≠ 0.24

*H*_{0}: *p* = 0.24;
*H*_{1}: *p* >
0.24

*H*_{0}: *p* ≠ 0.24;
*H*_{1}: *p* = 0.24

*H*_{0}: *p* = 0.24;
*H*_{1}: *p* < 0.24

(b) What sampling distribution will you use?

The Student's *t*, since *np* > 5 and
*nq* > 5.

The standard normal, since *np* < 5 and *nq*
< 5.

The standard normal, since *np* > 5 and *nq*
> 5.

The Student's *t*, since *np* < 5 and
*nq* < 5.

What is the value of the sample test statistic? (Round your answer
to two decimal places.)

(c) Find the *P*-value of the test statistic. (Round your
answer to four decimal places.)

Sketch the sampling distribution and show the area corresponding to
the *P*-value.

(d) Based on your answers in parts (a) to (c), will you reject or
fail to reject the null hypothesis? Are the data statistically
significant at level *α*?

At the *α* = 0.05 level, we reject the null hypothesis
and conclude the data are statistically significant.

At the *α* = 0.05 level, we reject the null hypothesis
and conclude the data are not statistically
significant.

At the *α* = 0.05 level, we fail to reject the null
hypothesis and conclude the data are statistically significant.

At the *α* = 0.05 level, we fail to reject the null
hypothesis and conclude the data are not statistically
significant.

(e) Interpret your conclusion in the context of the
application.

There is sufficient evidence at the 0.05 level to conclude that the true proportion of college students favoring the color blue differs from 0.24.

There is insufficient evidence at the 0.05 level to conclude that the true proportion of college students favoring the color blue differs from 0.24.

Answer #1

a)

α = 0.05

Below are the null and alternative Hypothesis,

Null Hypothesis, H0: p = 0.24

Alternative Hypothesis, Ha: p ≠ 0.24

b)

The standard normal, since np > 5 and nq > 5.

Test statistic,

z = (pcap - p)/sqrt(p*(1-p)/n)

z = (0.1923 - 0.24)/sqrt(0.24*(1-0.24)/52)

z = -0.81

c)

P-value Approach

P-value = 0.4179

shaded area in both tails

d)

As P-value >= 0.05, fail to reject null hypothesis.

At the α = 0.05 level, we fail to reject the null hypothesis and
conclude the data are not statistically significant.

e)

There is insufficient evidence at the 0.05 level to conclude that
the true proportion of college students favoring the color blue
differs from 0.24.

What is your favorite color? A large survey of countries,
including the United States, China, Russia, France, Turkey, Kenya,
and others, indicated that most people prefer the color blue. In
fact, about 24% of the population claim blue as their favorite
color.† Suppose a random sample of n = 58 college students
were surveyed and r = 13 of them said that blue is their
favorite color. Does this information imply that the color
preference of all college students is...

What is your favorite color? A large survey of countries,
including the United States, China, Russia, France, Turkey, Kenya,
and others, indicated that most people prefer the color blue. In
fact, about 24% of the population claim blue as their favorite
color.† Suppose a random sample of n = 59 college students
were surveyed and r = 11 of them said that blue is their
favorite color. Does this information imply that the color
preference of all college students is...

USA Today reported that about 47% of the general
consumer population in the United States is loyal to the automobile
manufacturer of their choice. Suppose Chevrolet did a study of a
random sample of 1006 Chevrolet owners and found that 488 said they
would buy another Chevrolet. Does this indicate that the population
proportion of consumers loyal to Chevrolet is more than 47%? Use
α = 0.01.
(a) State the null and alternate hypotheses. (Pick one)
H0: p = 0.47;...

Professor Jennings claims that only 35% of the students at Flora
College work while attending school. Dean Renata thinks that the
professor has underestimated the number of students with part-time
or full-time jobs. A random sample of 82 students shows that 37
have jobs. Do the data indicate that more than 35% of the students
have jobs? Use a 5% level of significance.
(a) State the null and alternate hypotheses. Options:
H0: μ = 0.35; H1: μ <
0.35
H0:...

USA Today reported that about 47% of the general
consumer population in the United States is loyal to the automobile
manufacturer of their choice. Suppose Chevrolet did a study of a
random sample of 1004 Chevrolet owners and found that 482 said they
would buy another Chevrolet. Does this indicate that the population
proportion of consumers loyal to Chevrolet is more than 47%? Use
α = 0.01.
(a) What is the level of significance?
State the null and alternate hypotheses....

USA Today reported that about 47% of the general
consumer population in the United States is loyal to the automobile
manufacturer of their choice. Suppose Chevrolet did a study of a
random sample of 1001 Chevrolet owners and found that 483 said they
would buy another Chevrolet. Does this indicate that the population
proportion of consumers loyal to Chevrolet is more than 47%? Use
α = 0.01.
(a) What is the level of significance?
State the null and alternate hypotheses....

Professor Jennings claims that only 35% of the students at Flora
College work while attending school. Dean Renata thinks that the
professor has underestimated the number of students with part-time
or full-time jobs. A random sample of 76 students shows that 36
have jobs. Do the data indicate that more than 35% of the students
have jobs? Use a 5% level of significance.
What are we testing in this problem?
single mean
single proportion
(a) What is the level of...

Professor Jennings claims that only 35% of the students at Flora
College work while attending school. Dean Renata thinks that the
professor has underestimated the number of students with part-time
or full-time jobs. A random sample of 84 students shows that 40
have jobs. Do the data indicate that more than 35% of the students
have jobs? Use a 5% level of significance. What are we testing in
this problem? single mean single proportion (a) What is the level
of...

USA Today reported that about 47% of the general
consumer population in the United States is loyal to the automobile
manufacturer of their choice. Suppose Chevrolet did a study of a
random sample of 1003 Chevrolet owners and found that 481 said they
would buy another Chevrolet. Does this indicate that the population
proportion of consumers loyal to Chevrolet is more than 47%? Use
α = 0.01.
(a) What is the level of significance?
State the null and alternate hypotheses....

USA Today reported that about 47% of the general
consumer population in the United States is loyal to the automobile
manufacturer of their choice. Suppose Chevrolet did a study of a
random sample of 1003 Chevrolet owners and found that 486 said they
would buy another Chevrolet. Does this indicate that the population
proportion of consumers loyal to Chevrolet is more than 47%? Use
α = 0.01.
(a) What is the level of significance?
State the null and alternate hypotheses....

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