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* = 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 different (either way) from
that of the general population? Use *α* = 0.05.

(b) What sampling distribution will you use?

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

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

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

D. The standard normal, 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.)

(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?

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

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

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

D. 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.

A. 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.

B. 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 #2

a)

H0 : p = 0.24

HA: p not = 0.24

This is a two taild test

b)

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

phat = 11/59 = 0.186

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

= (0.186 - 0.24)/sqrt(0.24*(1-0.24)/59)

= -0.97

c)

p value = 2 *P(z< -0.97)

= 0.3315

p value = 0.3315

d)

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

e)

B. 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.

answered by: anonymous

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,
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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...

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