What is your favorite color? A large survey of countries, including the United S

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 = 57 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 = 0.05.

(a) What is the level of significance?


State the null and alternate hypotheses.

H0: p = 0.24; H1: p > 0.24H0: p = 0.24; H1: p < 0.24    H0: p = 0.24; H1: p 0.24H0: p 0.24; H1: 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 Student's t, since np < 5 and nq < 5.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.)


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 ?

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

Explanation / Answer

Given that,
possibile chances (x)=10
sample size(n)=57
success rate ( p )= x/n = 0.1754
success probability,( po )=0.24
failure probability,( qo) = 0.76
null, Ho:p=0.24
alternate, H1: p!=0.24
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.17544-0.24/(sqrt(0.1824)/57)
zo =-1.1413
| zo | =1.1413
critical value
the value of |z | at los 0.05% is 1.96
we got |zo| =1.141 & | z | =1.96
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -1.1413 ) = 0.25375
hence value of p0.05 < 0.2537,here we do not reject Ho
ANSWERS
---------------
null, Ho:p=0.24
alternate, H1: p!=0.24
test statistic: -1.1413
critical value: -1.96 , 1.96
decision: do not reject Ho
p-value: 0.25375

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

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.