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 = 54 college students were surveyed and r = 9 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.

Answer 1

Answer:

the questionnaire is incomplete, however the questions with the answers are left below and the used graph is attached

Step-by-step explanation:

a) What is the level of significance?

H0= P=0.240

Ha=p different 0.240

for 0.05 level z is 1.96

reject the null hypothesis if the absolute value of the statistical test results |z|>1.96

X=8.

n=59

Stderror=Se= √(p*(1-p)/n)=0.0556

P’= x/n= 8/59=0.136

Test stat z= ( p’-p)/Se= -1.87

P value = 0.0307

a) What is the level of significance?

significance level = 0.05

H0: p = 0.24; H1: \ neq 0.24

B. What sampling distribution will you use?

The normal standard, in this way we know that np> 5 and nq> 5.

sample test statistic value = -1.87 (try -1.88 if this goes wrong)

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

P value of test statistic = 0.0307 (try 0.0301 if this goes wrong)

Regarding the distribution of the sampling, we analyze that the upper left curve is the right

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 ? = 0.05 level, given this result it can be concluded that the data are not statistically significant and that the null hypothesis cannot be rejected

E. Interpret your conclusion in the context of the application

thus, we conclude that at a level of o.05 there is insufficient evidence to report the proportion of university students who prefer the color blue when found at 0.24