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.t Suppose a random sample of n 60 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 different (either way) from that of the general population? Use a 0.05 (a) What is the level of significance? State the nul and alternate hypotheses. O Ho p 0.24; Hp 0.24 OMp: p 0.24; H,: p 0.24 O Mo p 0.24; H, p>0.24 Hgi p 0.24; H p0.24 (b) What samping distribution will you use?" The standard normal, since np <5 and ng<5 The Student's t, since np 5 and ng> 5 The standard normal, since np> 5 and ng 5 The Student's t, since np <5 and ng < 5 What is the yalue of the sample test statistic? (Round vour answer te two decimal places.) (c) Find the Pyalue of the test statistic. (Round your answer to four decimal places.)

Answer 1

Answer)

A)

Level of significance is 0.05

Ho : p = 0.24, H1 : p is not equal to 0.24

B)

N = 60 and p = 13/60

We need to check the conditions of normality, that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 13

N*(1-p) = 47

So we will use standard normal as np>5 and nq>5

Sample test statistics = (observed p - claimed p)/standard error

Standard error = √claimed p*(1-claimed p)/√n

N = 60

Claimed p = 0.24

Observed p = 13/60.

Test statistics z = -0.42

C)

From z table,p(z<-0.42) = 0.3372

But our test is two tailed, so P-Value is = 2*0.3372

= 0.6744

As our test is two tailed, so, first graph is the right answer

D)

As the obtained p-value is greater than the given significance level, we fail to reject the null hypothesis

So, at the alpha = 0.05, we fail to reject the null hypothesis and conclude that data are not statistically significant.

E)

There is insufficient evidence at the 0.05, level to conclude that the true proportion of college students differs from 0.24