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 = 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. (a) What is the level of significance? 0.05 Correct: Your answer is correct. State the null and alternate hypotheses. H0: p = 0.24; H1: p > 0.24 H0: p = 0.24; H1: p ≠ 0.24 H0: p ≠ 0.24; H1: p = 0.24 H0: p = 0.24; H1: p < 0.24 Correct: Your answer is correct. (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. Correct: Your answer is correct. What is the value of the sample test statistic? (Round your answer to two decimal places.) -0.04 Incorrect: Your answer is incorrect. (c) Find the P-value of the test statistic. (Round your answer to four decimal places.) 0.24 Incorrect: Your answer is incorrect.

Answer 1

a)α=0.05

Ho :   p =    0.24
H1 :   p ╪   0.24

b) The standard normal, since np > 5 and nq > 5

Number of Items of Interest,   x =   11                  
Sample Size,   n =    54                  
                          
Sample Proportion ,    p̂ = x/n =    0.2037                  
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.0581                  
Z Test Statistic = ( p̂-p)/SE = (   0.2037   -   0.24   ) /   0.0581   =   -0.62

c)

p-Value   =   0.5323