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 = 55 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 value of the sample test statistic? (Round your answer to two decimal places.)B  Find the P-value of the test statistic. (Round your answer to four decimal places.) C Will you reject or fail to reject the null hypothesis? Is the data statistically significant?

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Asked Jul 18, 2019
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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 = 55 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 value of the sample test statistic? (Round your answer to two decimal places.)

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

C Will you reject or fail to reject the null hypothesis? Is the data statistically significant?

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Expert Answer

Step 1

A).

State the appropriate hypothesis:

Let P be the population proportion of individuals who claim blue as their favorite color.

It is given that, about 24% of the population claim blue as their favorite color.

That is, P = 0.24.

The researcher’s objective is to test, whether or not the proportion of students who claim blue as their favorite color is 0.24.

The hypotheses are given below:

Null hypothesis:

H0 : P = 0.24

That is, the proportion of students who claim blue as their favorite color is equal to 0.24.

Alternative hypothesis:

Ha : P ≠ 0.24 (Two tailed test)

That is, the proportion of students who claim blue as their favorite color is not equal to 0.24.

Step 2

Obtain the sample proportion of students who claimed blue as their favorite color:

It is given that among a sample of 55 college students, 11 students claimed blue as their favorite color.

The number of college students surveyed is n = 55.

The number of students claimed blue as their favorite color is r = 11.

The sample proportion of students who claimed blue as their favorite color is obtained as 0.2 from the calculation given below:

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r p n 11 55 0.2

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Step 3

Obtain the test statistic value:

Here, P = 0.24 and p = 0.2.

The test statistic value is obtained...

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Under the null hypothesis p - P Z = (Px(1-P) P= 0.24 0.24 0.2 (0.24x (1-0.24)) 55 0.04 0.0576 =0.694 0.69 (Rounded to two decimal places)

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