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# Liberty BUSI 230 Week 8 Exercises 10.1-10.4 Answers Complete Solutions

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### Question 1

In general, are chi-square distributions symmetric or skewed? If skewed, are they skewed right or left?

### Question 2

The following table shows the Myers-Briggs personality preferences for a random sample of 406 people in the listed professions. E refers to extroverted and I refers to introverted.

occupation

Clegry

M.D.

Lawyer

Column Total

Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.05 level of significance.

(a) What is the level of significance?

Answer

State the null and alternate hypotheses.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

Are all the expected frequencies greater than 5?

Answer

What sampling distribution will you use?

## STATUS

Answer

What are the degrees of freedom?

(c) Find or estimate the P-value of the sample test statistic.

Answer

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?

Answer

(e) Interpret your conclusion in the context of the application.

### Question 3

The following table shows age distribution and location of a random sample of 166 buffalo in a national park.

Age

Calf

Yearling

Adult

Column Total

Use a chi-square test to determine if age distribution and location are independent at the 0.05 level of significance.

(a) What is the level of significance?

Answer

State the null and alternate hypotheses.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

Are all the expected frequencies greater than 5?

Answer

What sampling distribution will you use?

Answer

What are the degrees of freedom?

(c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)

Answer

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?

Answer

(e) Interpret your conclusion in the context of the application.

### Question 4

The following table shows the Myers-Briggs personality preference and area of study for a random sample of 519 college students. In the table, IN refers to introvert, intuitive; EN refers to extrovert, intuitive; IS refers to introvert, sensing; and ES refers to extrovert, sensing.

Myers-Briggs Preference

IN

EN

IS

ES

Column Total

Use a chi-square test to determine if Myers-Briggs preference type is independent of area of study at the 0.05 level of significance.

(a) What is the level of significance?

Answer

State the null and alternate hypotheses.

(b) Find the value of the chi-square statistic for the

Are all the expected frequencies greater than 5?

Answer

What sampling distribution will you use?

Answer

What are the degrees of freedom?

(c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)