Question

A random sample of students from a commuter college were surveyed and asked about their employment status. The results are recorded in the table below. Test the claim that the frequencies are evenly distributed throughout the categories. Use α = .05 .

# Hours per week     0-9   10-19   20-29   30-39   40+
Number of students    28     15      19      22     24

9) Express the claim in symbolic form.

Answer Choices

A) Independent

B) p_0-9 > p_10-19 > p_20-29 > p_30-39 > p₄₀₊

C) At most one proportion is different

D) p_0-9 = p_10-19 = p_20-29 = p_30-39 = p₄₀₊

E) Fewer than one proportion is different.

F) p_0-9 ≤ p_10-19 ≤ p_20-29 ≤ p_30-39 ≤ p₄₀₊

G) Dependent

H) p_0-9 ≥ p_10-19 ≥ p_20-29 ≥ p_30-39 ≥ p₄₀₊

I) More than one proportion is different.

J) p_0-9 ≠ p_10-19 ≠ p_20-29 ≠ p_30-39 ≠ p₄₀₊

K) At least one proportion is different.

L) p_0-9 < p_10-19 < p_20-29 < p_30-39 < p₄₀₊

10) What is the alternative hypothesis, H₁?

Answer choices

A) At least one proportion is different.

B) p_0-9 ≤ p_10-19 ≤ p_20-29 ≤ p_30-39 ≤ p₄₀₊

C) p_0-9 < p_10-19 < p_20-29 < p_30-39 < p₄₀₊

D) p_0-9 ≥ p_10-19 ≥ p_20-29 ≥ p_30-39 ≥ p₄₀₊

E) Independent

F) p_0-9 ≠ p_10-19 ≠ p_20-29 ≠ p_30-39 ≠ p₄₀₊

G) Fewer than one proportion is different.

H) p_0-9 = p_10-19 = p_20-29 = p_30-39 = p₄₀₊

I). At most one proportion is different.

J). More than one proportion is different.

K). p_0-9 > p_10-19 > p_20-29 > p_30-39 > p₄₀

L) Dependent

11)Find the critical value(s). (Round to the nearest thousandth. If more than one value is found, enter the smallest critical value.)

12)Find the value of the test statistic. (Round to the nearest ten-thousandth.)

13)What is the statistical conclusion?

Group of answer choices

A) Reject H₀

B) Fail to reject H₀

14) State the conclusion in words.

Group of answer choices

A) There is not sufficient sample evidence to support the claim that the frequencies are evenly distributed throughout the categories.

B) The sample data support the claim that the frequencies are evenly distributed throughout the categories.

C) There is sufficient evidence to warrant rejection of the claim that the frequencies are evenly distributed throughout the categories.

D) There is not sufficient evidence to warrant rejection of the claim that the frequencies are evenly distributed throughout the categories.

Answer 1

Answer 9.

D) p0-9 = p10-19 = p20-29 = p30-39 = p40+

Answer 10.

A) At least one proportion is different.

Answer 11.

9.488

At alpha = 0.05, and degrees of freedom = k - 1 = 4, the critical value is 9.488

Answer 12.

Test - Statistics: 8.4667

Answer 13: Fail to Reject Ho since chi-square calculated = 8.4667 < critical value = 9.488

Answer 14. C) There is sufficient evidence to warrant rejection of the claim that the frequencies are evenly distributed throughout the categories.