UCLA conducted a survey of more than 263,000 college freshmen from 385 colleges in fall 2005. The results of students' expected majors by gender were reported in The Chronicle of Higher Education (2/2/2006). Suppose a survey of 5,000 graduating females and 5,000 graduating males was done as a follow-up last year to determine what their actual majors were. The results for females are shown in the table below. The second column in the table does not add to 100% because of rounding.

Conduct a goodness-of-fit test to determine if the actual college majors of graduating females fit the distribution of their expected majors. (Use a significance level of 0.05.)

Major Women - Expected Major Women - Actual Major

Art & Humanities 14.0% 670

Biological Sciences 8.4% 410

Business 13.1% 685

Education 13.0% 650

Engineering 2.6% 145

Physical Sciences 2.6% 125

Professional 18.9% 975

Social Sciences 13.0% 605

Technical 0.4% 15

Other 5.8% 300

Undecided 8.0% 420

Part (a)

State the null hypothesis.
The actual college majors of graduating females and their expected majors are independent events.

The distributions of the actual college majors of graduating females and their expected majors are the same.

  The actual college majors of graduating females and their expected majors are dependent events.

The actual college majors of graduating females fit the distribution of their expected majors.

The actual college majors of graduating females do not fit the distribution of their expected majors.

Part (b)

State the alternative hypothesis.
The actual college majors of graduating females and their expected majors are independent events.

The actual college majors of graduating females and their expected majors are dependent events.

The actual college majors of graduating females do not fit the distribution of their expected majors.

The distributions of the actual college majors of graduating females and their expected majors are not the same.

The actual college majors of graduating females fit the distribution of their expected majors.

Part (c)

What are the degrees of freedom? (Enter an exact number as an integer, fraction, or decimal.)

Part (d)

State the distribution to use for the test.

t₁₁

t₁₀

?²₁₁

?²₁₀

Part (e)

What is the test statistic? (Round your answer to two decimal places.)

Part (f)

What is the p-value? (Round your answer to four decimal places.)

Explain what the p-value means for this problem.
If H₀ is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.If H₀
is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value.    If H₀
is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value.If H₀ is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.

Part (g)

Sketch a picture of this situation. Label and scale the horizontal axis, and shade the region(s) corresponding to the p-value.

Part (h)

Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write the appropriate conclusion.
(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)
? =

(ii) Decision:
reject the null hypothesis

do not reject the null hypothesis

(iii) Reason for decision:
Since ? > p-value, we reject the null hypothesis.Since ? < p-value, we reject the null hypothesis.    Since ? > p-value, we do not reject the null hypothesis.Since ? < p-value, we do not reject the null hypothesis.

(iv) Conclusion:
There is sufficient evidence to warrant a rejection of the claim that the distribution of actual college majors of graduating females fit the distribution of their expected majors.

There is not sufficient evidence to warrant a rejection of the claim that the distribution of actual college majors of graduating females fit the distribution of their expected majors.

Question

UCLA conducted a survey of more than 263,000 college freshmen from 385 colleges in fall 2005. The results of students' expected majors by gender were reported in The Chronicle of Higher Education (2/2/2006). Suppose a survey of 5,000 graduating females and 5,000 graduating males was done as a follow-up last year to determine what their actual majors were. The results for females are shown in the table below. The second column in the table does not add to 100% because of rounding.

Conduct a goodness-of-fit test to determine if the actual college majors of graduating females fit the distribution of their expected majors. (Use a significance level of 0.05.)

Major	Women - Expected Major	Women - Actual Major
Art & Humanities	14.0%	670
Biological Sciences	8.4%	410
Business	13.1%	685
Education	13.0%	650
Engineering	2.6%	145
Physical Sciences	2.6%	125
Professional	18.9%	975
Social Sciences	13.0%	605
Technical	0.4%	15
Other	5.8%	300
Undecided	8.0%	420

Part (a)

State the null hypothesis.
The actual college majors of graduating females and their expected majors are independent events.

The distributions of the actual college majors of graduating females and their expected majors are the same.

The actual college majors of graduating females and their expected majors are dependent events.

The actual college majors of graduating females fit the distribution of their expected majors.

The actual college majors of graduating females do not fit the distribution of their expected majors.
Part (b)

State the alternative hypothesis.
The actual college majors of graduating females and their expected majors are independent events.

The actual college majors of graduating females and their expected majors are dependent events.

The actual college majors of graduating females do not fit the distribution of their expected majors.

The distributions of the actual college majors of graduating females and their expected majors are not the same.

The actual college majors of graduating females fit the distribution of their expected majors.
Part (c)

What are the degrees of freedom? (Enter an exact number as an integer, fraction, or decimal.)
Part (d)

State the distribution to use for the test.

t₁₁

t₁₀

?²₁₁

?²₁₀
Part (e)

What is the test statistic? (Round your answer to two decimal places.)
Part (f)

What is the p-value? (Round your answer to four decimal places.)

Explain what the p-value means for this problem.
If H₀ is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.If H₀
is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value. If H₀
is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value.If H₀ is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.
Part (g)

Sketch a picture of this situation. Label and scale the horizontal axis, and shade the region(s) corresponding to the p-value.
Part (h)

Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write the appropriate conclusion.
(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)
? =

(ii) Decision:
reject the null hypothesis

do not reject the null hypothesis

(iii) Reason for decision:
Since ? > p-value, we reject the null hypothesis.Since ? < p-value, we reject the null hypothesis.    Since ? > p-value, we do not reject the null hypothesis.Since ? < p-value, we do not reject the null hypothesis.

(iv) Conclusion:
There is sufficient evidence to warrant a rejection of the claim that the distribution of actual college majors of graduating females fit the distribution of their expected majors.

There is not sufficient evidence to warrant a rejection of the claim that the distribution of actual college majors of graduating females fit the distribution of their expected majors.

Accepted Answer

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