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 males 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 males fit the distribution of their expected majors. (Use a significance level of 0.05.) Major Men - Expected Major Men - Actual Major Art & Humanities 11.0% 600 Biological Sciences 6.7% 330 Business 22.7% 1,130 Education 5.8% 305 Engineering 15.6% 800 Physical Sciences 3.6% 175 Professional 9.3% 460 Social Sciences 7.6% 370 Technical 1.8% 90 Other 8.2% 400 Undecided 6.6% 340 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 hypothesisdo 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 males 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 males fit the distribution of their expected majors.

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 males 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 males fit the distribution of their expected majors. (Use a significance level of 0.05.) Major Men - Expected Major Men - Actual Major Art & Humanities 11.0% 600 Biological Sciences 6.7% 330 Business 22.7% 1,130 Education 5.8% 305 Engineering 15.6% 800 Physical Sciences 3.6% 175 Professional 9.3% 460 Social Sciences 7.6% 370 Technical 1.8% 90 Other 8.2% 400 Undecided 6.6% 340 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 hypothesisdo 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 males 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 males fit the distribution of their expected majors.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 males 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 males fit the distribution of their expected majors. (Use a significance level of 0.05.)

Major	Men - Expected Major	Men - Actual Major
Art & Humanities	11.0%	600
Biological Sciences	6.7%	330
Business	22.7%	1,130
Education	5.8%	305
Engineering	15.6%	800
Physical Sciences	3.6%	175
Professional	9.3%	460
Social Sciences	7.6%	370
Technical	1.8%	90
Other	8.2%	400
Undecided	6.6%	340

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 hypothesisdo 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 males 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 males fit the distribution of their expected majors.

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