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Education. Post-secondary educational institutions in the United States (trade schools, colleges, universities, etc.) traditionally offer four...

Education. Post-secondary educational institutions in the United States (trade schools, colleges, universities, etc.) traditionally offer four different types of degrees or certificates. The U.S. Department of Education recorded the highest degree granted by each of these institutions in the year 2003. The percentages are shown in the table below. A random sample of 300 institutions was taken in 2013 and the number of institutions in the sample for each category is also shown in the table. Conduct a hypothesis test to determine whether there has been any change from the percentages reported in 2003. Round all calculated values to four decimal places.

Highest Degree Awarded Population percentages in 2003 Sample counts in 2013
Certificate 35.0% 107
Associates 26.6% 72
Bachelor's 11.3% 37
Graduate 27.1% 84

a. Enter the expected values for the hypothesis test in the table below.

Highest Degree Awarded Expected value
Certificate
Associates
Bachelor's
Graduate

b. Calculate the test statistic for this hypothesis test.  ? z t X^2 F  =

c. Calculate the degrees of freedom for this hypothesis test.

d. Calculate the p-value for this hypothesis test. p-value =

e. What is your conclusion using αα = 0.01?

A. Reject H0H0
B. Do not reject H0H0

Solutions

Expert Solution

Solution:

Given:

A random sample of 300 institutions was taken in 2013 and the number of institutions in the sample for each category is also shown in the table. Conduct a hypothesis test to determine whether there has been any change from the percentages reported in 2003

Highest Degree Awarded Population percentages in 2003 Sample counts in 2013
Certificate 35.00% 107
Associates 26.60% 72
Bachelor's 11.30% 37
Graduate 27.10% 84
100.00%                             N=300

Part a) nter the expected values for the hypothesis test in the table below.

Multiply each population percentage by N = 300

Highest Degree Awarded Expected value
Certificate 105
Associates 79.8
Bachelor's 33.9
Graduate 81.3

b. Calculate the test statistic for this hypothesis test.  ?

We use Chi-square test of goodness of fit test.

Highest Degree Awarded Sample counts in 2013 Oi Expected value Ei Oi^2/Ei
Certificate 107 105 109.0381
Associates 72 79.8 64.96241
Bachelor's 37 33.9 40.38348
Graduate 84 81.3 86.78967
                     300 301.1736

Thus

c. Calculate the degrees of freedom for this hypothesis test.

df = k - 1 = 4 - 1 = 3

d. Calculate the p-value for this hypothesis test. p-value =

Use excel command:

=CHISQ.DIST.RT( x , df)

=CHISQ.DIST.RT( 1.1736 , 3)

=0.7593

Thus p-value = 0.7593

e. What is your conclusion using α= 0.01?

Since p-value = 0.7593 > 0.01 level of significance , we do not reject H0

Thus correct option is B. Do not reject H0

milcah answered 5 months ago
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