Question

In 2010 the Maricopa Community College District's enrollment data showed the following breakdown of students by ethnicity: 54.9% White; 21.1% Hispanic; 7.9% Black; 4.5% Asian/Pacific Islander; 2.9% Native American; 8.8% Other. Information was collected from a random sample of 300 students in 2017 to determine whether or not the data has changed significantly. The sample data is given in the table below. At the alph=0.05 level of significance, test the claim that the ethnic breakdown of students at MCCCD has not changed significantly since 2010.

Which would be the correct hypothesis for this test?

H0: u1 = u2; H1: u1 ≠ u2

H0: p1 = p2; H1: p1 ≠ p2

H0: The breakdown of students by ethnicity has not changed significantly since 2010 (i.e. the given distribution still fits); H1: The breakdown of students by ethnicity has changed significantly since 2010 (i.e. the given distribution no longer fits)

H0: The breakdown of students by ethnicity has changed significantly since 2010 (i.e. the given distribution no longer fits); H1: The breakdown of students by ethnicity has not changed significantly since 2010 (i.e. the given distribution still fits)

Ethnicity of students in sample:

White - 160

Hispanic - 89

Black - 25

Asian/Pacific Islander - 11

Native American - 15

Other - 0

Test Statistic:

______________

Give the P-value

_____________

Answer 1

Solution:

   Given: In 2010 the Maricopa Community College District's enrollment data showed the following breakdown of students by ethnicity: 54.9% White; 21.1% Hispanic; 7.9% Black; 4.5% Asian/Pacific Islander; 2.9% Native American; 8.8% Other.

We have to test the claim that the ethnic breakdown of students at MCCCD has not changed significantly since 2010.

Level of significance =

Part a) Which would be the correct hypothesis for this test?

H0: The breakdown of students by ethnicity has not changed significantly since 2010 (i.e. the given distribution still fits);

H1: The breakdown of students by ethnicity has changed significantly since 2010 (i.e. the given distribution no longer fits)

Part b)

Given:

Ethnicity of students in sample:

White - 160

Hispanic - 89

Black - 25

Asian/Pacific Islander - 11

Native American - 15

Other - 0

We have to find test statistic:

where Oi = Observed frequencies and Ei = Expected frequencies.

To get Ei, we multiply given % values by N = 300

Thus we need to make following table:

Ethnicity of students	Expected %	Ei	Oi	Oi^2 /Ei
White	54.90%	164.7	160	155.434
Hispanic	21.10%	63.3	89	125.134
Black	7.90%	23.7	25	26.371
Asian/Pacific	4.50%	13.5	11	8.963
Naive American	2.90%	8.7	15	25.862
Other	8.80%	26.4	0	0.000
			N=300

Thus Chi-square test statistic is:

Test statistic =

Part c) P-value:

df = k -1 = 6 - 1 = 5

Use excel command:

=CHISQ.DIST.RT( x , df)

where x = and df = 5

Thus

=CHISQ.DIST.RT( 41.765 , 5 )

= 0.0000

Thus P-value= 0.0000

Conclusion: Since P-value = 0.0000 < 0.05 level of significance, hence we reject H0 and conclude that: The breakdown of students by ethnicity has changed significantly since 2010 (i.e. the given distribution no longer fits)