Question

In: Statistics and Probability

In 2010 the Maricopa Community College District's enrollment data showed the following breakdown of students by...

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

_____________

Solutions

Expert Solution

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)


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