Utilize the 7 step method. (Or the 5 step method) A local college recently made the news by offering foreign language-speaking dorms to its students. When questioned at another school, 50 randomly-selected students from each class responded as shown. Test to see if the proportion of students favoring foreign language-speaking dorms is the same for each class at α = 0.05. FreshmenSophomoresJuniorsSeniorsFavor9171820Don't favor41333230

Answered: Utilize the 7 step method. (Or the 5…

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Utilize the 7 step method. (Or the 5 step method) A local college recently made the news by offering foreign language-speaking dorms to its students. When questioned at another school, 50 randomly-selected students from each class responded as shown. Test to see if the proportion of students favoring foreign language-speaking dorms is the same for each class at α = 0.05.

	Freshmen	Sophomores	Juniors	Seniors
Favor	9	17	18	20
Don't favor	41	33	32	30

Expert Solution

Step 1

Step 1:

The claim of the test is the proportion of students favoring foreign language-speaking dorms is the same for each class or not. The hypothesis is,

Null hypothesis:

$H_{0} :$ The proportion of students favoring foreign language-speaking dorms is the same for each class.

Alternative hypothesis:

$H_{1} :$ The proportion of students favoring foreign language-speaking dorms is different for each class.

Step 2:

The row and column totals are,

	Freshmen	Sophomores	Juniors	Seniors	Total
Favor	9	17	18	20	64
Don't favor	41	33	32	30	136
Total	50	50	50	50	200

The expected values are,

	Freshmen	Sophomores	Juniors	Seniors	Total
Favor	$\frac{64 \times 50}{200} = 16$	$\frac{64 \times 50}{200} = 16$	$\frac{64 \times 50}{200} = 16$	$\frac{64 \times 50}{200} = 16$	64
Don't favor	$\frac{136 \times 50}{200} = 34$	$\frac{136 \times 50}{200} = 34$	$\frac{136 \times 50}{200} = 34$	$\frac{136 \times 50}{200} = 34$	136
Total	50	50	50	50	200

The test statistic is,

$\begin{array}{rcl} χ^{2} & = & Sum of [\frac{{(Observed - Expected)}^{2}}{Expected}] \\ = & \frac{{(9 - 16)}^{2}}{16} + \frac{{(17 - 16)}^{2}}{16} + \frac{{(18 - 16)}^{2}}{16} + \frac{{(20 - 16)}^{2}}{16} + \frac{{(41 - 34)}^{2}}{34} + \frac{{(33 - 34)}^{2}}{34} + \frac{{(32 - 34)}^{2}}{34} + \frac{{(30 - 34)}^{2}}{34} \\ = & 3.3.063 + 0.063 + 0.250 + 1.000 + 1.441 + 0.029 + 0.118 + 0.471 \\ = & 6.434 \end{array}$

Thus, the test statistic is 6.434.

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