Question

In: Math

The University of Arkansas recently approved out of state tuition discounts for high school students from...

The University of Arkansas recently approved out of state tuition discounts for high school students from any state. The students must qualify by meeting certain standards in terms of GPA and standardized test scores. The goal of this new policy is to increase the geographic diversity of students from states beyond Arkansas and its border states. Historically, 90% of all new students came from Arkansas or a bordering state. Ginger, a student at the U of A, sampled 180 new students the following year and found that 157 of the new students came from Arkansas or a bordering state. Does Ginger’s study provide enough evidence to indicate that this new policy is effective with a level of significance 10%? What would be the correct decision?

Reject H0; conclude that the new policy does not increase the percentage of students from states that don’t border Arkansas
		Fail to reject H0; conclude that the new policy increases the percentage of students from states that don’t border Arkansas
		Reject H0; conclude that the new policy increases the percentage of students from states that don’t border Arkansas
		Fail to reject H0; conclude that the new policy does not increase the percentage of students from states that don’t border Arkansas

Solutions

Expert Solution

Solution:

Given:

Sample size = n = 180

x = Number of new students came from Arkansas or a bordering state = 157

Thus sample proportion is:

Historically, 90% of all new students came from Arkansas or a bordering state.

thus population proportion is : p = 0.90

We have to test if Ginger’s study provide enough evidence to indicate that this new policy is effective ( p > 0.90) with a level of significance 10%.

Steps:

Step 1) State H0 and H1:

H0: p = 0.90 Vs H1: p > 0.90

Step 2) Find test statistic:

Step 3) Critical value:

Since this is right tailed test, use Area =1 - = 1 - 0.10 = 0.90

Look in z table for area = 0.9000 or its closest area and find z value:

Area 0.8997 is closest to 0.9000 and it corresponds to 1.2 and 0.08

thus z critical value= 1.28

Step 4) Decision Rule:

Reject H0 , if z test statistic > z critical value= 1.28, otherwise we fail to reject H0.

Since z test statistic -1.24 < z critical value= 1.28, we fail to reject H0.

Step 5) Conclusion:

the new policy does not increase the percentage of students from states that don’t border Arkansas

Thus correct option is:
Fail to reject H0; conclude that the new policy does not increase the percentage of students from states that don’t border Arkansas.

milcah answered 1 month ago

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