Suppose a private university claims that more than 2/3 of their students graduat

Question

Suppose a private university claims that more than 2/3 of their students graduate within four years. A random survey of 300 alumni finds that 190 of them graduated within 4 years.

Given that the pair of hypotheses that correspond to the claim are:

Ho: P less than or equal to 0.67

H1: P is greater than 0.67

Find the critical value for the hypothesis test. Assume that the significance level is = 0.01.

Remember that this is a right-tailed test, so your critical value will be positive. Remember also that in one-tailed tests, you dont' have to cut your -value in half.

Explanation / Answer

To find the critical value, you must first find the Z critical.

This can be found using a probabilities table. Since the =.01, the corresponding Z critical is 2.326.

Then you use this formula to calculate the critical p value.

Z = (pc - p0)/((p0(1-p0)/n))

Then just plug in the numbers and solve for pc

2.326 = (pc - .67) / ((.67(1-.67)/300)

.06315 = (pc - .67)

pc = .733

so your critical value is .733

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