1. State hypotheses by filling in the symbol (=,<,>, or not equal) and the popul

Question

1. State hypotheses by filling in the symbol (=,<,>, or not equal) and the population mean and determine if one or two tail:

2. Find critical z values is:

3. Z test value is:

4. Reject the null or do not reject the null:

5. Conclusion: is or is not enough evidence

It has been found that 85.6% of all enrolled college and university students in the United States are undergraduates. A random sample of 494 enrolled college students in a particular state revealed that 436 of them were undergraduates. Is there sufficient evidence to conclude that the proportion differs from the national percentage? Use -0.05.

Explanation / Answer

1.

Ho : p =.856
Ha : p !=.856

p = x/n = 436/494 = .8826

2. Critical Z value is 1.96 corresponding to alpha =.05

3. Z test value is (p-p0)/sqrt(p0*p0'/n) = (.8826-.856)/sqrt(.856*.144/494) = 1.684

4. We fail to reject H0, as Z test value < Z critical value.

5. There is not enough evidence that the proportion differ from national %age

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