Question

Determine the critical value of the problem. Show your Solution.

A researcher claims that 75% of college students would rather

spend their extra money for mobile phone loads than cigarettes.

Another researcher would like to verify this claim. She randomly

selected 400 college students. Two hundred ninety-six of these 400

student said that they would rather spend their extra money on mobile

phone loads than cigarettes. At 0.05 level of confidence, is there

enough evidence to conclude that the percentage of students who

would rather spend their extra money for mobile phone loads than

cigarettes is different from 75%?

Note: H0 = p=p0

H0 = p=.75

H1 = p ≠ .75

Solution:

Answer:

Answer 1

Solution:

$\hat p=\frac{296}{400}=0.74.$

$z=\frac{0.74-0.75}{\sqrt{\frac{0.75(1-0.75)}{400}}}=-0.46.$

Critical values: p=-1.96, p=1.96.

Answer:

Since the test statistic is greater than-1.96, fail to reject the null hypothesis.

There is no sufficient evidence that to conclude that the percentage of students who

would rather spend their extra money for mobile phone loads than

cigarettes is different from 75%.