Question

The local paper stated that in 2006, 75% of Florida high school graduates went on to four year higher education institutions. A sample of 210 Florida graduates from the class of 2015 found that 140 were accepted into four year institutions. Does this suggest that todays rate is different. Use alpha=0.05.

If you cant conduct the test, because of unmet assumptions, state the condition that was not met.

Ho:

H1:

Test statistic:

Critical value:

P value:

Conclusion:

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.75
Alternative Hypothesis, Ha: p ≠ 0.75

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.6667 - 0.75)/sqrt(0.75*(1-0.75)/210)
z = -2.79

Rejection Region
This is two tailed test, for α = 0.05
Critical value of z are -1.96 and 1.96.
Hence reject H0 if z < -1.96 or z > 1.96

P-value Approach
P-value = 0.0053
As P-value < 0.05, reject the null hypothesis.

Sufficient evidence to conclude that the proportion is different than 0.75