In: Statistics and Probability
It is claimed that Florida’s high-school graduation rate is 77.9%. You take a random sample of 300 Florida high-school seniors and discover that 41 of them withdrew during the year. At α=0.05, is there enough evidence to reject the claim?
Solution :
Given that,
= 0.779
1 - = 0.221
n = 300
x = 41
Level of significance = = 0.05
Point estimate = sample proportion = = x / n = 41/300 = 0.137
This a two tailed test.
A)
Ho: p = 0.779
Ha: p 0.779
Test statistics
z = ( - ) / *(1-) / n
= ( 0.137 - 0.779) / (0.779*0.0.221) / 300
= -26.81
p-value = 2* P(Z < z )
= 2* P(Z -26.81)
= 2*0
= 0
The p-value is p = 0.0, and since p = 0 < 0.05, it is concluded that the null hypothesis is rejected.
Conclusion:
It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population
proportion p is different than , at the 0.05 level of significance.