Question

In: Statistics and Probability

It is claimed that Florida’s high-school graduation rate is 77.9%. You take a random sample of...

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?

Solutions

Expert Solution

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.


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