Question

In the last decade, only 50.4% of high school students in Tampa’s school district graduated high school. Aiko believes her high school in St. Petersburg has a higher graduation rate. She collects a random sample of 54 former students of her high school and found that 33 of them graduated. Test Aiko’s belief using a significance level of 0.05.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H0 : p = 0.504

Ha : p >   0.504

n = 54

x = 33

= x / n = 33 / 54 =0.611

P0 = 0.504

1 - P0 = 1 - 0.504 = 0.496

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.611- 0.504 / [( 0.504*0.496) / 54]

= 1.57

Test statistic = z = 1.57

P(z > 1.57 ) = 1 - P(z < 1.57 ) = 1 -0.9418

P-value = 0.0582

= 0.05

P-value <

0.0582 > 0.05

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that