Question

A professor claimed that a majority (more than 50%) of her students believe in ghosts. To test her claim she polled 250 students. Of those polled 145 said yes, they believe in ghosts. With a significance level of α=0.05 do these results support her claim?

What is the decision, reject the null or fail to reject the null? Is the claim supported?

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H0 : p = 0.50

Ha : p > 0.50

n =250

x =145

= x / n = 145 / 250 = 0.58

P0 = 0.50

1 - P0 = 1 - 0.50 =0.50

Test statistic = z

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

= 0.58 - 0.50 / [(0.50*0.50) / 250]

= 2.53

Test statistic = z =2.53

P(z > 2.53 ) = 1 - P(z < 2.53) = 1 - 0.9943

P-value = 0.0057

= 0.05

P-value <

0.0057 <0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that