Question

A public university recently raised tuition in order to supplement the reduction in budget provided by the state. One semester after the tuition increase, a student organization contacted randomly selected students and asked whether the tuition increase was justifiable. The total number of responses was 250, of which 130 was “yes”. Test the hypothesis that more than half of the students felt the tuition increase was justifiable. Use level of significance alpha= 0.05. Write down the hypotheses: H_0: H_1: The test statistic value is: The p-value is: At alpha = 0.05, your conclusion is:

Answer #1

Solution :

This is theright tailed test .

The null and alternative hypothesis is

H0 : p = 0.50

Ha : p > 0.50

n = 250

x =130

= x / n = 130 / 250 = 0.52

P0 = 0.50

1 - P0 = 1 - 0.50

Test statistic = z

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

= 0.52 - 0.50/ [(0.50*0.50) / 250 ]

= 0.63

Test statistic = z = 0.63

P(z >0.63 ) = 1 - P(z < 0.63 ) = 1 - 0.7357

P-value = 0.2643

= 0.05

P-value >

0.2643 > 0.05

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that

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