Question

A student believes that no more than 20% (i.e., 20%) of the students who finish a statistics course get an A. A random sample of 100 students was taken. Twenty-four percent of the students in the sample received A's. Using the critical value approach, test the hypotheses at the 1% level of significance.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H0 : p = 0.20

Ha : p > 0.20

= 0.24

n = 100

P0 = 0.20

1 - P0 = 1 -0.20 =0.80

= 0.01

The right tailed test critical value is = 2.326

z < 2.326

Test statistic = z

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

=0.24 -0.20 / [0.20*(0.80) /100 ]

= 1

P(z > 1 ) = 1 - P(z < 1 ) = 0.1587

P-value = 0.1587

= 0.01

0.1587 > 0.01

Do not reject the null hypothesis .

There is insufficient evidence to suggest that