Question

A student believes that no more than 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 recieved A's. Using the critical value approach, test the hypotheses at the 1% level of significance.

Answer 1

Solution :

Given that,

n = 100

= 24% = 0.24

Hypothesis:

H0 : P 0.20   

Ha : P 0.20

Test Statistic:

Z =   - P / ( ((P * (1 - P)) / n)

  Z = 0.24 - 0.20 / ( ((0.20* 0.80) / 100)

Z = 1

Z = 1

P-value = 0.1587

P-value > 0.01 ,so fail to reject H0

d.) Fail to Reject the null hypothesis. there is not enough evidence to support the claim.