Question

The Ministry of Education has announced that, if there is strong evidence showing that the population proportion is 90% for private high schools recruiting new teachers, then the Ministry will also increase the recruitment of new teachers in public high schools. A survey of 70 personnel directors from private high schools revealed that 62 of them would be hiring new teachers over the next three months. At the 0.01 significance level, can we conclude that the population proportion of new recruits by private high schools is less than 90%?

a. What is the decision rule?

b.Compute the value of the test statistic.

c.What is your decision regarding the null hypothesis?

Answer 1

Solution :

Given that,

n = 70

x = 62

The null and alternative hypothesis is

H0 : p = 0.90

Ha : p < 0.90

This is left tailed test.

= x / n = 62 / 70 = 0.8857

P0 = 90% = 0.90

1 - P0 = 1 - 0.90 = 0.10

a. = 0.01   

Z  = Z0.01  = −2.33

Z < −2.33

b. Test statistic = z

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

= 0.8857 - 0.90 / [0.90 * (0.10) / 70]

= −0.398

The value of the test statistic is −0.398

c. P-value = 0.3452

= 0.01   

0.3452 > 0.01

P-value >

Fail to reject the null hypothesis .

There is not sufficient evidence to claim the test.