Question

Given the following Hypothesis:

  H_o: µ = 23

H₁: µ ≠ 23

If:

* a sample of n=40, mean=21 and σ =5 are given.

* Using significance level =0.05

After calculation, will the test Reject H_o or Fail to Reject H_o  and why?

Answer 1

Solution :

Given that,

= 23

= 21

= 5

n = 40

The null and alternative hypothesis is ,

H₀ :   = 23

H_a :    23

This is the two tailed test .

Test statistic = z

= ( - ) / / n

= (21 - 23) / 5 / 40

= -2.53

Test statistic = -2.53

P-value = 2 * P(z < -2.53)

= 2 * 0.0057

= 0.0114

P-value = 0.0114

= 0.05  

0.0114 < 0.05

P-value <

Reject the null hypothesis .

The test will be to Reject H_o because p-value is less than the significance level = 0.05