Question

Using a random sample of n = 50, the sample mean is = 13.5. Suppose that the population standard deviation is σ=2.5.

Is the above statistical evidence sufficient to make the following claim μ ≠15:

?o: μ=15

??: μ ≠15

α = 0.05.

p value = 0

Interpret the results using the p value test.

Reject Ho

or

Do not reject Ho

Answer 1

Solution :

= 15

= 13.5

= 2.5

n = 50

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 15

H_a :    15

Test statistic = z

= ( - ) / / n

= (13.5 - 15) /2.5 / 50

= -4.243

P (Z < -4.243 ) =0

P-value = 0

= 0.05  

p=0 < 0.05, it is concluded that the null hypothesis is rejected.

Reject Ho

There is enough evidence to claim that the population mean μ is different than 15, at the 0.05 significance level.