Question

Suppose you are testing the null hypothesis that a population mean is less than or equal to 80, against the alternative hypothesis that the population mean is greater than 80. The sample size is 49 and alpha =.05. If the sample mean is 84 and the population standard deviation is 14, the observed z value is _______.

Answer 1

Solution :

Given that,

= 80

= 84

=14

n = 49

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :   ≤ 80

H_a : >  80

Test statistic = z

= ( - ) / / n

= (84 - 80) /14 / 49

= 2

Test statistic = z = 2

P(z > 2 ) = 1 - P(z < 2 ) = 1 - 0.9772 =0.0228

P-value = 0.0228

= 0.05  

P-value <

0.0228 < 0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that