Question

Given the following null hypothesis H0: µ≤22.

A sample of 10 observations is taken from a normal population. The sample mean is 17.1 and the standard deviation  5.27. Calculate the test statistic to evaluate the hypothesis. Enter your answer to 2 decimal places.

A sample of 25 observations is taken from a normal population known to have a standard deviation of 18.7. The sample mean is 45.6. Calculate the test statistic to evaluate the hypothesis µ≤48. Enter your answer to 2 decimal places.

Answer 1

Solution,

1) The null and alternative hypothesis is ,

H0 :   = 22

Ha :    22

= 17.1

s = 5.27

n = 10

Test statistic = t =

= ( - ) / s / n

= (17.1-22 ) / 5.27 / 10

Test statistic = t = -2.94

2) The null and alternative hypothesis is ,

H0 :   = 48

Ha :    48

= 45.6

= 18.7

n = 25

Test statistic = z =

= ( - ) / / n

= (45.6 - 48) / 18.7 / 25

Test statistic = z = -0.64