Question

You wish to test the following hypotheses at a significance level of α=0.05α=0.05.

      H0:μ=62.1
      HA:μ<62.1

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=90 with mean ¯x=60.7 and a standard deviation of s=7.6

What is the test statistic for this sample? (Report answer accurate to two decimal places.)


t=

What is the degree of freedom?

df=

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is ,

H0 :  $\mu$ = 62.1

Ha : $\mu$ <  62.1

Test statistic = t

= ($\bar x$ - $\mu$ ) / s / $\sqrt$ n

= (60.7 - 62.1) / 7.6 / $\sqrt$ 90 =  -1.75

Test statistic = t = -1.75

sample size = n = 90

Degrees of freedom = df = n - 1 = 90 - 1 = 89