Question

. A random sample of 17 American marriages found that their mean length was 9.4 years with a standard deviation of 8.1 years. (a) At the 5% level of significance can we conclude that the mean length of all American marriages is less than 10 years? State and test appropriate hypotheses. State conclusions. (b) What assumption is needed for the above analysis to be appropriate?

Answer 1

Solution :

= 10

=9.4

S =8.1

n = 17

This is the left tailed test .

The null and alternative hypothesis is ,

H0 :    = 10

Ha : < 10

Test statistic = t

= ( - ) / S / n

= (9.4-10) / 8.1 / 17

= −0.305

Test statistic = t =−0.305  

P-value =0.3820

a ) = 0.05  

P-value ≥

0.3820 ≥ 0.05

b ) Fail to reject the null hypothesis .

There is insufficient evidence to suggest that