Question

Children of a certain age are known to have a mean weight of 85 pounds. A complaint is

made that the children living in a municipal home are overfed. As one bit of evidence, 25

randomly selected children are weighed and found to have a mean weight of 87 pounds. It is

known that the population standard deviation is 11.6 pounds. Is there convincing evidence

at 0.05 significance level that mean weight of the children is greater than 85 pounds?

Hypothesis:

Significance Level:

Test Statistics:

P-value:

Conclusion:

Answer 1

The null and alternative hypothesis

85

> 85

(Note : This is a right tailed test as the alternative hypothesis is

Test statistic

   

= 0.86

degrees of freedom = n-1 = 25-1 =24

P value = 0.1991

Note : excel formula for P value "=T.DIST.RT(0.86,24)"

Since P value > 0.05

Conclusion :

Fail to reject H0 .There is not sufficient evidence to support the claim that children living in municipal home are overfed .

Note Though population standard deviation is given , we use t distribution as sample size is small (n< 30) , and  we use value of in place of s .