Question

Boys of a certain age are known to have a mean weight of μ = 85 pounds. A complaint is made that the boys living in a municipal children's home are underfed. As one bit of evidence, n = 25 boys (of the same age) are weighed and found to have a mean weight of x = 80.94 pounds. It is known that the population standard deviation σ is 11.6 pounds (the unrealistic part of this example!). Based on the available data, what should be concluded concerning the complaint?

i want a clear answer please

Answer 1

Solution :

= 85

=80.94

=11.6

n = 25

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 85

Ha :     85

Test statistic = z

= ( - ) / / n

= (80.94-85) / 11.6 / 25

= -1.75

Test statistic = z = -1.75

P(z < -1.75 ) =  0.0401

P-value = 2 *0.0401 =0.0802