Question

1. In the united states the population mean height for 4 year old boys is 39 inches, Suppose a random sample of 32 NON -US  4 year old boys showed a sample mean of 38.2 inches with a standard deviation of 3.1inches. The boys were independently sampled. Assume the heights are normally distributed in the population. Determine weather the population mean for non us boys is significantly different from the US population mean, use a significance level of 5%

Answer 1

Solution :

= 39

= 38.2

s = 3.1

n = 32

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 39

H_a :    39

Test statistic = t

= ( - ) / s/ n

= (38.2 - 39) /3.1 / 32

= -1.46

P(z < -1.46 ) = 0.1544

P-value = 0.1544

= 0.05  

p = 0.1544 ≥ 0.05, it is concluded that the null hypothesis is not rejected.

There is not enough evidence to claim that the population mean μ is different than 39, at the 0.05 significance level.