Question

In the United States, the populations mean height for 4-year-old boys is 39 inches. A researcher believes that non-U.S. 4-year-old boys are shorter than U.S. 4- year-old boys. Suppose a random sample of 32 non-U.S. 4-year-old boys showed a sample mean of 38.2 inches with a standard deviation of 3.1 inches. The boys were independently sampled. Assume that heights are Normally distributed in the population. Determine whether the population mean for non-U.S. boys is significantly shorter than the U.S. population mean. Use a significance level of 5%.

a)State the null and alternative hypotheses. Specify the type of test.

b)Compute the test statistic Tt

C)Use the z-table to find the P-value

D)Whether you support the claim? Show detailed comparison and explanation

Answer 1

Solution :

= 39

=38.2

S =3.1

n = 32

This is the left tailed test .

The null and alternative hypothesis is ,

H0 :    = 39

Ha : < 39

Test statistic = t

= ( - ) / S / n

= (38.2 -39) / 3.1 / 32

= -1.46

Test statistic = t =  -1.46

P-value = 0.0772

= 0.05  

P-value ≥

0.0772 ≥ 0.05

Fail to reject the null hypothesis .

Therefore, there is not enough evidence to claim that the population mean μ is less than 39, at the 0.05 significance level