Answer to Question #331323 in Statistics and Probability for chelsea ann castro

Question

It is claimed that the average weight of babies at birth is 3.4 kg. The average weight of a random sample of 30 newly born babies was determined. It was found out that the average weight was 3.1 kg. Is there a reason to believe that the average weight of babies at birth is not 3.4 kg? Assume that the population standard deviation is 1.1 kg. Use 0.05 level of significance. 

Answer 1

$μ=3.4,σ=1.1,n=30,\bar x=3.1,α=0.05.$

Null and alternative hypotheses:

$H_0:μ=3.4;\\ H_1:μ\ne3.4.$

 

Because σ is known and $n=30\ge30,$ we can use the z-test.

The standardized test statistic is

$z=\cfrac{\bar x-\mu}{\sigma/\sqrt n}=\cfrac{3.1-3.4}{1.1/\sqrt {30}}=-1.49.$

In z-table the area corresponding to $z=-1.49$ is 0.0681. Because the test is a two-tailed test, the P-value is equal to twice the area to the left of $z=-1.49$,

$P=2\cdot0.0681=0.1362.$

Because the P-value is greater than α = 0.05, we fail to reject the null hypothesis, there is not enough evidence at the 5% level of significance to support the claim that the average weight of babies at birth is not 3.4 kg.