Question #331323

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. 


1
Expert's answer
2022-04-21T09:47:24-0400

μ=3.4,σ=1.1,n=30,xˉ=3.1,α=0.05.μ=3.4,σ=1.1,n=30,\bar x=3.1,α=0.05.


Null and alternative hypotheses:

H0:μ=3.4;H1:μ3.4.H_0:μ=3.4;\\ H_1:μ\ne3.4.

 

Because σ is known and n=3030,n=30\ge30, we can use the z-test.

The standardized test statistic is

z=xˉμσ/n=3.13.41.1/30=1.49.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=1.49z=-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=1.49z=-1.49,

P=20.0681=0.1362.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.


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