Answer to Question #175852 in Statistics and Probability for Anna Watson

Question

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

Answer 1

Ho: µ₁ = µ₀, (the average weight of babies is not different from 3.4kgs (µ₀))

Ha: µ₁ $\neq$ µ₀, (µ₀ =3.4kg), (the average weight of babies is different from 3.4kgs)

Level of Significance: α=0.05

Test- statistic: Z- statistics (this is because the sample size is large enough, $n\geq 30$ ). Thus we have $Z=\frac{\bar{X}-\mu_0}{\frac{s}{\sqrt{n}}}$

Tails in Distribution: Two-tailed

Reject H₀ if $Z\geq 1.960 \text{ or if } Z\leq -1.960$.

Test statistics

$Z=$ $\frac{\bar{X}-\mu_0}{\frac{s}{\sqrt{n}}}=\frac{3.1-3.4}{\frac{1.1}{\sqrt{30}}}=-1.494$

We fail to reject H₀ because $Z=-1.494>-1.960$.

We do not have statistically significant evidence at α=0.05, to show that the average weight of babies at birth is not 3.4kg.