Answer to Question #322467 in Statistics and Probability for Kim

Question

It is claimed that the average weight of babies at birth is 3.4 kg. The average weight of the 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 the 0.05 level of significance

1) What are the null hypotheses and alternative hypotheses of the research scenario?

2) What is the level of significance?

3) What is the test statistic?

4) What is the critical value in the scenario?

5) What could be the conclusion?

Answer 1

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

Ha: $\mu_1 \not= \mu_0$ (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≥30 ). Thus we have

$Z=\frac{x-\mu}{\frac{s}{\sqrt{n}}}$

Tails in Distribution: Two-tailed

Reject H0 if $(Z \ge 1.96)$ or if $(Z \le -1.96)$

Test statistics

$Z=\frac{3.1-3.4}{\frac{1.1}{\sqrt{30}}}=-1.494$

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.