Question-33
Chisq-Test
The weight of new born babies in a town is reported to have a standard deviation of \(0.25\) kg, which you suspect is too low. A sample of 10 newborn babies had weights(in kg) as \(2.25, 2.5, 3, 2.75, 2.40, 2.20, 3.10, 2.50, 2.80, 2.75\). Based on this information, what conclusion can you reach about your suspicion at significance level of \(5\%?\)
Use \(F_{\chi^2_9}^{-1}(0.95) = 16.918977\)
Hint
Null and alternative hypothesis will be:
\(H_0 : \sigma = 0.25\) and \(H_1 : \sigma > 0.25\)
Test will be : Reject \(H_0\) if \(S^2 > c^2\), where \(S^2\) is the sample variance of the given dataset.
Use \(\alpha = P\left(\text{Reject}~~ H_0 ~|~ H_0 \right)\).
Find the value of \(c\) by solving the above part and then make conclusion.
Answer
Solution