Question-32
The average diameter of pipes manufactured by a company is reported to be 25mm, which you suspect to be too low. You observed a random sample of diameters of 10 pipes (in mm) as \(24.58, 24.67, 24.99, 25.22, 25.32, 25.25, 24.96, 24.87, 25.52, 24.85\). Based on this information, what conclusion can you reach about your suspicion at significance level of \(5\%?\)
Use \(F_{t_9}^{-1}(0.95) = 1.8331129\)
Null and alternative hypothesis will be:
\(H_0 : \mu = 25\) and \(H_1 : \mu > 25\) Here, we don’t know the population variance \(\sigma^2\). Therefore, we will use t-test.
Test will be : Reject \(H_0\) if \(\overline{X} > c\)
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.