Question

Statistics question; please help.

Answer 1

Answer:

Does this sample provide convincing evidence that the machine is working properly?

Yes.

Step-by-step explanation:

Normal distribution test:

$z=\frac{x- \mu }{ \frac{\sigma}{\sqrt{n}} }=\frac{ (x-\mu)\sqrt{n}}{\sigma}$

Where,

$x: \text{ sample mean}$

$\sigma: \text{ standard deviation}$

$n: \text{ sample size determination}$

$\mu: \text{ hypothesized size of the screw}$

$z=\frac{(1.476-1.5)\sqrt{200} }{0.203 }$

$z=\frac{(-0.024)10\sqrt{2} }{0.203 }$

$z \approx -1.672$

Once the significance level was not given, It is usually taken an assumption of a 5% significance level.

Taking the significance level of 5%, which means a confidence level of 95%, we have a z-value of $\pm 1.96$

Therefore, we fail to reject the null. It means that the hypothesis test is not statistically significant: the average length is not different from 1.5!