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In-s [12.5K]
3 years ago
12

Statistics question; please help.

Mathematics
1 answer:
Alex_Xolod [135]3 years ago
7 0

Answer:

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

Yes.

Step-by-step explanation:

<u>Normal distribution test:</u>

$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 <u>fail to reject the null</u>. It means that the hypothesis test is not statistically significant: the average length is not different from 1.5!

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