Question

A sample of size 400 was drawn and the sample mean was found to be 99. Test whether this sample would have come from a Normal population with mean 100 and standard deviation 8 at 5% level of significance​

Answer 1

Answer:

z=2.5, reject H0

Step-by-step explanation:

there is no explanation

it's a 1 mark question

Answer 2

Answer:

No, the sample would not come from the normal population.

Step-by-step explanation:

Given that

Standard deviation $=8$

mean $=99$

population mean $=100$

n $=400$

$\alpha =5 \%$

To find:

Test whether this sample would have come from a Normal population with mean $100$ and standard deviation $8$ at $5\%$ level.​

Formula used:

$z=\left | \frac{\bar{x}-\mu }{\frac{s}{\sqrt{n}}} \right |$

Now we substitute all the values, we get

$z=\left |\frac{99-100}{\frac{8}{\sqrt{400}}} \right |\\z=\left | \frac{-1}{\frac{8}{20}} \right |\\z=2.5$

Thus,

$z_{calculated}=2.5\\z_{critical}=1.96\\z_{cal} > z_{cr}$

Therefore, the sample is not drawn from the normal population.

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Question: A random sample is taken and the sample size is $25$ .The sample is normally distributed, then sample mean is $89$, and the standard deviation is $5.5$. Find a $90\%$ confidence interval for the population mean.​

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