Find a confidence interval given the mean of a sample, ,

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Question 1

A company produces vending machines which fill cups with tea. The process variance is $\var{sd[s]}$ ml.

A random sample of $\var{n}$ filled cups gives a mean of $\var{m[s]}$ ml.

a)

Calculate a $\var{confl}$ % confidence interval $(a,b)$ for the population mean:

$a=\;$ ml $b=\;$ Expected answer:ml

Enter both to 2 decimal places.

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b)

The vending machines are supposed to fill 100ml cups. Is the machine working satisfactorily?

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Expected answer:

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Advice

We use the z tables to find the confidence interval as we know the population variance.

We now calculate the $\var{confl}$ % confidence interval.

Note that $z_{\var{confl}}=\var{zval}$ and the confidence interval is given by:

$\var{m[s]} \pm z_{\var{confl}}\sqrt{\frac{\var{sd2}}{\var{n}}}$

Hence:

Lower value of the confidence interval $=\;\displaystyle \var{m[s]} -\var{zval} \sqrt{\frac{\var{sd2}} {\var{n}}} = \var{lci}$ ml to 2 decimal places.

Upper value of the confidence interval $=\;\displaystyle \var{m[s]} +\var{zval} \sqrt{\frac{\var{sd2}} {\var{n}}} = \var{uci}$ ml to 2 decimal places.

Since $\var{aim}$ lies in the confidence interval the answer is yes.

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Numbas has failed

Find a confidence interval given the mean of a sample, ,

a)

b)

Gap 0

Advice