## Related questions with answers

Some students checked 6 bags of Doritos marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the following weights (in grams): 29.2, 28.5, 28.7, 28.9, 29.1, 29.5.

Create a 95% confidence interval for the mean weight of such bags of chips.

Solution

VerifiedGiven:

$\begin{align*} n&=\text{Sample size}=6 \\ c&=\text{Confidence level}=95\%=0.95 \end{align*}$

### Descriptive measures

The mean is the sum of all values divided by the number of values:

$\overline{x}=\dfrac{29.2+28.5+28.7+28.9+29.1+29.5}{6}=\dfrac{174.2}{6}\approx 29.0333$

$n$ is the number of values in the data set.

$n=6$

The variance is the sum of squared deviations from the mean divided by $n-1$. The standard deviation is the square root of the variance:

$s=\sqrt{\dfrac{(29.2-29.0333)^2+....+(29.5-29.0333)^2}{6-1}}\approx 0.4131$

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