Question

The accompanying data represent the actual amount poured (in ml) into a short, wide glass for bartenders who were asked to pour 44.3 ml (1.5 ounces). 89.4 68.6 32.8 37.3 39.9 46.7 66.2 79.1 66.3 52.3 47.3 64.1 53.9 63.4 46.2 63.0 92.2 57.8 (a) Compute the values of the mean and standard deviation. (Round your answers to three decimal places.) mean ml standard deviation ml Interpret the values of the mean and standard deviation. (Round your answers to three decimal places.) A typical amount poured into a short, wide glass is ml. A typical deviation from the mean amount poured is ml. (b) The mean amount poured into a tall, slender glass for bartenders who were asked to pour 44.3 ml (1.5 ounces) was 51.333 ml. What do the values of the mean amount poured in the short, wide glass and the mean amount poured in the tall, slender glass suggest about the shape of glasses used? The mean amount for a short, wide glass is the mean amount for a tall, slender glass. This suggests that bartenders tend to pour into a short, wide glass compared to a tall, slender glass.

Answer 1

a) mean 59.25, standard deviation 16.688

b) The mean amount for a short, wide glass is less than the mean amount for a tall, slender glass. This suggests that bartenders tend to pour less amount into a short, wide glass compared to a tall, slender glass.

Explanation:

The size of the sample is n = 18

Let
`x_i` be the value of each sample, then the mean is

`\bar x=(\sum_(i=1)^(18)x_i)/(18)=(1066.5)/(18)=59.25`

and the standard deviation is

`s=\sqrt{(\sum_(i=1)^(18)(x_i- \bar x)^2)/(n-1)}=\sqrt{(4734.445)/(17)}=16.688`

if the mean amount poured into a tall, slender glass for bartenders who were asked to pour 44.3 ml (1.5 ounces) was 51.333 ml, then the mean amount for a short, wide glass is less than the mean amount for a tall, slender glass.

This suggests that bartenders tend to pour less amount into a short, wide glass compared to a tall, slender glass.