Question

4. Some high school teachers, teaching schools in outer islands demand an increase in meal allowance. According to a recent survey, the average cost of a meal is $6 in Ba. Suppose this figure is based on a sample of 27 different restaurants with a sample standard deviation of $1. Construct a 95% confidence interval for the population mean cost of a fast food meal in Ba. Assume that the cost of fast food meals in Ba is normally distributed. (5 marks)

Answer 1

$$Solution$$

Consider,

The mean of the population $\$6$ ,

Standard Deviation $\$1$

Sample size $27$

Therefore, for a $95\%$ Confidence interval the $Z^*-Value$ is $1.96$. The population mean cost for a fast food meal will be obtained as below,

$(1.96\times1)\div\sqrt27\\ =0.377 (this\ is\ referred\ to\ as\ the\ margin\ of\ error)$

The lower end of the interval is;

$6-0.377=5.62$

The upper end is;

$6+0.377=6.38$