Question

In a survey, 32 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $45 and standard deviation of $19. Construct a confidence interval at a 80% confidence level.

Give your answers to one decimal place.

Answer 1

{40.7,49.3}

Explanation:

`\displaystyle CI=\bar{x}\pm z(s)/(√(n))\\\\CI_(80\%)=45\pm1.282\biggr((19)/(√(32))\biggr)\\ \\CI_(80\%)\approx45\pm 4.3\\\\CI_(80\%)=\{40.7,49.3\}`

Thus, we are 80% confident that the true sample mean amount spent is between $40.70 and $49.30