Question

In a survey, 15 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $42 and standard deviation of $3. Construct a confidence interval at a 95% confidence level.

Answer 1

Answer: (40.33, 43.67)

Explanation:

Given : Sample size : n= 15<30 , which is a small sample so we use t-test.

Sample mean :
`\overline{x}=42`

Standard deviation :
`\sigma=3`

Significance level :
`\alpha: 1-0.95=0.05`

Critical value :
`t_(n-1,alpha/2)=t_(14,0.025)=2.15`

The confidence interval for population mean is given by :-

`\overline{x}\pm\ t_(n-1,\alpha/2)(\sigma)/(√(n))\\\\=42\pm(2.15)(3)/(√(15))\\\\\approx42\pm1.67\\\\=(40.33,\ 43.67)`

Hence, the 95% confidence level. interval for the population mean is (40.33, 43.67).