Question

In a survey of twelve Harbor Business School graduates, the mean starting salary was $93,000, with a standard deviation of $17,000. What is the 95% confidence interval for the average starting salary among all Harvard graduates

Answer 1

Answer:
`(82198.72,\ 103801.28)`

Explanation:

Given : Sample size : n=12 , which is small sample (n<30), so we use t-test.

Sample mean :
`\overline{x}=93,000`

Standard deviation :
`s=17000`

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

Then , Critical value :
`t_(n-1,\alpha/2)=2.200985`

The formula to find the confidence interval is given by : -

`\overline{x}\pm t_(n-1,\alpha/2)(s)/(√(n))\\\\\Rightarrow\ 93000\pm (2.200985)(17000)/(√(12))\\\\\approx9,000\pm0.4011=(93000-10801.28,\ 93000+10801.28)=(82198.72,\ 103801.28)`

Hence, the 95% confidence interval for the average starting salary among all Harvard graduates =
`(82198.72,\ 103801.28)`