Question

Suppose that the standard deviation of the collected data from 144 alumni is $3k and the mean is $58k, please estimate the confidence interval of the population’s average salary (Hint: Hypothesis Testing and Confidence Interval - One sample; sample standard deviation is known)

Answer 1

as no confidence level is mentioned , i am using 95% confidence level.

given data are:-

sample mean () = 58 (k)

sample sd(s) = 3 (k)

sample size (n) = 144

degrees of freedom = (n-1) = (144-1) = 143

t critical value for 95% confidence level, both tailed test be:-

[ using t distribution table for df=143,alpha=0.05, both tailed test]

the 95% confidence interval for the population’s average salary is:-

(k)

* as nothing is mentioned i have rounded off the final answer to 2 decimal places.

interpretation:-

we are 95% confident that the population’s average salary will be within $ 57.51 k and $ 58.49 k.

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