Question

You want to estimate the average starting salary of San Jose graduates. You call a random sample
of 200 students who graduated in the last two years. After collecting the data, you are about to
calculate the 95% confidence interval when you remember that incomes
are skewed to the right. Isn’t a 95% confidence interval based on a normal curve? Was all your
work in vain? Explain, making reference to the assumptions required for confidence intervals to
be valid.

Answer 1

SoL

For constructing confidence interval for mean

the sample to simple independent random sample

and sample follows normal distribution (n>30)

as for large smaple (n>30),according to central limit theorem,sample follows normal distribution

Independence Assumption

Random sampling

Sample size condition: n > 30

Here n=200

so given sample follows normal distribution as n>30

And given sample is random sample

95% confidence interval based on a normal curve so work is not in vain

we can calculate 95% confidence interval for average starting salary of San Jose graduates based on sample of 200  students who graduated in the last two years