The average wage in a particular country supposedly is $35,752. Suppose a researcher selected a simple random sample of 144 citizens and recorded their wages. The sample mean was $38,535 with a standard deviation of $14,500.
(i) Construct a 95% confidence interval for the mean wage in the population. Use EViews to get the correct critical t values for constructing the interval.
(ii) Test the hypothesis that the true mean population wage is $35,752. Is there sufficient evidence to indicate that the population mean is significantly different from $35,752? Use a 10% significance level.
(iii) What is the p-value for your test statistic in (ii), still assuming a two-sided alternative hypothesis? Would you reject the null hypothesis at the 5% significance level?
(iv) What assumption have you made about the distribution of the population data?