Solve the following:
Q1: In a random sample of 100 manufacturing firms, 67 indicated that their company attained ISO certification within the last two years. Find a 95% confidence interval for the population proportion of companies that have been certified within the last two years. In solving the above question you must write the formula of the confidence interval and show necessary calculations.
The total amount of hydrogen chloride (HCL) in columns above an altitude of 12 km was measured at selected sites over a certain volcano both before and after an eruption. The summary of the samples are as follows:
Preeruption (X) Posteruption (Y)
n_1 = 40 n_2 = 20
X = 1.28 Y = 1.40
s_1 = 0.14 s_2 = 0.04
a) First test at 5% level of significance whether the population variance of X and Y are equal or not.
b) Next test at 5% level of significance whether the population mean of X and Y are equal or not. Your choice of test must based on the result of part (a).
For both tests clearly state the hypotheses, formula and value of test statistics, rejection region and the final conclusion.