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Confidence Interval for ISO Certification

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.


Solution Preview

Please see the attachment.

Question 1

Confidence interval for proportion is given by

Confidence Interval Estimate for the Mean

Sample Size 100
Number of Successes 67
Confidence Level 95%

Intermediate Calculations
Sample Proportion 0.67
Z Value 1.95996398
Standard Error of the Proportion 0.047021272
Interval Half Width 0.092159999

Confidence Interval
Interval Lower Limit 0.577840001
Interval Upper Limit 0.762159999


H0: There is no significant difference in the population variance of X and ...

Solution Summary

The solution provides step by step method for the calculation of c . Formula for the calculation and Interpretations of the results are also included.