In a random sampleof 100 manufacturing firms, 67 indicated that their company attained ISO certification within the last two years. Find a 95% confidence intervalfor 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 varianceof X and Y are equal or not.

b) Next test at 5% level of significance whether the population meanof 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.

Please see the attachment.

Answer

Question 1

Confidence interval for proportion is given by

Details

Confidence Interval Estimate for the Mean

Data

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

a).

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

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