Calculation and Analysis of Confidence Interval, Hypothesis Testing, Correlation Coefficient and Chi-Square Test

Question 15 – Option C
Question 16
It is apparent that the population standard deviation is unknown for the two populations and hence
t value would be used for computation of the 95% confidence interval.
Difference in mean of the two samples = 7,123-6,957 = 166
The pooled variance needs to be estimated using the following formula.
Pooled variance = ((144-1)*1752 + (144-1)*2252)/(144+144-2) = 40,625
The standard error for the difference in means is given by the following formula.
Hence, standard error = [(40625/144) + (40625/144))]0.5= 23.7536
The formula for confidence interval is indicated below.
Lower limit of 95% confidence interval = 166 – 1.9767*23.7536 = 119.05
Upper limit of 95% confidence interval = 166 + 1.9767*23.7536 = 212.95
Question 17
The relevant hypotheses are stated below.
H0: μ ≥ 20 ppm
H1: μ < 20 ppm
Considering that population standard deviation is not known, hence t statistics would be used. The
given test would be a left tail single sample t test.
The level of significance has been given as 1%.
T stat = (17.57-20)/(2.95/100.5) = -2.605