Question

1. You want to compare the contents of the soda cans. A random sample of 80 CC brand cans was randomly selected obtaining an average content of 355.9 ml with a standard deviation of 3.7 ml. While a random sample of 70 cans marks PC, an average content of 354.5 was obtained with a standard deviation of 9.7 ml.
a) Obtain the 95% confidence interval for the average content difference in the cans of both refresh brands.
b) Determine if there is statistical evidence that the average content of the cans is the same for both brands of soda.
c) What assumptions are required for the confidence interval to be valid?

You also want to know if the standard deviations of the soda content in the cans are the same for both brands.
d) Calculate the 95% confidence interval for the standard deviation ratio of the refreshment content of the cans of both brands.
e) State the necessary assumptions so that the confidence interval of d) has validity.
f) Interpret the confidence interval  in the context of the problem.

STANDARD DEVIATION IS GIVEN:

A random sample of 80 CC brand cans was randomly selected obtaining an average content of 355.9 ml with a standard deviation of 3.7 ml. While a random sample of 70 cans marks PC, an average content of 354.5 was obtained with a standard deviation of 9.7 ml.

Answer 1

Null hypothesis:

Alternative hypothesis is claim.

Here we have

Since it is not given that variances are equal so degree of freedom of the test is

The critical value for 95% confidence interval is "=TINV(1-0.95,86)" is

And standard error for difference in mean will be

So required confidence interval is

b)

Since confidence interval contains zero so there is statistical evidence that the average content of the cans is the same for both brands of soda.

c)

No assumption required becuase sample sizes are large.

d)

Here degree of freedom of numerator is df1=80-1=79 and degree of freedom for denominator is df2=70-1=69. Since so critical values are:

Excel function used for critical values: "=FINV(0.025,79,69)", "=FINV(0.975,79,69)"

So

e)

Populations should be normally distributed.

f)

Confidence does not contain 1 so we cannot concldue that the standard deviations of the soda content in the cans are the same for both brands.