Question

In: Statistics and Probability

A random sample of 36 cans of regular Coke had a sample mean of 12.19 oz...

A random sample of 36 cans of regular Coke had a sample mean of 12.19 oz with a standard deviation of 0.11 oz. A sample of 36 cans of regular Pepsi had a sample mean of 12.29 oz with a standard deviation of 0.09 oz. Find a 90% confidence interval for the difference in volume between cans of regular Coke and cans of regular Pepsi.

Solutions

Expert Solution

Let,

Polulation Mean Volume of Coke     Polulation Mean Volume of Pepsi

Given:

   Sample Mean Volume of Coke = 12.19 oz Sample Mean Volume of Pepsi = 12.29 oz        Sample Standard Deviation of Coke = 0.11 oz   Sample Standard Deviation of Pepsi = 0.09 oz Sample sizes

A 100()% CI for difference in population mean can be obtained using the formula:

where, Pooled variance

Substituting the given values,

  = 0.01

And t value for (36+36-2) = 70 degrees of freedom at 10% significance level can be obtained using the excel function:

we get t0.10,70 = 1.667

Substituting the values in the formula,

= (-0.139, -0.061)

Hence, 90% confidence interval for the difference in volume between cans of regular Coke and cans of regular Pepsi is obtained as (-0.139, -0.061).

This implies that if 100 such repeated samples of volume of Coke and Pepsi are obtained and 90% CI constructed for each of them; 90 out of the 100 intervals would contain the true mean difference in volume between cans of regular Coke and cans of regular Pepsi. Also, since, the interval constructed, does not contain the null value zero (), we may conclude that there is a significanct difference in volume between cans of regular Coke and cans of regular Pepsi.


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