Question

Asked May 21, 2019

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Is there a difference in the weights of contents in a can of Diet Coke versus a regular can of Coke? In a random sample of n=36 cans of Diet Coke, the mean weight of the contents of a can was 0.78479 lbs with a standard deviation of 0.00439 lbs. In an independent random sample of n=36 cans of regular Coke, the mean weight of the contents of a can was 0.81682 lbs with a standard deviation of 0.00751 lbs.

- Assuming that both populations are normally distributed and that sigma1 to the power of 2 = sigma2 to the power of 2, determine whether there is a difference in the mean weight of the contents of a can of Diet Coke vs. regular Coke with a 5% significance level.

Step 1

**Solution:**

**Null and alternative hypotheses:**

Null hypothesis: µ_{1}−µ_{2 }= 0

Alternative hypothesis: µ_{1}−µ_{2} ≠ 0

**Test statistic:**

The population standard deviation is unknown. Hence, the test statistic for this problem is shown below.

Step 2

**Calculation of test statistic value:**

Here, for diet coke, *x*_{1}-bar=0.78479, *s*_{1}=0.00439, *n*_{1}=36

For regular coke,* x*_{2}-bar=0.81682, *s*_{2}=0.00751, *n*_{2}=36

Step 3

**Degrees of freedom:**

*df* = n1 + n2 – 2 = 36 + 36 – 2 = 70.

**Rejection region:**

The rejection region for 5% significance level can be obtained using the EXCEL formula. “=T.INV.2T(0.05,70)”

Thus, the critical value of Student’s *t* is *t*tab= 1.9944.

**Decision rule for two-tailed t...**

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