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Data on the weights (lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. Use a 0.01 significance level for both parts. Assume that the standard deviations of both are equal.

  Diet Regular
mu mu1 mu2
n 22 22
X_bar 0.78025lb 0.80627lb
s 0.00444lb 0.00752lb


a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda.

What are the null and the alternative hypothesis?

The test statistic, t, is ?

The p-value is?

For this question I will use Minitab to generate the output, although Excel can also be used.

Two-Sample T-Test and CI 

Sample   N     Mean    StDev  SE Mean
1       22  0.78025  0.00444  0.00095
2       22  0.80627  0.00752   0.0016


Difference = μ (1) - μ (2)
Estimate for difference:  -0.02602
95% upper bound for difference:  -0.02287
T-Test of difference = 0 (vs <): T-Value = -13.98  P-Value = 0.000  DF = 34

 

The t-statistic is -13.98, the p -value is 0.000, 

Evidence reveal that the null hypothesis should be rejected. Thus, there is sufficient evidence to support the claim. 

 

 

 

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