Answer :
Answer:
Using the Wilcoxon signed-rank test with a 0.01 significance level, if the null hypothesis is rejected, indicating a median different from 12 oz, consumers might be receiving less soda.
Explanation:
To test the claim that the median amount of soda in the cans is 12 oz, we can use the Wilcoxon signed-rank test, which is a non-parametric test used to compare the median of a sample to a specified value.
Let's denote the null hypothesis ([tex]\( H_0 \)[/tex]) as "the median amount of soda is 12 oz" and the alternative hypothesis ([tex]\( H_1 \)[/tex]) as "the median amount of soda is not 12 oz."
If the null hypothesis is rejected, it suggests that the median amount of soda is significantly different from 12 oz. In this case, if the median amount is less than 12 oz, consumers might be receiving less soda than advertised.
Here's how we can perform the test:
1. Calculate the differences between the observed amounts and 12 oz.
2. Assign ranks to the absolute differences, ignoring the signs.
3. Sum the ranks of the positive differences to get the positive sum of ranks ([tex]\( W_+ \)[/tex]).
4. Calculate the test statistic [tex]\( W \)[/tex] using the formula [tex]\( W = \min(W_+, W_-) \)[/tex], where [tex]\( W_- \)[/tex] is the sum of the ranks of the negative differences.
5. Use the Wilcoxon signed-rank table to find the critical value of [tex]\( W \)[/tex] for the given sample size and significance level.
6. Compare the calculated test statistic [tex]\( W \)[/tex] with the critical value.
7. If [tex]\( W \)[/tex] is greater than the critical value, reject the null hypothesis and conclude that the median amount of soda is significantly different from 12 oz.
If the null hypothesis is rejected, indicating that the median amount is significantly different from 12 oz, consumers may indeed be receiving less soda than advertised. However, it's essential to consider other factors such as production variability before concluding that consumers are being cheated.
Answer:
https://brainly.com/question/24258518
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