A consumer advocacy group claims that the mean amount of juice in a 16 ounce bottled drink is not 16 ounces, as stated by the bottler.
You cannot copy and paste here.
To determine whether the consumer advocacy group's claim is valid, we can conduct a hypothesis test. Here are the steps to perform the hypothesis test in this scenario:
1. Formulate the null hypothesis (H0) and the alternative hypothesis (H1):
- Null hypothesis (H0): The mean amount of juice in a 16-ounce bottled drink is equal to 16 ounces.
- Alternative hypothesis (H1): The mean amount of juice in a 16-ounce bottled drink is not equal to 16 ounces.
2. Collect a random sample of 16-ounce bottled drinks. The sample size should be sufficiently large to meet the assumptions for hypothesis testing.
3. Measure the amount of juice in each of the sampled drinks. Calculate the sample mean (X̄) and the sample standard deviation (s) of the amounts.
4. Determine the significance level (α) for the hypothesis test. The most common choice is α = 0.05, which corresponds to a 95% confidence level.
5. Choose the appropriate test statistic and probability distribution. Since we are comparing a sample mean to a known value (16 ounces), a t-test is suitable.
6. Calculate the t-statistic using the formula:
t = (X̄ - μ) / (s / √n)
Where X̄ is the sample mean, μ is the null hypothesis value (16 ounces), s is the sample standard deviation, and n is the sample size.
7. Determine the critical region based on the significance level (α) and the degrees of freedom (df = n - 1). Look up the critical t-value from the t-distribution table or use statistical software.
8. Compare the calculated t-statistic to the critical t-value. If the calculated t-statistic falls within the critical region, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.
9. Draw a conclusion based on the result. If the null hypothesis is rejected, it provides evidence to support the consumer advocacy group's claim. If the null hypothesis is not rejected, there is insufficient evidence to support the claim.
10. Report the findings and discuss the implications of the result.
By following these steps, you can determine whether the mean amount of juice in the 16-ounce bottled drink provided by the bottler is significantly different from 16 ounces, supporting or refuting the claim made by the consumer advocacy group.