Is the weight of Diet Coke less than the weight of Regular Coke? For the following test, assume that the two samples are independent simple random samples selected from normally distributed populations and that the population standard deviations are equal (σ1σ1 = σ2σ2) so that the standard error of the difference between means is obtained by pooling the sample variances.
Is the weight of Diet Coke less than the weight of Regular Coke?
For the following test, assume that the two samples are independent simple random samples selected from
Two independent simple random samples of weights (in pounds) of Diet Coke are taken from 18 cans and the weights of Regular Coke are taken from 18 cans and the data is in the tables below. All of the cans contain 12 oz.
Diet Coke
| 0.7842 | 0.7863 | 0.7869 | 0.7964 |
| 0.7922 | 0.7848 | 0.7816 | 0.7882 |
| 0.7867 | 0.7873 | 0.7853 | 0.7914 |
| 0.7864 | 0.7768 | 0.7828 | 0.7832 |
| 0.7861 | 0.7861 |
Regular Coke
| 0.8156 | 0.8058 | 0.8205 | 0.8304 |
| 0.8071 | 0.8119 | 0.8298 | 0.8216 |
| 0.8264 | 0.8133 | 0.8197 | 0.8166 |
| 0.8073 | 0.8129 | 0.8169 | 0.8051 |
| 0.817 | 0.8161 |
Use a 0.01 significance level to test the claim that the mean amount of the weight of Diet Coke is less than the weight of Regular Coke.
What are the correct hypotheses? (Select the correct symbols and use decimal values not percentages.)
H0: Select an answer μ(Diet Coke) p₁ p₂ μ₂ p̂₁ σ₁² μ₁ p μ x̄₂ x̄₁ s₁² ? > ≠ ≤ < ≥ = Select an answer x̄₂ p̂₁ p₂ μ μ₂ σ₁² p₁ s₁² μ₁ x̄₁ p μ(Regular Coke)
H1: Select an answer p₁ x̄₂ x̄₁ s₂² μ p p̂₂ p₂ μ₂ μ₁ σ₂² μ(Diet Coke) ? ≥ > ≠ < ≤ = Select an answer x̄₁ μ₁ μ x̄₂ s₁² p̂₁ μ(Regular Coke) μ₂ p₁ p p₂ σ₁²
Original Claim = Select an answer H₀ H₁
df =
Based on the hypotheses, find the following:
Test Statistic = (Round to three decimal places.)
Critical value(s) = (Round to three decimal places.)
Shade the sampling distribution curve with the correct critical value(s) and shade the critical regions. The arrows can only be dragged to t-scores that are accurate to 1 place after the decimal point (these values correspond to the tick marks on the horizontal axis). Select from the drop down menu to shade to the left, to the right, between or left and right of the t-score(s).
Shade: Left of a valueRight of a valueBetween two values2 regions. Click and drag the arrows to adjust the values.
Decision: Select an answer Fail to reject the null hypothesis Accept the alternative hypothesis Reject the null hypothesis Accept the null hypothesis .
Conclusion: Select an answer The sample data supports There is not enough evidence to support There is not sufficient evidence to warrant rejection of There is sufficient evidence to warrant rejection of the claim that the mean amount of the weight of Diet Coke is less than the weight of Regular Coke.
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