The hypotheses for the ANOVA test comparing the mean vacuum cleaner weights for bagged upright (BU), bagless upright (BLU), and top canister (TC) vacuums can be stated as follows:
Null Hypothesis (H₀): The mean weights of the three types of vacuums (BU, BLU, TC) are equal.
Alternative Hypothesis (H₁): At least one of the mean weights is different from the others.
In mathematical notation, the hypotheses can be expressed as:
H₀: μ BU = μ BLU = μ TC
H₁: At least one of μ BU, μ BLU, μ TC is different
These hypotheses assume that the population mean weights for the three types of vacuums are equal under the null hypothesis. The alternative hypothesis suggests that there is at least one type of vacuum cleaner whose mean weight differs from the others. By conducting the ANOVA test and analyzing the results, we can determine if there is sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.