Math  /  Data & Statistics

QuestionWeights of Vacuum Cleaners Upright vacuum cleaners have either a hard body type or a soft body type. Shown are the weights in pounds of a random sample of each type. Find the 90%90 \% confidence interval for the difference of the means. Assume the variables are normally distributed and the variances are unequal. Round the sample mean and sample standard deviation to two decimal places and the final answers to at least one decimal place. \begin{tabular}{llll|llll} \multicolumn{4}{c|}{ Hard body types } & \multicolumn{4}{c}{ Soft body types } \\ \hline 21 & 17 & 17 & 20 & 24 & 13 & 11 & 13 \\ 16 & 17 & 15 & 20 & 12 & 15 & & \\ 23 & 16 & 17 & 17 & & & & \\ 13 & & & & & & \end{tabular}
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Use μ1\mu_{1} for the mean weight of the hard body type. <μ1μ2<\square<\mu_{1}-\mu_{2}<\square

Studdy Solution
Calculate the confidence interval for the difference in means.
(xˉ1xˉ2)±t×SE(\bar{x}_1 - \bar{x}_2) \pm t^* \times SE
Where tt^* is the critical value from the t-distribution.
The 90%90\% confidence interval for the difference in means is:
Lower bound<μ1μ2<Upper bound\boxed{ \text{Lower bound} < \mu_1 - \mu_2 < \text{Upper bound} }

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