Three assembly lines are used to produce a certain component for an airliner. To examine the production rate, a random sample of six hourly periods is chosen for each assembly line and the number of components produced during these periods for each line is recorded. The output from a statistical software package is: Summary Groups Count Sum Average Variance Line A 6 250 41.66667 0.266667 Line B 6 260 43.33333 0.666667 Line C 6 249 41.5 0.7 ANOVA Source of Variation SS df MS F p-value Between Groups 12.33333 2 6.166667 11.32653 0.001005 Within Groups 8.166667 15 0.544444 Total 20.5 17 a. Use a .01 level of significance to test if there is a difference in the mean production of the three assembly lines. b. Develop a 99% confidence interval for the difference in the means between Line B and Line C.
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Step 1: Calculate the F-statistic using the formula F = MS_between / MS_within, where MS_between is the mean square between groups and MS_within is the mean square within groups. Show more…
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Three assembly lines are used to produce a certain component for an airliner. To examine the production rate, a random sample of six hourly periods is chosen for each assembly line and the number of components produced during these periods for each line is recorded. The output from a statistical software package is: a. Use a .01 level of significance to test if there is a difference in the mean production of the three assembly lines. b. Develop a $99 \%$ confidence interval for the difference in the means between Line B and Line $C$
An assembly line does a quality check by sampling 50 of its products. It finds that 16% of the parts are defective. Create a 95% confidence interval for the percent of
Lucas F.
Three different methods for assembling products were proposed by an industrial engineer. To investigate the number of units assembled correctly with each method, 30 employees were randomly selected and randomly assigned to the three proposed methods in such a way that each method was used by 10 workers. The number of units assembled correctly was recorded, and the analysis of variance procedure was applied to the resulting dataset. The following results were obtained: SST = 10,840; SSTR = 4,580. To calculate the exact p-value using Excel (instead of the F-table), enter "=F.DIST.RT(f test statistic, df_numerator, df_denominator)" in any cell of Excel. Set up the ANOVA table for this problem (to the decimals necessary). Source of Variation Sum of Squares Degrees of Freedom Mean Square Treatments Error Total Use α = 0.05 to test for any significant difference in the means for the three assembly methods. The p-value is [Select] less than [Select] between 0.1 and 0.25 [Select] between 0.25 and 0.05 [Select] between 0.05 and [Select] greater than [Select].
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