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Question
NARRBEGIN: SA_123_125Joe owns a sandwich shop near a large university. He wants to know if he is serving approximately the same number of customers as his competition. His closest competitors are Bob and Ted. Joe decides to use a couple of college students to collect some data for him on the number of lunch customers served by each sandwich shop during a weekday. The summary data for two weeks (10 days) and output from an ANOVA analysis are shown below.
| Summary stats for samples | ||||||||||||||||||||
| Joe's | Bob's | Ted's | ||||||||||||||||||
| Sample sizes | 10 | 10 | 10 | |||||||||||||||||
| Sample means | 50.700 | 46.200 | 43.500 | |||||||||||||||||
| Sample standard deviations | 4.244 | 4.492 | 3.598 | |||||||||||||||||
| Sample variances | 18.011 | 20.178 | 12.944 | |||||||||||||||||
| Weights for pooled variance | 0.333 | 0.333 | 0.333 | |||||||||||||||||
| | ||||||||||||||||||||
| Number of samples | 3 | |||||||||||||||||||
| Total sample size | 30 | |||||||||||||||||||
| Grand mean | 46.800 | |||||||||||||||||||
| Pooled variance | 17.044 | |||||||||||||||||||
| Pooled standard deviation | 4.128 | |||||||||||||||||||
| One-way ANOVA Table | ||||||||||||||||||||
| Source | SS | df | MS | F | p-value | |||||||||||||||
| Between variation | 264.60 | 2 | 132.30 | 7.762 | 0.0022 | |||||||||||||||
| Within variation | 460.20 | 27 | 17.044 | |||||||||||||||||
| Total variation | 724.80 | 29 | ||||||||||||||||||
| Difference | Mean diff | Lower | Upper |
| Joe's " Bob's | 4.500 | -0.282 | 9.282 |
| Joe's " Ted's | 7.200 | 2.418 | 11.982 |
| Bob's " Ted's | 2.700 | -2.082 | 7.482 |
(A) Are all three sandwich shops serving the same number of customers, on average, for lunch each weekday? Test the appropriate hypotheses at the 5% level of significance.
(B) Explain why the weights for the pooled variance are the same for each of the samples.
(C) Use the information related to the 95% confidence interval to explain how the number of customers Joe has each weekday compares to his competition.
Answer
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