Math Problem Statement
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Topic 6 Homework (Nonadaptive) Question 7 of 11 (1 point)|Question Attempt: 1 of Unlimited
1 2 3 4 5 6 7 8 9 10 11 Question 7 The owner of a chain of mini-markets wants to compare the sales performance of two of her stores, Store 1 and Store 2. After choosing 12 days at random, she records the sales (in dollars) at Store 1 for these days. Then, she records the sales at Store 2 for these same days. The data and the differences (Store 1 minus Store 2) are shown in the table below. Day 1 2 3 4 5 6 7 8 9 10 11 12 Store 1 955 552 442 687 552 729 488 776 461 815 859 518 Store 2 989 599 500 680 451 528 452 741 446 758 960 421 Difference (Store 1 − Store 2) −34 −47 −58 7 101 201 36 35 15 57 −101 97
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Assume that the population of these differences in daily sales (Store 1 minus Store 2) is approximately normally distributed.
Construct a 95% confidence interval for μd, the population mean difference in daily sales between the two stores. Then find the lower and upper limits of the 95% confidence interval. Carry your intermediate computations to three or more decimal places. Round your answers to two or more decimal places. (If necessary, consult a list of formulas.) Lower limit: Upper limit:
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Math Problem Analysis
Mathematical Concepts
Confidence Intervals
Hypothesis Testing
Mean and Standard Deviation
Standard Error
t-distribution
Formulas
Mean of Differences: \(\bar{d} = \frac{\sum d_i}{n}\)
Standard Deviation: \(s_d = \sqrt{\frac{\sum (d_i - \bar{d})^2}{n-1}}\)
Standard Error: \(SE_d = \frac{s_d}{\sqrt{n}}\)
Confidence Interval: \(\bar{d} \pm t^* \times SE_d\)
Theorems
Central Limit Theorem
Student's t-distribution
Suitable Grade Level
Undergraduate (Statistics or Business)
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