Math  /  Data & Statistics

Questionn 10 of 16 Side-by-Side
A research firm supplies manufacturers with estimates of the sales of their products from samples of stores. Marketing managers often look at the sales estimates and ignore sampling error. An SRS of 50 stores this month shows mean sales of 41 units of a particular appliance with standard deviation of 11 units. During the same month last year, an SRS of 52 stores gave mean sales of 38 units of the same appliance with a standard deviation of 13 units. An increase from 38 to 41 is a rise of 7.9%7.9 \%. The marketing manager is happy because sales are up 7.9%7.9 \%. (a) Give a 95%95 \% confidence interval for the difference in mean number of units of the appliance sold at all retail stores. Give your answers to three decimal places. lower bound: \square upper bound: \square

Studdy Solution
Compute the confidence interval for the difference in means:
(xˉ1xˉ2)±ME(\bar{x}_1 - \bar{x}_2) \pm ME
Substitute the values:
(4138)±4.667=3±4.667(41 - 38) \pm 4.667 = 3 \pm 4.667
Calculate the lower and upper bounds:
Lower bound: 34.667=1.6673 - 4.667 = -1.667
Upper bound: 3+4.667=7.6673 + 4.667 = 7.667
The 95%95\% confidence interval for the difference in mean number of units sold is:
Lower bound: 1.667-1.667
Upper bound: 7.6677.667

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