3.02 Quiz: Matched Pairs Confidence Intervals and t Tests

Elite Foods, a supermarket, is losing customers and suspects it's because another neighborhood market has lower prices. To determine whether this is the case, researchers from Elite Foods take a random sample of ten items from their store and compare their prices to prices for the same items at the other store: Item Elite Foods Neighborhood Markets 1 1.65 1.49 2 2.19 2.00 3 1.99 2.09 4 3.49 2.99 5 .99 .99 6 1.59 1.79 7 2.89 2.39 8 4.50 4.25 9 1.19 .99 10 1.99 1.79

(-.16, -.19, .1, -.5, 0, .2, -.5, -.25, -.2, -.2)

A whale-watching company noticed that many customers wanted to know whether it was better to book an excursion in the morning or the afternoon. To test this question, the company collected the following data on 15 randomly selected days over the past month: Number of Whales Spotted Morning (A) Afternoon (B) (B - A) 8 8 0 9 10 1 7 9 2 9 8 -1 10 9 -1 13 11 -2 10 8 -2 8 10 2 2 4 2 5 7 2 7 8 1 7 9 2 6 6 0 8 6 -2 7 9 2 What's the 95% confidence interval for the true population mean difference for these data?

(-.507, 1.307)

A whale-watching company noticed that many customers wanted to know whether it was better to book an excursion in the morning or the afternoon. To test this question, the company collected the following data on 15 randomly selected days over the past month. (Note: Though in the table they're labeled 1 through 15, the days aren't consecutive.) Number of Whales Spotted Day Morning Afternoon 1 8 8 2 9 10 3 7 9 4 9 8 5 10 9 6 13 11 7 10 8 8 8 10 9 2 4 10 5 7 11 7 8 12 7 9 13 6 6 14 8 6 15 7 9 If you take the difference between each pair, what set of numbers do you get for analysis in a single-sample procedure? (Calculate differences so that if the afternoon number is higher, the result is a positive number.)

(0, 1, 2, -1, -1, -2, -2, 2, 2, 2, 1, 2, 0, -2, 2)

High Voltage, Inc., a light bulb manufacturer, has gathered data for a matched pairs analysis of whether there's a difference in the life span between its light bulbs and those of a competitor. They have two data sets: the number of hours its bulbs lasted on various lamps and the number of hours its competitor's bulbs lasted on various lamps. Observations are paired by lamp (there are two observations for each type of lamp; one observation for a High Voltage bulb and another observation for a competitor's bulb). What should High Voltage do next?

Calculate the difference within each pair of observations.

High Voltage, Inc., a light bulb manufacturer, wants to know if there's a difference in mean life span between its product and that of a competitor. They collect paired data and calculate the difference in each pair to create one set of numbers that represents the differences within each pair. What notation should High Voltage use to construct its null and alternative hypotheses?

H subscript 0 : mu open parentheses H. v o l t minus C o m p. close parentheses equals 0 (The mean of the differences in life spans equals 0.) H subscript a : mu open parentheses H. v o l t minus C o m p. close parentheses not equal to 0 (The mean of the differences in life spans doesn't equal 0.)

Management at High Voltage, a light bulb manufacturer, wants to know if there's a difference in mean life span between its product and that of a competitor. To answer this question, what would be an appropriate test using matched pairs single-sample analysis?

High Voltage should set up an experiment where randomly selected bulbs from both companies are paired, with each pair consisting of a High Voltage bulb and a competitor's bulb. Researchers should place each pair of bulbs in identical light fixtures and measure the difference in their life spans.

Elite Foods, a supermarket, is losing customers and suspects it's because another neighborhood market has lower prices. To determine whether this is the case, researchers from Elite Foods collected data on ten items found in both stores. They created a single set of numbers by subtracting their prices from those of the neighborhood market. For the test H subscript 0 : mu open parentheses B minus A close parentheses equals 0 and H subscript 0 : mu open parentheses B minus A close parentheses less than 0, where mu open parentheses B minus A close parentheses represents the mean difference in price between the two stores (A = Elite, B = neighborhood market), researchers found that t equals minus 2.237 comma space p equals.021. What can you conclude from these results if alpha equals.05?

The neighborhood market has lower prices than Elite Foods.

High Voltage, Inc., a light bulb manufacturer, wants to know if there's a difference in mean life span between its product and that of a competitor. The company has collected data for a matched pairs analysis, calculated the differences in the pairs of data to make one set of values, and set up the test H subscript 0 : mu open parentheses H. V o l t minus C o m p. close parentheses equals 0 H subscript a : mu open parentheses H. V o l t minus C o m p. close parentheses not equal to 0 where mu open parentheses H. v o l t minus C o m p. close parentheses stands for the population mean difference between the life spans of the two brands of light bulbs. What conclusion can be drawn if p = .001 and alpha equals.05?

There's a difference between the mean life span of High Voltage's bulbs and those of its competitor.

A whale-watching company noticed that many customers wanted to know whether it was better to book an excursion in the morning or the afternoon. To test this question, the company recorded the number of whales seen in the morning and afternoon on 15 randomly selected days over the past month, calculated differences between the observations in each pair (afternoon minus morning), and then constructed a 95% confidence interval for the true population mean difference. What conclusion can you draw from the 95% confidence interval (-.507, 1.307) for AP Statistics Semester 2, the population mean difference?

There's no significant difference between the number of whales seen in the morning and the number seen in the afternoon.

Elite Foods, a supermarket, is losing customers and suspects it's because another neighborhood market has lower prices. To determine whether this is the case, researchers from Elite Foods collected the following data on ten items found in both stores: Elite Foods Neighborhood Markets (B - A) 1.65 1.49 minus.16 2.19 2.00 minus.19 1.99 2.09 .1 3.49 2.99 minus.5 .99 .99 0 1.59 1.79 .2 2.89 2.39 minus.5 4.50 4.25 minus.25 1.19 .99 minus.2 1.99 1.79 minus.2 Compute the test statistic and P-value for H subscript 0 : mu open parentheses B minus A close parentheses equals 0 and H subscript a : mu open parentheses B minus A close parentheses less than 0, where mu open parentheses B minus A close parentheses represents the true population mean difference in price between the two stores.

t = -2.37, 9 = 0.21