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j7l| Sweetening colas Cola makers test new recipesfor loss of sweetness during storage. Trained tastersrate the sweetness before and after storage. From

experience, the population distribution of sweetnesslosses will be close to Normal. Here are thesweetness losses (sweetness before storage minussweetness after storage) found by tasters from arandom sample of 10 batches of a new cola recipe:

"2.0 0.4 0.7 2.0 -0.4 2.2 -1.3 1.2 1.1 2.3

Are these data good evidence that the cola lost sweet-ness? Carry out a test to help you answer this question.

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I 7 3.\Healthy bones The recommended dailyallowance (RDA) of calcium for women betweenthe ages of 18 and 24 years is 1200 milligrams (mg).Researchers who were involved in a large-scalestudy of women's bone health suspected thattheir participants had significantly lower calciumintakes than the RDA. To test this suspicion, theresearchers measured the daily calcium intake of arandom sample of 36 women from the study whofell in the desired age range. The Minitab outputbelow displays descriptive statistics for these data,along with the results of a significance test.

, Descriptive Statistics: Calcium intake (mg)Variable N Mean SE Mean StDev Min Ql Med Q3 KaxiJ»»

Calcium 36 856.2 51.1 306.7 374.0 632.3 805.0 1090.5 1425.0

One-Sample T: Calcium intake (mg)Test of mu = 12.00 vs < 1200

Variable N Mean StDev SE Mean T.

Calcium 36 856.2 306.7 51.1 -6.73

(a) Determine whether there are any outliers.your work.

(b) Interpret the P-value in context.

(c) Do these data give convincing evidence tosupport the researchers' suspicion? Carry out a teto help you answer this question.

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y-75.\Growing tomatoes An agricultural field trial- " compares the yield of two varieties of tomatoes for —

commercial use. Researchers randomly select10 Variety A and 10 Variety B tomato plants. Thenthe researchers divide in half each of 10 small plotsof land in different locations. For each plot, a cointoss determines which half of the plot gets a VarietyA plant; a Variety B plant goes in the other half.After harvest, they compare the yield in pounds forthe plants at each location. The 10 differences(Variety A - Variety B) give x = 0.34 and sx = 0.83.A graph of the differences looks roughly symmetricand single-peaked with no outliers. Is there convinc-mg evidence that Variety A has the higher meanyield? Perform a significance test using a = 0.05 toanswer the question.

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j 771 The power of tomatoes The researchers whocarried out the experiment in Exercise 75 suspectthat the large P-value (0.114) is due to low power.

(a) Describes Type I and a Type II error in thissetting. Which type of error could you have made inExercise 75? Why?

(b) Explain two ways that the researchers couldhave increased the power of the test to detect

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531 Do you Twitter? In late 2009, the Pew Internet andAmerican Life Project asked a random sample of U.S.adults, "Do you ever . . . use Twitter or another ser-vice to share updates about yourself or to see updatesabout others?" According to Pew, the resulting 95%confidence interval is (0.167, 0.213).15 Can we usethis interval to conclude that the actual proportion ofU.S. adults who would say they Twitter differs from0.20? Justify your answer. /\-/0 5ui t 3

c \s and sex The Gallup Youth Survey asked a

random sample of U.S. teens aged 13 to 17 whetherthey thought that young people should wait to havesex until marriage.17 The Minitab output below showsthe results of a significance test and a 95% confidenceinterval based on the survey data.

Test and Cl for One ProportionTeat of p B 0.5 vs p DOC * 0.5

Saaple X H Sanple' p 951 CI Z-Value P-Value1 246 439 0.560364 (O.S1393S, 0.606794} 2.53 0.011

(a) Define the parameter of interest.

(b) Check that the conditions for performing thesignificance test are met in this case.

(c) Interpret the P-value in context.

(d) Do these data give convincing evidence that theactual population proportion differs from 0.5? Justifyyour answer with appropriate evidence.

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