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Do people feel hungrier after sampling a healthy food? The authors of a consumer research paper carried out a study to answer this question. They randomly assigned volunteers into one of three groups. The people in the first group were asked to taste a snack that was billed as a new health bar containing high levels of protein, vitamins, and fiber. The people in the second group were asked to taste the same snack but were told it was a tasty chocolate bar with a raspberry center. After tasting the snack, participants were asked to rate their hunger level on a scale from 1 (not at all hungry) to 7 (very hungry). The people in the third group were asked to rate their hunger but were not given a snack. The data in the table are consistent with summary quantities given in the paper (although the sample sizes in the actual study were larger). Treatment Group Hunger Rating Sample Mean Sample Standard Deviation Healthy 5 7 7 4 7 3 4 7 6 5.6 1.59 Tasty 4 1 5 2 6 2 5 3 4 3.6 1.67 No Snack 3 4 5 6 5 5 2 4 4 4.2 1.20 Overall mean = 4.4 (a) Do these data provide evidence that the mean hunger rating differs for at least two of the treatments ("healthy" snack, "tasty" snack, no snack)? Test the relevant hypotheses using a significance level of 0.05. State the appropriate null and alternative hypotheses. (Let M1, M2, and 3 be the true means for the three different treatments.) Ho at least two of the three μ's are different Ha H₁ =H2 H3 : O Ho H1 H2 H3 Ha at least two of the three μ's are different Ho H₁ =H2 H3 Ha all three of the μ's are different different

Do people feel hungrier after sampling a healthy food? The authors of a consumer research paper carried out a study to answer this question. They randomly assigned volunteers into one of three groups. The people in the first group were asked to taste a snack that was billed as a new health bar containing high levels of protein, vitamins, and fiber. The people in the second group were asked to taste the same snack but were told it was a tasty chocolate bar with a raspberry center. After tasting the snack, participants were asked to rate their hunger level on a scale from 1 (not at all hungry) to 7 (very hungry). The people in the third group were asked to rate their hunger but were not given a snack. The data in the table are consistent with summary quantities given in the paper (although the sample sizes in the actual study were larger). Treatment Group Hunger Rating Sample Mean Sample Standard Deviation Healthy 5 7 7 4 7 3 4 7 6 5.6 1.59 Tasty 4 1 5 2 6 2 5 3 4 3.6 1.67 No Snack 3 4 5 6 5 5 2 4 4 4.2 1.20 Overall mean = 4.4 (a) Do these data provide evidence that the mean hunger rating differs for at least two of the treatments ("healthy" snack, "tasty" snack, no snack)? Test the relevant hypotheses using a significance level of 0.05. State the appropriate null and alternative hypotheses. (Let M1, M2, and 3 be the true means for the three different treatments.) Ho at least two of the three μ's are different Ha H₁ =H2 H3 : O Ho H1 H2 H3 Ha at least two of the three μ's are different Ho H₁ =H2 H3 Ha all three of the μ's are different different

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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Do people feel hungrier after sampling a healthy food? The authors of a consumer research paper carried out a study to answer this question. They randomly assigned volunteers into one of three groups. The people in the first group were asked to taste a snack that was billed as a new health bar containing high levels of protein, vitamins, and fiber. The people in the second group were asked to taste the same snack but were told it was a tasty chocolate bar with a raspberry center. After tasting the snack, participants were asked to rate their hunger level on a scale from 1 (not at all hungry) to 7 (very hungry). The people in the third group were asked to rate their hunger but were not given a snack. The data in the table are consistent with summary quantities given in the paper (although the sample sizes in the actual study were larger). Treatment Group Hunger Rating Sample Mean Sample Standard Deviation Healthy 5 7 7 4 7 3 4 7 6 5.6 1.59 Tasty 4 1 5 2 6 2 5 3 4 3.6 1.67 No Snack 3 4 5 6 5 5 2 4 4 4.2 1.20 Overall mean = 4.4 (a) Do these data provide evidence that the mean hunger rating differs for at least two of the treatments ("healthy" snack, "tasty" snack, no snack)? Test the relevant hypotheses using a significance level of 0.05. State the appropriate null and alternative hypotheses. (Let M1, M2, and 3 be the true means for the three different treatments.) Ho at least two of the three μ's are different Ha H₁ =H2 H3 : O Ho H1 H2 H3 Ha at least two of the three μ's are different Ho H₁ =H2 H3 Ha all three of the μ's are different different
Transcribed Image Text:Do people feel hungrier after sampling a healthy food? The authors of a consumer research paper carried out a study to answer this question. They randomly assigned volunteers into one of three groups. The people in the first group were asked to taste a snack that was billed as a new health bar containing high levels of protein, vitamins, and fiber. The people in the second group were asked to taste the same snack but were told it was a tasty chocolate bar with a raspberry center. After tasting the snack, participants were asked to rate their hunger level on a scale from 1 (not at all hungry) to 7 (very hungry). The people in the third group were asked to rate their hunger but were not given a snack. The data in the table are consistent with summary quantities given in the paper (although the sample sizes in the actual study were larger). Treatment Group Hunger Rating Sample Mean Sample Standard Deviation Healthy 5 7 7 4 7 3 4 7 6 5.6 1.59 Tasty 4 1 5 2 6 2 5 3 4 3.6 1.67 No Snack 3 4 5 6 5 5 2 4 4 4.2 1.20 Overall mean = 4.4 (a) Do these data provide evidence that the mean hunger rating differs for at least two of the treatments ("healthy" snack, "tasty" snack, no snack)? Test the relevant hypotheses using a significance level of 0.05. State the appropriate null and alternative hypotheses. (Let M1, M2, and 3 be the true means for the three different treatments.) Ho at least two of the three μ's are different Ha H₁ =H2 H3 : O Ho H1 H2 H3 Ha at least two of the three μ's are different Ho H₁ =H2 H3 Ha all three of the μ's are different different
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