Suppose the average score over all the contestants to date on Dancing with the Stars (a TV show) has been 7.0. Fred believes that the students at his dancing school would do better than that. He is willing to make a Type I error 5% of the time. A random sample of 25 students in Fred's school is selected and they get to dance for the judges. Their average score is 7.5, with a standard deviation of 2.5. What should Fred (and we) conclude? Are they significantly better? Yes, this is a rare outcome even though the difference (7.5 - 7) is only .5 No, by the standards we are using this is not a rare enough outcome to be considered significant. O It would be significant if we had chosen a Type I error of 1%, but not in this case where we picked it to be 5%. There is not enough information given to answer the question.

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Suppose the average score over all the contestants to date on Dancing with the Stars (a TV show) has been 7.0. Fred believes that the students at his dancing school would do better than that. He is willing to make a Type I error 5% of the time. A random sample of 25 students in Fred’s school is selected and they get to dance for the judges. Their average score is 7.5, with a standard deviation of 2.5.

What should Fred (and we) conclude? Are they significantly better?

- ○ Yes, this is a rare outcome even though the difference (7.5 – 7) is only .5

- ○ No, by the standards we are using this is not a rare enough outcome to be considered significant.

- ○ It would be significant if we had chosen a Type I error of 1%, but not in this case where we picked it to be 5%.

- ○ There is not enough information given to answer the question.
Transcribed Image Text:Suppose the average score over all the contestants to date on Dancing with the Stars (a TV show) has been 7.0. Fred believes that the students at his dancing school would do better than that. He is willing to make a Type I error 5% of the time. A random sample of 25 students in Fred’s school is selected and they get to dance for the judges. Their average score is 7.5, with a standard deviation of 2.5. What should Fred (and we) conclude? Are they significantly better? - ○ Yes, this is a rare outcome even though the difference (7.5 – 7) is only .5 - ○ No, by the standards we are using this is not a rare enough outcome to be considered significant. - ○ It would be significant if we had chosen a Type I error of 1%, but not in this case where we picked it to be 5%. - ○ There is not enough information given to answer the question.
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