Question

1. Thirty years ago, the mean number of rides that were disabled (broken) for more than two

hours at Disneyland was 10.2 per month. The current CEO, Bob Iger, believes that number has

gone down and randomly selects 11 months from the past three years and checks on the number

of disabled rides. If the mean has decreased, he will give the members of the maintenance staff a

$50K bonus this year. If not, they will all be immediately fired.

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10

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8

10

10

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9

9

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a. At the 10% significance level, do the data provide evidence that the mean number of disabled

rides per month has decreased?

b. In the context of this problem, describe Type I and Type II errors and their consequences.

Which one, in your opinion, is more severe?

Type I:

Type II:

Answer 1

Mean and standard deviation calculated from data :

Sample mean, = 8.73

Sample standard deviation, s = 2.41

Sample size, n = 11

a) Null and Alternative Hypothesis:

Critical value:

At = 0.10 and df = 11-1=10, the critical value,

Test statistic:

Decision:

As t = -2.023 < t_a = -1.372, we reject the null hypothesis.

At the 10% significance level, there is enough evidence to prove that the mean number of disabled

rides per month has decreased.

b) Type I error is rejecting the null hypothesis when it is true.

In this context type I error would be to that the members of the maintenance staff will receive a $50K bonus this year but in reality they should be immediately fired.

Type II error is failing to reject the null hypothesis when it is false.

In this context type II error would be to that the members of the maintenance staff will be immediately fired but in reality they should receive a $50K bonus this year.

Type II is more severe.