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Chapter 11: Q. 124 (page 669)

Airline companies are interested in the consistency of the number of babies on each flight, so that they have adequate safety equipment. They are also interested in the variation of the number of babies. Suppose that an airline executive believes the average number of babies on flights is six with a variance of nine at most. The airline conducts a survey. The results of the 18 flights surveyed give a sample average of 6.4 with a sample standard deviation of 3.9. Conduct a hypothesis test of the airline executive’s belief.

Short Answer

Expert verified

If we take α=0.05, we can see that p<α. This means that we reject null hypothesis.

There is sufficient evidence to conclude that the standard deviation is greater than 3.

Step by step solution

01

Given Information

We want to test these hypotheses:

H0:σ≤3H1:σ>3

There are 18 flights surveys so n=18. We know that the number of degrees of freedom isn-1=17.

02

Explanation

We are using χ2distribution with 17degrees of freedom to test our hypothesis. We are given s=3.9, thus the value of test statistic is:

χ2=(n-1)s2σ2=28.73

Using the applet for χ2distribution, we can find the p-value and the result is 0.0371:

Chi-Square Distribution

X~χ(df)2

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Most popular questions from this chapter

Where is μlocated on a chi-square curve?

Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes.

How did you know to test the variance instead of the mean?

Graph the situation. Label and scale the horizontal axis. Mark the mean and test statistic. Shade the p-value.

If df=2, the chi-square distribution has a shape that reminds us of the exponential.

Is this a right-tailed, left-tailed, or two-tailed test?
See all solutions

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