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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鈥檚 belief.

Short Answer

Expert verified

If we take 伪=0.05, we can see that p<伪. 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:蟽鈮�3H1:蟽>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 蠂2distribution with 17degrees of freedom to test our hypothesis. We are given s=3.9, thus the value of test statistic is:

蠂2=(n-1)s2蟽2=28.73

Using the applet for 蠂2distribution, we can find the p-value and the result is 0.0371:

Chi-Square Distribution

X~蠂(df)2

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