91Ó°ÊÓ

Let$\mathrm{Î\pm }=0.05$

Decision: ________

Conclusion (write out in a complete sentence.): ________

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.

If an additional test were done on the claim of the average delay, which distribution would you use?

Consumers may be interested in whether the cost of a particular calculator varies from store to store. Based on surveying $43$ stores, which yielded a sample mean of $\backslash (84$ and a sample standard deviation of $\backslash )12$, test the claim that the standard deviation is greater than $\$15$.

Isabella, an accomplished Bay to Breakers runner, claims that the standard deviation for her time to run the $7.5$mile race is at most three minutes. To test her claim, Rupinder looks up five of her race times. They are $55$minutes, $61$minutes, $58$minutes, $63$ minutes, and $57$ minutes.

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.

The number of births per woman in China is $1.6$down from $5.91$in $1966$. This fertility rate has been attributed to the law passed in $1979$restricting births to one per woman. Suppose that a group of students studied whether or not the standard deviation of births per woman was greater than $0.75$. They asked $50$women across China the number of births they had had. The results are shown in Table. Does the students’ survey indicate that the standard deviation is greater than $0.75$?

$\begin{array}{|ll|}\hline \text{\# of births}& \text{Frequency}\\ 0& 5\\ 1& 30\\ 2& 10\\ 3& 5\\ \hline\end{array}$

The manager of "Frenchies" is concerned that patrons are not consistently receiving the same amount of French fries with each order. The chef claims that the standard deviation for a ten-ounce order of fries is at most $1.5$oz., but the manager thinks that it may be higher. He randomly weighs$49$ orders of fries, which yields a mean of $11$ oz. and a standard deviation of two oz.

A teacher predict that the distribution of grades on the final exam will be and they are recorded in table 11.27

The actual distribution for a class of 20 is in table 11.28

At the$5\%$significance level, what can you conclude?

The owner of a baseball team is interested in the relationship between player salaries and team winning percentage. He takes a random sample of $100$ players from different organizations.

Transit Railroads is interested in the relationship between travel distance and the ticket class purchased. A random sample of $200$passengers is taken. Table 11.31 shows the results. The railroad wants to know if a passenger’s choice in ticket class is independent of the distance they must travel.

$\begin{array}{|lllll|}\hline \text{Traveling Distance}& \text{Third class}& \text{Second class}& \text{First class}& \text{Total}\\ 1-100\text{miles}& 21& 14& 6& 41\\ 101-200\text{miles}& 18& 16& 8& 42\\ 201-300\text{miles}& 16& 17& 15& 48\\ 301-400\text{miles}& 12.00\%& 14& 21& 47\\ 401-500\text{miles}& 6& 6& 10& 22\\ \text{Total}& 73& 67& 60& 200\\ \hline\end{array}$

State the hypothesis:

$H_0$:

$H_{\mathrm{Î\pm }}$: