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How many passengers are expected to travel between $201$ and $300$ miles and purchase second-class tickets?

Use the following information to answer the next seven exercises: 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.

What is the \(p-\)value?

Determine the appropriate test to be used in the next three exercises.

An archeologist is calculating the distribution of the frequency of the number of artifacts she finds in a dig site. Based on

previous digs, the archeologist creates an expected distribution broken down by grid sections in the dig site. Once the site has been fully excavated, she compares the actual number of artifacts found in each grid section to see if her expectation was accurate.

The standard deviation of heights for students in a school is $0.81$. A random sample of $50$students is taken, and the standard deviation of heights of the sample is $0.96$. A researcher in charge of the study believes the standard deviation of heights for the school is greater than $0.81$.

What type of test should be used?

Decide whether the following statements are true or false:

As the number of degrees of freedom increases, the graph of the chi-square distribution looks more and more symmetrical.

Determine the appropriate test to be used in the next three exercises.

An economist is deriving a model to predict outcomes on the stock market. He creates a list of expected points on the stock market index for the next two weeks. At the close of each day's trading, he records the actual points on the index. He wants to see how well his model matched what actually happened.

The mean and the median of the chi-square distribution are the same if $df=24$.

A six-sided die is rolled $120$times. Fill in the expected frequency column. Then, conduct a hypothesis test to determine if the die is fair. The data in Table $11.34$are the result of the $120$rolls.

The marital status distribution of the U.S. male population, ages 15 a nd older, is as shown in Table

Suppose that a random sample of 400 U.S. young adult males, 18 to 24 years old, yielded the following frequency distribution. We are interested in whether this age group of males fits the distribution of the U.S. adult population. Calculate the frequency one would expect when surveying 400 people. Fill in Table 11.35, rounding to two decimal places.

The marital status distribution of the U.S. male population, ages $15$and older, is as shown in Table 11.35.