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A sample of $300$students is taken. Of the students surveyed,$50$were music students, while $250$were not. Ninetyseven were on the honor roll, while$203$ were not. If we assume being a music student and being on the honor roll are independent events, what is the expected number of music students who are also on the honor roll?

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

If the number of degrees of freedom for a chi-square distribution is 25, what is the population mean and standard deviation?

A psychologist is interested in testing whether there is a difference in the distribution of personality types for business majors and social science majors. The results of the study are shown in Table. Conduct a test of homogeneity. Test at a $5\%$level of significance.

$\begin{array}{|llllll|}\hline & \text{Open}& \text{Conscientious}& \text{Extrovert}& \text{Agreeable}& \text{Neurotic}\\ \text{Business}& 41& 52& 46& 61& 58\\ \text{Social Science}& 72& 75& 63& 80& 65\\ \hline\end{array}$

Do men and women select different breakfasts? The breakfasts ordered by randomly selected men and women at a popular breakfast place are shown in Table. Conduct a test for homogeneity at a $5\%$level of significance.

$\begin{array}{|lllll|}\hline & \text{French Toast}& \text{Pancakes}& \text{Waffles}& \text{Omelettes}\\ \text{Men}& 47& 35& 28& 53\\ \text{Women}& 65& 59& 55& 60\\ \hline\end{array}$

A fisherman is interested in whether the distribution of fish caught in Green Valley Lake is the same as the distribution of fish caught in Echo Lake. Of the 191 randomly selected fish caught in Green Valley Lake, 105 were rainbow trout, 27 were other trout, 35 were bass, and 24 were catfish. Of the 293 randomly selected fish caught in Echo Lake, 115 were rainbow trout, 58 were other trout, 67 were bass, and 53 were catfish. Perform a test for homogeneity at a 5% level of significance.

When looking at energy consumption, we are often interested in detecting trends over time and how they correlate among different countries. The information in Table 11.57 shows the average energy use (in units of kg of oil equivalent per capita) in the USA and the joint European Union countries (EU) for the six-year period 2005 to 2010. DoW? Perform the analysis at the 5% significance level.

Is there a difference between the distribution of community college statistics students and the distribution of university statistics students in what technology they use on their homework? Of some randomly selected community college students, 43 used a computer, 102 used a calculator with built in statistics functions, and 65 used a table from the textbook. Of some randomly selected university students, 28 used a computer, 33 used a calculator with built in statistics functions, and 40 used a table from the textbook. Conduct an appropriate hypothesis test using a 0.05 level of significance.

Read the statement and decide whether it is true or false.

Teachers want to know which night each week their students are doing most of their homework. Most teachers think that students do homework equally throughout the week. Suppose a random sample of 56 students were asked on which night of the week they did the most homework. The results were distributed as in Table 11.8.$\begin{array}{|llllllll|}\hline & \text{Sunday}& \text{Monday}& \text{Tuesday}& \text{Wednesday}& \text{Thursday}& \text{Friday}& \text{Saturday}\\ \begin{array}{l}\text{Number of}\\ \text{Students}\end{array}& 11& 8& 10& 7& 10& 5& 5\\ \hline\end{array}$

From the population of students, do the nights for the highest number of students doing the majority of their homework occur with equal frequencies during a week? What type of hypothesis test should you use?

Students in a social studies class hypothesize that the literacy rates across the world for every region are \(82%\). Table 11.14 shows the actual literacy rates across the world broken down by region. What are the test statistic and the degrees of freedom?