Use the two-way table below and answer the questions. 1) P (< 3 cars | 3 to 5 kids) = ? 2) P ( > 3 kids or >= 2 cars) = ?

You randomly survey students in your school about whether they have a pet. You display your results in the two-way table. How many female students took the survey?
$\begin{array}{}& & Pet\\ Gender& Male& 33& 8\\ & Female& 35& 11\end{array}$

One hundred adults and children were randomly selected and asked whether they spoke more than one language fluently. The data were recorded in a two-way table. Maria and Brennan each used the data to make the tables of joint relative frequencies shown below, but their results are slightly different. The difference is shaded. Can you tell by looking at the tables which of them made an error?

Please, tell whether the statement is TRUE or FALSE.
1) The F distribution is symmetric, and its mean is close to 1.
2) A small P-value indicates that the two variables in a two-way table are associated.
3) If the null hypothesis of an ANOVA F-test is true, the F statistic is greater than 1.
4) The more similar the conditional distributions in a two-way table are, the smaller the P-value of the chi-square test becomes.
5) In a two-way table, if the expected counts are about the same as the observed counts, we reject the null hypothesis.
6) The larger the chi-square statistic, the stronger the evidence against the null hypothesis.
7) In a two-way table, if the expected counts are about the same as the observed counts, we reject the null hypothesis.

Statistics students at a state college compiled the following two-way table from a sample of randomly selected students at their college:
$\begin{array}{|ccc|}\hline & \text{Play chess}& \text{Don`t play chess}\\ \text{Male students}& 25& 162\\ \text{Female students}& 19& 148\\ \hline\end{array}$
Answer the following questions about the table. Be sure to show any calculations.
What question about the population of students at the state college would this table attempt to answer?
State $H^0$ and $H^1$ for the test related to this table.

Tell whether the statement is TRUE or FALSE.
1. The F distribution is not symmetric but skewed to the right (or skewed positively).
2. If the null hypothesis of an ANOVA F-test is true, the F statistic is close to one.
3. In a two-way table, if the expected counts are about the same as the observed counts, we fail to reject the null hypothesis.
4. If the conditional distributions in a two-way table are similar to each other, the P-value of the test is close to zero.
5. A small P-value indicates that the two variables in a two-way table are not associated.

Find ${\displaystyle P(A\cup B)}$

Complete the table.
GradeFrequencyRelative frequency
A5
B11
C16
D5
F1
(Round to two decimal places as needed.)