Question 1

When performing a hypothesis test to compare two or more population proportions, the null hypothesis is always that not all population proportions are equal.

Accepted Answer

In hypothesis testing for comparing two or more population proportions, the null hypothesis typically states that all population proportions are equal.

Question 2

The chi- square test for independence is used to decide if observed frequencies follow a known probability distribution.

Accepted Answer

The chi-square test for independence is used to determine if there is a significant association between two categorical variables, not to decide if observed frequencies follow a known probability distribution.

Question 3

Nationwide Insurance would like to perform a chi- square test to investigate whether a difference exists in the proportion of male and female teenagers who text while they drive. A random sample of 80 male teenagers found that 50 indicated they texted while driving. A random sample of 120 female teenagers found that 65 indicated they texted while driving. The chi- square critical value using α = 0.5 is ______ .

Accepted Answer

The chi-square test for independence requires a significance level (α) to determine the critical value from the chi-square distribution table. However, the provided α = 0.5 seems to be a mistake, as common significance levels are 0.01, 0.05, or 0.10. Assuming the intended significance level was α = 0.05 (5%), for a chi-square test with 1 degree of freedom (which is the case for a 2x2 contingency table comparing two proportions), the correct critical value is 3.841.

Question 4

The _____ frequencies refer to the frequencies that are most likely to occur if the null hypothesis is true when performing a hypothesis test comparing two or more population proportions.

Accepted Answer

Expected frequencies are the frequencies that we would expect to observe in each category if the null hypothesis were true. They are calculated based on the assumption that the null hypothesis is correct, and are used to compare against the observed frequencies to determine if there is a significant difference that would lead to rejecting the null hypothesis.

Question 5

Nationwide Insurance would like to perform a chi- square test to investigate whether a difference exists in the proportion of male and female teenagers who text while they drive. A random sample of 80 male teenagers found that 50 indicated they texted while driving. A random sample of 120 female teenagers found that 65 indicated they texted while driving. The degrees of freedom for the chi- square critical value is ______.

Accepted Answer

The degrees of freedom for a chi-square test in this context is calculated as (number of rows - 1) * (number of columns - 1). Since there are 2 groups (male and female) and 2 outcomes (texted while driving, did not text while driving), the calculation is (2-1)*(2-1) = 1.

Question 6

When testing for a normal distribution with the chi- square goodness- of- fit test with a sample size of 240 observations, the number of intervals needed to satisfy the minimum number of expected frequencies is ______ .

Accepted Answer

The chi-square goodness-of-fit test typically requires that each interval or category used in the analysis has an expected frequency of at least 5 to ensure the validity of the test. With a sample size of 240 observations, dividing the data into 6 intervals would give an expected frequency of 40 observations per interval (240/6 = 40), which satisfies the minimum requirement. Fewer intervals might not provide a detailed enough assessment of the distribution, and more intervals could result in some having expected frequencies less than 5, which would not meet the test's assumptions.

Question 7

When testing for a normal distribution with the chi- square goodness- of- fit test with a sample size of 50 observations, the number of intervals needed to satisfy the minimum number of expected frequencies is _____-_ .

Accepted Answer

The answer of When testing for a normal distribution with...

Question 8

Nationwide Insurance would like to perform a chi- square test to investigate whether a difference exists in the proportion of male and female teenagers who text while they drive. A random sample of 80 male teenagers found that 50 indicated they texted while driving. A random sample of 120 female teenagers found that 65 indicated they texted while driving. The expected frequency of female teenagers who text is ______.

Accepted Answer

The expected frequency is calculated using the formula for expected counts in a chi-square test, which is (Row Total * Column Total) / Grand Total. Here, the grand total of teenagers is 200 (80 males + 120 females), and the total number who text while driving is 115 (50 males + 65 females). The expected frequency of female teenagers who text while driving is (120 * 115) / 200 = 69.

Question 9

The rejection region for the chi- square test to compare two or more population proportions lies on the right tail of the chi- square distribution.

Accepted Answer

The chi-square test is used to compare categorical variables, and its distribution is not symmetrical but skewed to the right. Therefore, the rejection region for a chi-square test, when testing for differences in proportions or frequencies, is located in the right tail of the chi-square distribution.

Question 10

When performing a hypothesis test to compare two or more population proportions, the test statistic follows the ______.

Accepted Answer

When comparing two or more population proportions, the test statistic follows the chi-square distribution, particularly when using the chi-square test for independence or homogeneity.

Question 11

The ______ frequencies refer to the sample data collected from a population of interest when performing a hypothesis test comparing two or more population proportions.

Accepted Answer

Observed frequencies refer to the actual data collected from a sample when comparing two or more population proportions in hypothesis testing. Expected frequencies would be the hypothesized or theoretical frequencies based on the null hypothesis. Cumulative frequencies are the sum of frequencies up to a certain point, and relative frequencies are the proportion of the total count.

Question 12

The chi- square test requires that each expected frequency be equal to or greater than _____.

Accepted Answer

The chi-square test requires that each expected frequency be at least 5 to ensure the validity of the test's assumptions.

Question 13

When using the chi- square hypothesis test and the observed frequencies are relatively close to the expected frequencies, which one of the following statements is true?

Accepted Answer

When observed frequencies are close to expected frequencies, the chi-square statistic tends to be smaller, indicating a smaller difference between observed and expected values. This smaller chi-square value increases the likelihood of not rejecting the null hypothesis, suggesting that the observed frequencies are consistent with the expected frequencies under the null hypothesis.

Question 14

Nationwide Insurance would like to perform a chi- square test to investigate whether a difference exists in the proportion of male and female teenagers who text while they drive. A random sample of 80 male teenagers found that 50 indicated they texted while driving. A random sample of 120 female teenagers found that 65 indicated they texted while driving. Using α = 0.5, the conclusion for this chi- square test would be that because the test statistic is

Accepted Answer

The alpha level provided (α = 0.5) seems to be a typographical error since standard alpha levels are typically 0.05, 0.01, etc. Regardless, the explanation for the chi-square test conclusion is based on comparing the test statistic to the critical value. If the test statistic is less than the critical value, it indicates that the observed differences could be due to chance, and we cannot reject the null hypothesis, which posits no difference in proportions. Therefore, without specific values for the test statistic and critical value, the general principle is that being less than the critical value leads to not rejecting the null hypothesis.

Question 15

Nationwide Insurance would like to perform a chi- square test to investigate whether a difference exists in the proportion of male and female teenagers who text while they drive. A random sample of 80 male teenagers found that 50 indicated they texted while driving. A random sample of 120 female teenagers found that 65 indicated they texted while driving. The expected frequency of male teenagers who text is _______.

Accepted Answer

To find the expected frequency of male teenagers who text while driving, we first calculate the total number of teenagers surveyed (80 males + 120 females = 200) and the total number who text while driving (50 males + 65 females = 115). The expected frequency is calculated by multiplying the total number of males by the proportion of teenagers who text while driving (115/200). So, for males, it's (80/200) * 115 = 46.

Question 16

When testing for a normal distribution with the chi- square goodness- of- fit test with a sample size of 100 observations, the number of intervals needed to satisfy the minimum number of expected frequencies is _______ .

Accepted Answer

To satisfy the minimum number of expected frequencies (at least 5 per interval) with a sample size of 100, you need at least 5 intervals.

Question 17

The airline industry defines no- shows as passengers who have purchased a ticket but fail to arrive at the gate on time for departure. Southwest Airlines operates many flights from Philadelphia to Dallas and experienced the following no- show probability distribution last year.
$$\begin{array} { l | l | l | l | l | l | l | l } 
\text { No-shows } & 0 & 1 & 2 & 3 & 4 & 5 & 6 \
\hline \text { Probability } & 6 \% & 12 \% & 22 \% & 28 \% & 17 \% & 11 \% & 4 \%
\end{array}$$
The following data represent the number of no-show has changed between last year on flights between these cities using ?=0.05. The degrees of freedom for the critical value is _____

Accepted Answer

The degrees of freedom for a chi-square test, which is likely the test being referred to for comparing distributions, is calculated as the number of categories minus one. Here, there are 7 categories of no-shows (0, 1, 2, 3, 4, 5, 6), so the degrees of freedom would be 7 - 1 = 6.

Question 18

When testing for a normal distribution with the chi- square goodness- of- fit test with a sample size of 30 observations, the number of intervals needed to satisfy the minimum number of expected frequencies is ________ .

Accepted Answer

The answer of When testing for a normal distribution with...

Question 19

Nationwide Insurance would like to perform a chi- square test to investigate whether a difference exists in the proportion of male and female teenagers who text while they drive. A random sample of 80 male teenagers found that 50 indicated they texted while driving. A random sample of 120 female teenagers found that 65 indicated they texted while driving. The chi- square test statistic for this sample is ______.

Accepted Answer

The answer of Nationwide Insurance would like to perform a...

Question 20

For a chi- square test of independence, the expected frequencies are calculated under the assumption that the null hypothesis is true.

Accepted Answer

In a chi-square test of independence, expected frequencies are indeed calculated based on the assumption that the null hypothesis (which typically posits no association between the variables) is true. This allows for the comparison of observed frequencies with what would be expected if the variables were independent of each other.

Quiz 12: Infectious Conditions

When performing a hypothesis test to compare two or more population proportions, the null hypothesis is always that not all population proportions are equal.

The chi- square test for independence is used to decide if observed frequencies follow a known probability distribution.

The _____ frequencies refer to the frequencies that are most likely to occur if the null hypothesis is true when performing a hypothesis test comparing two or more population proportions.

When testing for a normal distribution with the chi- square goodness- of- fit test with a sample size of 240 observations, the number of intervals needed to satisfy the minimum number of expected frequencies is ______ .

When testing for a normal distribution with the chi- square goodness- of- fit test with a sample size of 50 observations, the number of intervals needed to satisfy the minimum number of expected frequencies is _____-_ .

The rejection region for the chi- square test to compare two or more population proportions lies on the right tail of the chi- square distribution.

When performing a hypothesis test to compare two or more population proportions, the test statistic follows the ______.

The ______ frequencies refer to the sample data collected from a population of interest when performing a hypothesis test comparing two or more population proportions.

The chi- square test requires that each expected frequency be equal to or greater than _____.

When using the chi- square hypothesis test and the observed frequencies are relatively close to the expected frequencies, which one of the following statements is true?

When testing for a normal distribution with the chi- square goodness- of- fit test with a sample size of 100 observations, the number of intervals needed to satisfy the minimum number of expected frequencies is _______ .

When testing for a normal distribution with the chi- square goodness- of- fit test with a sample size of 30 observations, the number of intervals needed to satisfy the minimum number of expected frequencies is ________ .

For a chi- square test of independence, the expected frequencies are calculated under the assumption that the null hypothesis is true.