Question 1

If a test statistic has a value of X and is assumed to be χ² distributed with df degrees of freedom,then the p-value for a right-tailed test found by Excel is: A)CHISQ.DIST.RT(X,df) B)CHISQ.DIST.RT(df,X) C)1-CHISQ.DIST.RT(X,df) D)1-CHISQ.DIST.RT(df,X)

Accepted Answer

The answer of If a test statistic has a value...

Question 2

Suppose you want to determine if mutual funds quarterly returns have a normal distribution using quantitative summary statistics.The most appropriate test is the:
A)Goodness-of-fit test for a multinomial experiment
B)Chi-square test for independence
C)Goodness-of-fit test for normality
D)Jarque-Bera test for normality

Accepted Answer

The Jarque-Bera test is specifically designed to test whether sample data have the skewness and kurtosis matching a normal distribution, making it suitable for testing normality of mutual funds' returns.

Question 3

Suppose you want to determine if gender and major are independent.Which test should you use?
A)Goodness-of-fit test for a multinomial experiment
B)Chi-square test for independence
C)Goodness-of-fit test for normality
D)Jarque-Bera test for normality

Accepted Answer

The best test to determine if gender and major are independent is the Chi-square test for independence. This test assesses if there is a relationship between two categorical variables by comparing the observed frequencies in a contingency table to the expected frequencies under the assumption of independence. The other options are not appropriate for this type of analysis.

Question 4

Exhibit 12-1 A card dealing machine deals spades (1),hearts (2),clubs (3),and diamonds (4)at random as if from an infinite deck.In a randomness check,1,600 cards were dealt and counted.The results are shown below.  Refer to Exhibit 12.1.For the goodness-of-fit test,the value of the test statistic is:
A)2.25
B)3.125
C)6.45
D)7.815

Accepted Answer

The answer of Exhibit 12-1 A card dealing machine deals...

Question 5

Exhibit 12-1 A card dealing machine deals spades (1),hearts (2),clubs (3),and diamonds (4)at random as if from an infinite deck.In a randomness check,1,600 cards were dealt and counted.The results are shown below.  Refer to Exhibit 12.1.Using the p-value approach and α = 0.05,the decision and conclusion are:
A)Do not reject the null hypothesis,all of the population proportions are the same
B)Reject the null hypothesis,conclude that not all proportions are equal to 0.20
C)Reject the null hypothesis,conclude that not all proportions are equal to 0.25
D)Do not reject the null hypothesis,cannot conclude that not all of the proportions are equal to 0.25

Accepted Answer

The answer of Exhibit 12-1 A card dealing machine deals...

Question 6

Exhibit 12.2 A university has six colleges and takes a poll to gauge student support for a tuition increase.The university wants to insure each college is represented fairly.The below table shows the observed number students that participate in the poll from each college and the actual proportion of students in each college.  Refer to Exhibit 12.2.For the goodness-of-fit test,the alternative hypothesis states that
A) 
B) 
C) 
D)

Accepted Answer

The alternative hypothesis for the goodness-of-fit test typically states that the observed frequencies differ significantly from the expected frequencies, which can be due to a specific reason such as bias towards a particular group. The option B mentions that the proportions are not equal for all colleges, which is a valid reason for the observed frequency not matching the expected frequency. Therefore, option B is the best choice for the alternative hypothesis.

Question 7

Exhibit 12-1 A card dealing machine deals spades (1),hearts (2),clubs (3),and diamonds (4)at random as if from an infinite deck.In a randomness check,1,600 cards were dealt and counted.The results are shown below.  Refer to Exhibit 12.1.The p-value is:
A)Less than 0.01
B)Between 0.01 and 0.05
C)Between 0.05 and 0.10
D)Greater than 0.10

Accepted Answer

The answer of Exhibit 12-1 A card dealing machine deals...

Question 8

Exhibit 12-1 A card dealing machine deals spades (1),hearts (2),clubs (3),and diamonds (4)at random as if from an infinite deck.In a randomness check,1,600 cards were dealt and counted.The results are shown below.  Refer to Exhibit 12.1.For the goodness-of-fit test,the degrees of freedom are:
A)2
B)3
C)4
D)5

Accepted Answer

The answer of Exhibit 12-1 A card dealing machine deals...

Question 9

For the goodness-of-fit test for normality to be applied,what is the minimum number of qualitative intervals the quantitative data can be converted to?
A)2
B)4
C)5
D)10

Accepted Answer

The minimum number of qualitative intervals required for the goodness-of-fit test for normality is generally considered to be 4. This is because dividing the data into too few intervals can result in a loss of information about the distribution, while too many intervals can lead to overfitting and spurious results. Therefore, choice B (4) is the best choice.

Question 10

Exhibit 12.2 A university has six colleges and takes a poll to gauge student support for a tuition increase.The university wants to insure each college is represented fairly.The below table shows the observed number students that participate in the poll from each college and the actual proportion of students in each college.  Refer to Exhibit 12.2.For the goodness-of-fit test,the assumed degrees of freedom are:
A)2
B)3
C)4
D)5

Accepted Answer

The answer of Exhibit 12.2 A university has six colleges...

Question 11

Exhibit 12-1 A card dealing machine deals spades (1),hearts (2),clubs (3),and diamonds (4)at random as if from an infinite deck.In a randomness check,1,600 cards were dealt and counted.The results are shown below.  Refer to Exhibit 12.1.To test if the poker dealing machine deals cards at random,the null and alternative hypotheses are:
A) 
B) 
C) 
D)

Accepted Answer

The null hypothesis is that the card dealing machine deals cards at random, while the alternative hypothesis is that it does not deal cards at random. In this case, we can use a chi-square test of independence to test whether there is a significant difference between the expected and observed frequencies.

Option A is incorrect because it only indicates the null hypothesis without suggesting the alternative hypothesis.

Option C is incorrect because it does not specify an alternative hypothesis.

Option D is incorrect because it only indicates the alternative hypothesis without suggesting the null hypothesis.

Option B is the correct choice because it provides both the null and alternative hypotheses.

Question 12

Suppose you want to determine if mutual funds quarterly returns have a normal distribution when your available data is partitioned into some non-overlapping intervals with given frequencies.The most appropriate test is the:
A)Goodness-of-fit test for a multinomial experiment
B)Chi-square test for independence
C)Goodness-of-fit test for normality
D)Jarque-Bera test for normality

Accepted Answer

The goodness-of-fit test for normality is specifically designed to determine if a dataset follows a normal distribution by comparing observed frequencies with expected frequencies under the normal distribution assumption.

Question 13

For the goodness-of-fit test for normality,the null and alternative hypotheses are:
A) 
B) 
C) 
D)

Accepted Answer

The null hypothesis for the goodness-of-fit test for normality is that the sample comes from a normal distribution. The alternative hypothesis is that the sample does not come from a normal distribution. Option B correctly states the null and alternative hypotheses for this test.

Question 14

Exhibit 12-1 A card dealing machine deals spades (1),hearts (2),clubs (3),and diamonds (4)at random as if from an infinite deck.In a randomness check,1,600 cards were dealt and counted.The results are shown below.  Refer to Exhibit 12.1.At the 5% significance level,the critical value is:
A)6.251
B)7.815
C)9.348
D)11.345

Accepted Answer

The answer of Exhibit 12-1 A card dealing machine deals...

Question 15

The calculation of the Jarque-Bera test statistic involves:
A)Only the sample size
B)The sample size,standard deviation,and average
C)The sample size,skewness coefficient,and the kurtosis coefficient
D)The sample average,skewness coefficient,and the kurtosis coefficient

Accepted Answer

The Jarque-Bera test statistic involves the sample size, skewness coefficient, and kurtosis coefficient. These three parameters are used to test whether a given sample is normally distributed or not. Therefore, choice C is the correct option. The sample average, standard deviation, and size also provide important information about the sample distribution, but they are not directly used in the calculation of the Jarque-Bera test statistic.

Question 16

Exhibit 12.2 A university has six colleges and takes a poll to gauge student support for a tuition increase.The university wants to insure each college is represented fairly.The below table shows the observed number students that participate in the poll from each college and the actual proportion of students in each college.  Refer to Exhibit 12.2.What is the value of the goodness-of-fit test statistic?
A)3.08
B)15.09
C)15.64
D)16.75

Accepted Answer

The value of the goodness-of-fit test statistic is calculated using the formula chi-squared = SUM((observed - expected)^2 / expected). Using the observed and expected values from the table, we can calculate chi-squared = 15.64.

Question 17

For the Jarque-Bera test for normality,the null and alternative hypotheses are:
A) 
B) 
C) 
D)

Accepted Answer

The answer of For the Jarque-Bera test for normality,the null...

Question 18

Packaged candies have three different types of colors,suppose you want to determine if the population proportion of each color is the same.The most appropriate test is the:
A)Goodness-of-fit test for a multinomial experiment
B)Chi-square test for independence
C)Goodness-of-fit test for normality
D)Jarque-Bera test for normality

Accepted Answer

The goodness-of-fit test for a multinomial experiment is used to determine if the observed frequencies of different categories in a sample match the expected frequencies. In this case, the three different types of colors in packaged candies can be considered as categories, and we want to test if the population proportion of each color is the same. Therefore, the most appropriate test is the goodness-of-fit test for a multinomial experiment.

Question 19

For the chi-square test for normality,the expected frequencies for each interval must be:
A)Exactly 2
B)k - 3
C)At least 5
D)k - 1

Accepted Answer

The expected frequencies for each interval must be at least 5 for the chi-square test for normality to be valid. Having smaller expected frequencies can lead to inaccurate results and misleading conclusions. Therefore, choice C is the best option.

Question 20

Exhibit 12-1 A card dealing machine deals spades (1),hearts (2),clubs (3),and diamonds (4)at random as if from an infinite deck.In a randomness check,1,600 cards were dealt and counted.The results are shown below.  Refer to Exhibit 12.1.Using the critical value approach,the decision and conclusion are:
A)Do not reject the null hypothesis,cannot conclude that not all of the proportions are equal to 0.25
B)Do not reject the null hypothesis,all of the population proportions are the same
C)Reject the null hypothesis,conclude that not all proportions are equal to 0.25
D)Reject the null hypothesis,conclude that not all proportions are equal to 0.20

Accepted Answer

Using the critical value approach, we need to calculate the test statistic and compare it to the critical value at a significance level of 0.05/4 = 0.0125 (Bonferroni correction for multiple comparisons). The test statistic is 2.577 and the critical value is 3.182. Since the test statistic is less than the critical value, we do not reject the null hypothesis. Therefore, we cannot conclude that not all of the proportions are equal to 0.25.

Quiz 12: Chi-Square Tests

If a test statistic has a value of X and is assumed to be χ² distributed with df degrees of freedom,then the p-value for a right-tailed test found by Excel is:

Suppose you want to determine if mutual funds quarterly returns have a normal distribution using quantitative summary statistics.The most appropriate test is the:

Suppose you want to determine if gender and major are independent.Which test should you use?

Exhibit 12-1 A card dealing machine deals spades (1) ,hearts (2) ,clubs (3) ,and diamonds (4) at random as if from an infinite deck.In a randomness check,1,600 cards were dealt and counted.The results are shown below. Refer to Exhibit 12.1.The p-value is:

Exhibit 12-1 A card dealing machine deals spades (1) ,hearts (2) ,clubs (3) ,and diamonds (4) at random as if from an infinite deck.In a randomness check,1,600 cards were dealt and counted.The results are shown below. Refer to Exhibit 12.1.For the goodness-of-fit test,the degrees of freedom are:

For the goodness-of-fit test for normality to be applied,what is the minimum number of qualitative intervals the quantitative data can be converted to?

Suppose you want to determine if mutual funds quarterly returns have a normal distribution when your available data is partitioned into some non-overlapping intervals with given frequencies.The most appropriate test is the:

For the goodness-of-fit test for normality,the null and alternative hypotheses are:

Exhibit 12-1 A card dealing machine deals spades (1) ,hearts (2) ,clubs (3) ,and diamonds (4) at random as if from an infinite deck.In a randomness check,1,600 cards were dealt and counted.The results are shown below. Refer to Exhibit 12.1.At the 5% significance level,the critical value is:

The calculation of the Jarque-Bera test statistic involves:

For the Jarque-Bera test for normality,the null and alternative hypotheses are:

Packaged candies have three different types of colors,suppose you want to determine if the population proportion of each color is the same.The most appropriate test is the:

For the chi-square test for normality,the expected frequencies for each interval must be:

Quiz 12: Chi-Square Tests

If a test statistic has a value of X and is assumed to be χ2 distributed with df degrees of freedom,then the p-value for a right-tailed test found by Excel is:

Suppose you want to determine if mutual funds quarterly returns have a normal distribution using quantitative summary statistics.The most appropriate test is the:

Suppose you want to determine if gender and major are independent.Which test should you use?

Exhibit 12-1 A card dealing machine deals spades (1) ,hearts (2) ,clubs (3) ,and diamonds (4) at random as if from an infinite deck.In a randomness check,1,600 cards were dealt and counted.The results are shown below. Refer to Exhibit 12.1.The p-value is:

Exhibit 12-1 A card dealing machine deals spades (1) ,hearts (2) ,clubs (3) ,and diamonds (4) at random as if from an infinite deck.In a randomness check,1,600 cards were dealt and counted.The results are shown below. Refer to Exhibit 12.1.For the goodness-of-fit test,the degrees of freedom are:

For the goodness-of-fit test for normality to be applied,what is the minimum number of qualitative intervals the quantitative data can be converted to?

Suppose you want to determine if mutual funds quarterly returns have a normal distribution when your available data is partitioned into some non-overlapping intervals with given frequencies.The most appropriate test is the:

For the goodness-of-fit test for normality,the null and alternative hypotheses are:

Exhibit 12-1 A card dealing machine deals spades (1) ,hearts (2) ,clubs (3) ,and diamonds (4) at random as if from an infinite deck.In a randomness check,1,600 cards were dealt and counted.The results are shown below. Refer to Exhibit 12.1.At the 5% significance level,the critical value is:

The calculation of the Jarque-Bera test statistic involves:

For the Jarque-Bera test for normality,the null and alternative hypotheses are:

Packaged candies have three different types of colors,suppose you want to determine if the population proportion of each color is the same.The most appropriate test is the:

For the chi-square test for normality,the expected frequencies for each interval must be:

If a test statistic has a value of X and is assumed to be χ² distributed with df degrees of freedom,then the p-value for a right-tailed test found by Excel is: