Random Numbers

Are the random numbers produced by RANDOM.ORG truly random?RANDOM.ORGgenerates true random number using atmospheric noise as opposed to the pseudo random number generator used by most computers. To test the "randomness" of RANDOM.ORG's generator, 10,000 random integers between 0 and 9 were generated. The random numbers are contained in the Random.org.csv data file available from the data repository. Using this data, answer the following questions. Which of the followingstatisticaltests is most appropriate in this situation?

Group of answer choices

Independent samplest-test

Chi-square test of association

Chi-square Goodness of Fit test

Correlation

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Question 2

1pts

Which one of the following hypotheses is the correct Alternate hypothesis for the statistical test chosen above?

Group of answer choices

HA: Each random integer between 0 to 9 has a population proportion = 0.1

HA: Each random integer between 0 to 9 has a population proportion = 1.

HA: Each random integer between 0 to 9 in the population is independent.

HA: At least two random integers between 0 to 9 has a population proportion NOT equal to 0.1.

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Question 3

1pts

Which one of the following hypotheses is the correct Null hypothesis for the statistical test chosen above?

Group of answer choices

H0: Each random integer between 0 to 9 has a population proportion = 0.1

H0: Each random integer between 0 to 9 has a population proportion = 1.

H0: Each random integer between 0 to 9 in the population is independent.

H0: At least two random integers between 0 to 9 has a population proportion NOT equal to 0.1

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Question 4

1pts

Produce a frequency distribution of the random integers. Which integer was the most underrepresented?

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Question 5

1pts

Which integer was the most overrepresented?

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Question 6

1pts

What proportion of random integers were 0? (Round answer to three decimal places)

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Question 7

1pts

What proportion of random integers were 7? (Round answer to three decimal places)

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Question 8

1pts

Determine the degrees of freedom to use for the appropriate hypothesis test.

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Question 9

1pts

Calculate the appropriate test statistic for the hypothesis test. (Round answer to two decimal places)

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Question 10

1pts

How many random integers has expected counts below 5?

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Question 11

1pts

Report thep-value for the appropriate hypothesis test. (Round answer to three decimal places. If thep-value < .001, answer 0.001)

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Question 12

1pts

Using the p-value, make a decision about the Null hypothesis:

Group of answer choices

As thep-value was less than the 0.05 significance level, the decision was to reject H0.

As thep-value was greater than the 0.05 significance level, the decision was to fail to reject H0.

As thep-value was greater than the 0.05 significance level, the decision was to accept HA.

As thep-value was less than the 0.05 significance level, the decision was to fail to accept H0.

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Question 13

1pts

Which one of the following was the correct conclusion to reach?

Group of answer choices

The assumption that the integers produced by RANDOM.ORG are truly random holds as the result of the test was NOT statistically significant.

The result of the test was not statistically significant, suggesting that the integers produced by RANDOM.ORG are NOT truly random.

The assumption that the integers produced by RANDOM.ORG are truly random holds as the result of the test was statistically significant.

The result of the test was statistically significant, suggesting that the integers produced by RANDOM.ORG are NOT truly random.

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Question 14

1pts

Colour

The Colour.csvdataset (available from the data repository) contains the eye colour, hair colour and gender of 592 university students. Researchers want to know if there is an association between these categorical variables. First, the researchers wants to look at the association between gender and eye colour (see the table below). Which of the followingstatisticaltests is most appropriate in this situation?

BlueBrownGreenHazelFemale143528137Male143564634

Group of answer choices

Chi-square test of association.

Chi-square goodness of fit test.

Paired-samples t-test.

One sample t-test.

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Question 15

1pts

Which of the following is the correct Alternate hypothesis?

Group of answer choices

There is no association in the population between gender and eye colour.

There is an association in the population between gender and eye colour.

There is no difference between gender and mean eye colour in the population.

There is no correlation between gender and eye colour in the population.

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Question 16

1pts

Which of the following is the correct Null hypothesis?

Group of answer choices

There is no association in the population between gender and eye colour.

There is an association in the population between gender and eye colour.

There is no difference between gender and mean eye colour in the population.

There is no correlation between gender and eye colour in the population.

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Question 17

1pts

Perform the appropriate statistical test using R.What was the expected count for females with green eyes? (Round answer to two decimal places.)

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Question 18

1pts

What was the expected count for males with blue eyes? (Round answer to two decimal places.)

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Question 19

1pts

How many cells in the cross-tabulation have expected counts below 5?

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Question 20

1pts

What is the correctdffor the appropriate statistical test?

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Question 21

1pts

Calculate and report the test statistic for the association between gender and eye colour. (Round answer to two decimal places.)

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Question 22

1pts

What was thep-value from the statistical test looking at the association between gender and eye colour? (Round answer to three decimal places If thep-value is less than .001, answer 0.001)

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Question 23

1pts

Based on the results of the statistical test looking at the association between gender and eye colour, which of the following is the correct decision?

Group of answer choices

REJECT H0.

FAIL TO REJECT H0.

ACCEPT H0.

ACCEPT HA.

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Question 24

1pts

Which of the following is the correct conclusion to reach from theresultsof the statistical test looking at the association between gender and eye colour?

Group of answer choices

There was no statistically significant evidence of anassociationbetween gender and eye colour.

There was astatisticallysignificant association between gender and eye colour.

The was no significant difference between male and females mean eye colour.

There was no significant correlation between gender and eye colour.

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Question 25

1pts

The following clustered bar chart depicts the association between gender and eye colour. Looking at this plot, select the statement that is TRUE.

Group of answer choices

People with blue eyes are more likely to be male.

People with brown eyes are more likely to be male.

People with green eyes are less likely to be female.

People with hazel eyes are equally likely to be male or female.