Practice Test 1.3 Chi Square Test for Goodness of Fit

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A poker-dealing machine is supposed to deal cards at random, as if from an infinite deck. You suspect that the machine is rigged! In a test, you counted 1600 cards, and observed the following:

Spades = 404, Hearts = 420, Diamonds = 400, Clubs = 376

Which of the following is the null hypothesis for this experiment?

The machine is unfair.

The machine is fair.

Poker-dealing machines do not exist.

The machine does not deal any cards.

Which of the following is the null hypothesis for this experiment? (again)

The proportion of cards of each of the four suits are not equal.

There are fewer of one suit than the others.

The chi square value will be below the critical value.

The proportion of cards of each of the four suits are equal.

How many degrees of freedom are there?

What is the level of significance (α) that we will always use in this class?

What is the critical value?

What is the decision rule?

If the chi-square value is greater than the critical value, reject the null hypothesis.

If the chi-square value is less than the critical value, accept the null hypothesis.

If the chi-square value is less than the critical value, reject the null hypothesis.

If the chi-square value is greater than the critical value, accept the null hypothesis.

Calculate χ2. Use 2 decimal places.

Based on the chi square value, which of the following is the corresponding p-value?

Which of the following is the best conclusion?

Which of the following is an accurate statement. Insert your calculated value for "<p-value>".

There is a <p-value> probability that the hypothesis is true.

There is a <p-value> probability that the null hypothesis is true.

If the hypothesis is true, there is a probability of <p-value> of obtaining results at least as extreme as our results.

If the null hypothesis is true, there is a probability of <p-value> of obtaining results at least as extreme as our results.

There isn't a <p-value> chance that the hypothesis isn't not false.

Which of the following is the null hypothesis for this experiment?

The machine is unfair.

The machine is fair.

Poker-dealing machines do not exist.

The machine does not deal any cards.

Which of the following is the null hypothesis for this experiment? (again)

The proportion of cards of each of the four suits are not equal.

There are fewer of one suit than the others.

The chi square value will be below the critical value.

The proportion of cards of each of the four suits are equal.

What is the decision rule?

If the chi-square value is greater than the critical value, reject the null hypothesis.

If the chi-square value is less than the critical value, accept the null hypothesis.

If the chi-square value is less than the critical value, reject the null hypothesis.

If the chi-square value is greater than the critical value, accept the null hypothesis.

Based on the chi square value, which of the following is the corresponding p-value?

p<0.005

0.005<p<0.01

0.01<p<0.05

0.05<p<0.10

0.10<p<0.20

0.20<p<0.30

0.30<p<0.50

0.50<p<0.70

0.70<p<0.80

0.08<p<0.95

p>0.95

Which of the following is the best conclusion?

Fail to reject the null hypothesis

Fail to reject the hypothesis

Reject the hypothesis

Accept the hypothesis

Accept the null hypothesis

Reject the null hypothesis

Which of the following is an accurate statement. Insert your calculated value for "<p-value>".

There is a <p-value> probability that the hypothesis is true.

There is a <p-value> probability that the null hypothesis is true.

If the hypothesis is true, there is a probability of <p-value> of obtaining results at least as extreme as our results.

If the null hypothesis is true, there is a probability of <p-value> of obtaining results at least as extreme as our results.

There isn't a <p-value> chance that the hypothesis isn't not false.