Unit 5 Prelab: Chi Square

What is the primary purpose of the Chi-squared test?

• To calculate the average of a dataset.

• To determine if the variation in collected data is due to chance or a tested variable.

• To predict future outcomes based on past data.

• To measure the correlation between two continuous variables.

In the Chi-squared test formula, what do 'O' and 'E' represent?

• 'O' for original data, 'E' for error.

• 'O' for observed data, 'E' for expected data.

• 'O' for outcome, 'E' for experiment.

• 'O' for overall total, 'E' for individual entry.

Which statement accurately describes the null hypothesis in the context of the Chi-squared test?

• There is a significant difference between observed and expected frequencies.

• The observed frequencies are always greater than the expected frequencies.

• There is no significant difference between the observed and expected frequencies.

• The expected frequencies are always greater than the observed frequencies.

If an experiment has two possible outcomes (e.g., heads or tails), what is the degrees of freedom for a Chi-squared test?

• 0

• 1

• 2

• The number of trials.

What is the calculated chi-squared value for the coin toss experiment with 28 heads and 22 tails out of 50 tosses?

• 0.36

• 0.72

• 1.44

• 3.841

Based on the calculated chi-squared value of 0.72 and a critical value of 3.841 (at 1 degree of freedom and 0.05 significance), what conclusion can be drawn about the fairness of the coin?

• The coin is biased, and the null hypothesis should be rejected.

• The coin is fair, and the null hypothesis should be accepted.

• More data is needed to determine the coin's fairness.

• The critical value is too high to draw a conclusion.

For the dice roll experiment with 36 dice, what is the calculated chi-squared value given the observed outcomes (1:2, 2:4, 3:8, 4:9, 5:3, 6:10) and an expected value of 6 for each face?

• 5.8

• 9.6

• 11.070

• 16.0

Given a calculated chi-squared value of 9.6 and a critical value of 11.070 (at 5 degrees of freedom and 0.05 significance), what conclusion can be drawn about the fairness of the dice?

• The dice are biased, and the null hypothesis should be rejected.

• The dice are fair, and the null hypothesis should be accepted.

• The experiment was flawed, and results are inconclusive.

• The critical value is too low for a definitive conclusion.