Chi-Squared Test Concepts

Kenny plays rock-paper-scissors and suspects his outcomes aren't evenly distributed. He samples 24 games, recording 4 wins, 13 losses, and 7 ties. To test if his outcomes deviate from an even distribution, he performs a chi-squared goodness-of-fit test. The null hypothesis assumes equal probability for each outcome. Conditions for the test include randomness, large counts, and independence. Calculating the chi-squared statistic involves comparing observed and expected outcomes. With 2 degrees of freedom, the p-value is between 0.05 and 0.10, leading to a failure to reject the null hypothesis.

What was Kenny's suspicion about his rock-paper-scissors game outcomes?

• He was winning too often.

• The outcomes were not equally distributed.

• He was losing too often.

• The outcomes were always ties.

What is the null hypothesis in Kenny's chi-squared test?

• Kenny wins more often than he loses.

• All outcomes have different probabilities.

• Kenny loses more often than he ties.

• All outcomes have equal probabilities.

Which condition is NOT required for a chi-squared goodness-of-fit test?

• Equal sample sizes

• Independence

• Large counts

• Random sampling

What is the expected number of wins, losses, and ties if the outcomes are equally probable?

• 6, 9, 9

• 5, 10, 9

• 8, 8, 8

• 4, 13, 7

How is the chi-squared statistic calculated?

• Difference between expected values

• Product of observed and expected values

• Difference between observed and expected values squared, divided by expected values

• Sum of observed values

What is the chi-squared statistic value calculated from Kenny's data?

• 5.25

• 4.25

• 6.25

• 7.25

What does a p-value indicate in a chi-squared test?

• The probability of the null hypothesis being true

• The probability of observing a result as extreme as the test statistic

• The probability of the alternative hypothesis being true

• The probability of the test statistic being zero

What is the range of the p-value for Kenny's test?

• Greater than 0.10

• Between 0.01 and 0.05

• Less than 0.01

• Between 0.05 and 0.10

What is the significance level typically used to decide whether to reject the null hypothesis?

• 5%

• 1%

• 15%

• 10%

What conclusion can be drawn if the p-value is greater than the significance level?

• The test is inconclusive

• Accept the alternative hypothesis

• Fail to reject the null hypothesis

• Reject the null hypothesis