Question
State whether you think the differences between what occurred and what you would expect by chance is statistically significant
You draw a card at random from a deck of cards and replace it. You repeat this 100 times and get an ace 40 times
You draw a card at random from a deck of cards and replace it. You repeat this 100 times and get an ace 40 times
Answers
GPT 3.5
To determine if the difference between the observed frequency of getting an ace (40 times) and the expected frequency by chance is statistically significant, we need to perform a statistical test.
The appropriate test to use in this scenario is the binomial test since we are dealing with a categorical variable (ace or non-ace) and a known population size (52 cards in a deck).
Let's set up the hypotheses:
- Null hypothesis (H0): The observed frequency of getting an ace is not significantly different from the expected frequency by chance.
- Alternative hypothesis (Ha): The observed frequency of getting an ace is significantly different from the expected frequency by chance.
Using the binomial test, we can calculate the probability of getting 40 or more aces out of 100 trials under the null hypothesis. If this probability is very low (typically less than 0.05 or 5%), we would reject the null hypothesis and conclude that the difference is statistically significant.
However, we would need to know the baseline chance of an ace occurring in a single draw from the deck to complete this calculation. If the baseline probability of drawing an ace is known, please provide that information so that a proper statistical analysis can be performed.
The appropriate test to use in this scenario is the binomial test since we are dealing with a categorical variable (ace or non-ace) and a known population size (52 cards in a deck).
Let's set up the hypotheses:
- Null hypothesis (H0): The observed frequency of getting an ace is not significantly different from the expected frequency by chance.
- Alternative hypothesis (Ha): The observed frequency of getting an ace is significantly different from the expected frequency by chance.
Using the binomial test, we can calculate the probability of getting 40 or more aces out of 100 trials under the null hypothesis. If this probability is very low (typically less than 0.05 or 5%), we would reject the null hypothesis and conclude that the difference is statistically significant.
However, we would need to know the baseline chance of an ace occurring in a single draw from the deck to complete this calculation. If the baseline probability of drawing an ace is known, please provide that information so that a proper statistical analysis can be performed.