You suspect one of the employees in a casino is using loaded dice. You observe them rolling the dice 66 times and record the following results: Face "1" "2" "3" "4" "5" "6" Observed count 10 7 16 7 9 17 Is the sample size large enough? A. Yes, because the Expected count is at least 5 for every category. B. No, because some categories have less than 10. C. Yes, because the Expected count is close to the Observed cell count for every category. D. No, because some categories have less than 30. (d) Suppose you got a relatively small test statistic. What would this imply? The observed counts are the expected counts, providing evidence that the dice are unfair (Ha). This would lead to a relatively p-value. (e) The test statistic is ?2 = 8.91. What is the p-value? (Use 4 decimals.) (f) What is the appropriate test conclusion, for ? = 0.05? H0: there is ______ evidence the dice are ______ . (g) Interpret the p-value as a probability: A. The p-value is the probability that the dice are fair. B. The p-value is the probability that the dice are unfair. C. The p-value is the probability of getting ?2 = 8.91 or greater if the dice are actually fair. D. The p-value is the probability of getting ?2 = 8.91 or greater if the dice are actually unfair.
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
You suspect one of the employees in a casino is using loaded dice. You observe them rolling the dice 66 times and record the following results:
| Face | "1" | "2" | "3" | "4" | "5" | "6" |
|---|---|---|---|---|---|---|
| Observed count | 10 | 7 | 16 | 7 | 9 | 17 |
Is the sample size large enough?
(d) Suppose you got a relatively small test statistic. What would this imply?
The observed counts are the expected counts, providing evidence that the dice are unfair (Ha). This would lead to a relatively p-value.
(e) The test statistic is ?2 = 8.91. What is the p-value? (Use 4 decimals.)
(f) What is the appropriate test conclusion, for ? = 0.05?
H0: there is ______ evidence the dice are ______ .
(g) Interpret the p-value as a
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