AP Statistics 4.2 Estimating Probabilities Using Simulation- MCQs - Exam Style Questions
▶️ Answer/Explanation
1. Identify the Event:
We need to find the probability of Audrey selling “at least 7” of the 30 selected tickets. In the simulation, this corresponds to selecting 7 or more red chips.
2. Sum Frequencies from the Histogram:
We sum the frequencies for 7, 8, 9, 10, and 11 red chips from the provided histogram.
Total trials with $\geq 7$ red chips = (Frequency of 7) + (Frequency of 8) + (Frequency of 9) + (Frequency of 10) + (Frequency of 11)
Total = $78 + 39 + 15 + 5 + 1 = 138$
3. Calculate the Estimated Probability (p-value):
The probability is the sum of these frequencies divided by the total number of trials (1,000).
$p\text{-value} = \frac{138}{1000} = 0.138$
4. Compare to Significance Level ($\alpha$):
The significance level is $\alpha = 0.05$. We compare our p-value to this level.
$0.138 > 0.05$
5. Conclusion:
Since the p-value is greater than the significance level, we fail to reject the null hypothesis. There is not convincing statistical evidence that the event is unlikely to have occurred by chance alone. This matches the reasoning in option (E).
✅ Answer: (E)
▶️ Answer/Explanation
1. Effect on Bias:
Bias is a measure of the accuracy of an estimator. Since the sample is random, the sample mean is an unbiased estimator of the population mean. Increasing the sample size does not affect the bias.
2. Effect on Variance:
Variance is a measure of the precision of an estimator. The variance of the sample mean is \(\frac{\sigma^2}{n}\). As the sample size (\(n\)) increases, the variance decreases.
Therefore, the bias will remain the same, and the variance will decrease.
✅ Answer: (C)