6.8.1: Review Questions

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Page ID: 58311

Felix Amoruwa
De Anza College

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Review Questions

Multiple Choice

According to the empirical rule, approximately what percentage of data falls within 2 standard deviations of the mean in a normal distribution?
- a) 68% b) 95% c) 99.7% d) 100%
A coin is flipped 10 times. The number of heads follows which distribution?
- a) Normal b) Poisson c) Binomial d) Uniform
A researcher obtains a p-value of 0.03 with α = 0.05. The correct conclusion is:
- a) The null hypothesis is proven true b) Reject the null hypothesis c) The alternative hypothesis is proven d) The result is meaningless

Short Answer

Explain the difference between mean and median. When is the median a better measure of central tendency than the mean? Give a real-world example.
Describe the Central Limit Theorem in plain language. Why is it important for statistical inference even when the underlying data is not normally distributed?
A 95% confidence interval for average customer spend is [$42.50, $47.50]. Interpret this interval. Does it mean there is a 95% probability the true mean is in this range?
Explain the difference between Type I and Type II errors using a medical testing example (e.g., testing for a disease). Which error is more costly in this context, and why?

True/False

True or False: The mean is always the best measure of center for any dataset.
True or False: A p-value of 0.04 means there is a 4% chance the null hypothesis is true.
True or False: The Poisson distribution is appropriate for modeling the number of customer arrivals per hour at a store, assuming arrivals are independent and occur at a constant rate.

Answer Key:

1-b, 2-c, 3-b, 4. Mean uses all values (sensitive to outliers); median is the middle value (resistant to outliers). Median better for skewed data. Example: income — a few billionaires skew the mean far above the median, so median better represents "typical" income. 5. CLT says: regardless of the population's shape, the distribution of sample means becomes approximately normal as sample size grows. Important because it lets us use normal-based inference (CIs, z-tests) even for non-normal data, as long as samples are large enough. 6. If we repeated sampling many times, 95% of such intervals would contain the true mean. It does NOT mean 95% probability for this specific interval — the true mean is fixed; the interval either contains it or doesn't. 7. Type I: healthy person diagnosed as sick (false positive) — unnecessary treatment, anxiety. Type II: sick person diagnosed as healthy (false negative) — missed diagnosis, disease progresses. In medical testing, Type II is often more costly (missing a treatable disease). 8. False, 9. False, 10. True.

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