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QMB 3200 MIDTERM UCF PRACTICE
EXAM 1 QUESTIONS AND CORRECT
ANSWERS (VERIFIED ANSWERS) PLUS
RATIONALES 2025
- A population consists of 5,000 observations. A sample of 100 observations is taken to estimate the population mean. What is this sample called? a) Parameter b) Statistic c) Census d) Population Answer: b) Statistic A statistic is a numerical value calculated from a sample, used to estimate a population parameter.
- Which of the following is an example of qualitative data? a) Number of employees b) Employee ID numbers c) Marital status d) Salary levels Answer: c) Marital status Marital status describes a category or label, not a measurable number, so it is qualitative (categorical) data.
- The variance is best described as: a) The square root of the standard deviation b) The average of the deviations c) The average of the squared deviations d) The sum of the deviations Answer: c) The average of the squared deviations Variance measures how far each data point is from the mean by averaging the squared differences.
- The standard deviation of a sampling distribution is known as: a) Mean b) Margin of error c) Standard error d) Confidence interval
- Which sampling method gives every member of the population an equal chance of being selected? a) Stratified sampling b) Cluster sampling c) Convenience sampling d) Simple random sampling Answer: d) Simple random sampling Simple random sampling ensures each element has an equal chance of being included.
- When the null hypothesis is true, but we reject it, what type of error have we made? a) Type I error b) Type II error c) Sampling error d) Measurement error Answer: a) Type I error A Type I error occurs when you incorrectly reject a true null hypothesis.
- The level of significance (alpha) in hypothesis testing is the probability of: a) Making a Type II error b) Making a Type I error c) Accepting the alternative hypothesis d) Accepting the null hypothesis Answer: b) Making a Type I error Alpha is the probability of rejecting the null hypothesis when it is true.
- A p-value less than the level of significance means: a) Accept the null hypothesis b) Reject the null hypothesis c) Increase the sample size d) Do not reject the alternative hypothesis Answer: b) Reject the null hypothesis A small p-value indicates strong evidence against the null hypothesis.
- In hypothesis testing, the critical value approach means: a) Comparing the test statistic to the p-value b) Comparing the test statistic to the critical value c) Comparing the sample mean to the population mean d) Comparing alpha to the sample size
- Which of the following is not an assumption for using the Z test for means? a) Population is normally distributed b) Population standard deviation is known c) Sample size is large (n > 30) d) Population variance is unknown Answer: d) Population variance is unknown The Z test assumes the population standard deviation is known.
- If the correlation coefficient is - 0.85, the relationship between variables is: a) Weak and positive b) Weak and negative c) Strong and positive d) Strong and negative Answer: d) Strong and negative A correlation coefficient close to - 1 indicates a strong negative linear relationship.
- Which of the following is not a characteristic of the normal distribution?
a) Symmetrical shape b) Mean equals median equals mode c) It is skewed right d) It extends indefinitely in both directions Answer: c) It is skewed right The normal distribution is perfectly symmetrical, so it is never skewed.
- What is the area under the entire normal curve? a) 0. b) 1 c) 2 d) Depends on the mean Answer: b) 1 The total area under a probability distribution must equal 1.
- The mean of a sampling distribution equals: a) Zero b) The standard deviation of the population c) The population mean d) The median of the population Answer: c) The population mean
- If the mean of a Poisson distribution is 3, what is its variance? a) 0 b) 1 c) 3 d) Cannot be determined Answer: c) 3 In a Poisson distribution, the mean equals the variance.
- Which measure of central tendency is most affected by extreme values? a) Mode b) Median c) Mean d) Variance Answer: c) Mean The mean can be pulled in the direction of extreme values.
- A point estimator is: a) A single value estimate of a population parameter b) Always equal to the parameter c) The same as the population variance d) Always unbiased
Answer: a) A single value estimate of a population parameter A point estimator provides one estimate for the unknown parameter.
- Which sampling method divides the population into groups and then randomly selects some of the groups for study? a) Systematic sampling b) Cluster sampling c) Stratified sampling d) Simple random sampling Answer: b) Cluster sampling Cluster sampling selects entire groups rather than individuals.
- The Central Limit Theorem is important because it states that: a) The population mean equals the sample mean b) The sampling distribution of the mean will be normal regardless of population shape, given a large enough sample size c) The population standard deviation equals zero d) The sampling distribution will be skewed if the population is skewed Answer: b) The sampling distribution of the mean will be normal regardless of population shape, given a large enough sample size This is the foundation of many inferential techniques.
Answer: b) The null hypothesis is false and you fail to reject it This means you missed a real effect.
- Which of the following increases the power of a hypothesis test? a) Increasing the sample size b) Decreasing the significance level c) Increasing standard error d) Using a two-tailed test instead of one-tailed Answer: a) Increasing the sample size A larger sample size reduces standard error and increases power.
- Which symbol represents the population mean? a) p b) s c) μ d) x̄ Answer: c) μ Greek letter mu (μ) denotes the population mean.
- The coefficient of determination (R²) measures: a) The slope of the regression line b) The proportion of total variation explained by the regression
c) The standard error of estimate d) The mean value of X Answer: b) The proportion of total variation explained by the regression R² indicates how well the model fits the data.
- The expected value of a discrete random variable is: a) Always zero b) Always negative c) The weighted average of possible values d) The median Answer: c) The weighted average of possible values Expected value uses probabilities as weights.
- In a hypothesis test for a mean, if the population variance is unknown and n < 30, you should use: a) Z test b) t test c) F test d) Chi-square test Answer: b) t test The t-distribution is appropriate when σ is unknown and sample size is small.
d) The slope coefficient Answer: c) The unexplained variation It captures variation not explained by the model.
- A decision tree is used in: a) Hypothesis testing b) Regression analysis c) Decision making under uncertainty d) Descriptive statistics Answer: c) Decision making under uncertainty It visually maps decisions and outcomes.
- If the correlation coefficient r = 0, the variables are: a) Perfectly positively correlated b) Perfectly negatively correlated c) Independent d) Uncorrelated Answer: d) Uncorrelated A correlation of 0 means no linear relationship.
- If the sample mean is 60, population mean is 55, and standard error is 2, what is the z-score?
a) - 2. b) 2. c) 5 d) - 5 Answer: b) 2. z = (60 – 55) / 2 = 2.5.
- In a payoff table, the expected monetary value (EMV) is calculated by: a) Taking the worst outcome b) Taking the best outcome c) Multiplying payoffs by probabilities and summing d) Maximizing regrets Answer: c) Multiplying payoffs by probabilities and summing EMV is the weighted average for each decision.
- Which probability rule applies when two events cannot occur at the same time? a) Multiplication rule for independent events b) Addition rule for mutually exclusive events c) Bayes’ theorem d) Complement rule Answer: b) Addition rule for mutually exclusive events
b) Every kth element is selected after a random start c) It is the same as stratified sampling d) It is used when population is infinite Answer: b) Every kth element is selected after a random start Systematic sampling uses a fixed periodic interval.
- The width of the confidence interval for the mean decreases when: a) Sample size decreases b) Population standard deviation increases c) Confidence level increases d) Sample size increases Answer: d) Sample size increases A larger sample size reduces standard error, narrowing the interval.
- A researcher wants to test whether the mean weight of widgets is greater than 50 grams. What is the null hypothesis? a) μ ≠ 50 b) μ > 50 c) μ < 50 d) μ ≤ 50 Answer: d) μ ≤ 50
The null always states the status quo; in this case, “not greater than” is ≤.
- The alternative hypothesis represents: a) The assumption of no change b) The status quo c) What the researcher wants to prove d) Always equality Answer: c) What the researcher wants to prove The alternative states what you’re testing for.
- When using a t-distribution, the degrees of freedom for a single mean is: a) n + 1 b) n – 1 c) n – 2 d) n Answer: b) n – 1 t-distribution for a single mean uses n – 1 degrees of freedom.
- Which statistic is used to estimate a population proportion? a) μ
