UCF QMB 3200 Final Exam and Practice Questions

What is statistical inference?

The process of using data from a sample to make conclusions about a population.

What is sampling error?

The difference between a sample result and the population value.

What happens to the standard error as the sample size increases?

It decreases.

What does the Central Limit Theorem imply?

The sampling distribution becomes approximately normal as sample size increases.

What does a 95% confidence interval mean?

95% of such intervals would contain the true parameter.

How can a company achieve a smaller margin of error?

By increasing sample size.

What is a p-value?

The probability of observing the sample result if the null hypothesis is true.

What does failing to reject the null hypothesis mean?

There is not enough evidence to support the alternative hypothesis.

What occurs during a Type I error?

A true null hypothesis is rejected.

What is an example of matched samples?

Measuring the same group of employees before and after training.

Why is a pooled proportion used when comparing two population proportions?

The null hypothesis assumes the proportions are equal.

What does the dependent variable (y) represent in regression?

The outcome being explained.

What does the slope (b₁) in a regression model represent?

The change in y for a one-unit increase in x.

What is a residual?

The difference between actual and predicted values.

What does R² = 0.75 indicate?

75% of the variation in y is explained by x.

What does correlation measure?

The strength and direction of a linear relationship.

What does testing H₀: β₁ = 0 determine in regression?

If there is a linear relationship between x and y.

What does the F-test in simple linear regression evaluate?

The overall usefulness of the regression model.

What is a key assumption of regression?

The error term has constant variance.

Why is a prediction interval wider than a confidence interval?

It accounts for both estimation error and individual variability.

What happens to the confidence interval when sample size increases?

It becomes narrower due to reduced standard error.

What does a very large p-value indicate?

There is insufficient evidence to reject the null hypothesis.

What increases the margin of error?

Increasing the confidence level.

What happens to the spread of a sampling distribution when sample size increases?

It has a smaller spread.

What effect does reducing the level of significance (α) have?

It decreases the probability of a Type I error.

Why is a matched sample design preferred?

It reduces variability by controlling individual differences.

What does the pooled proportion provide?

A combined estimate when populations are assumed equal.

What conclusion can be drawn if the slope (b₁) is not statistically significant?

There is no evidence of a linear relationship between x and y.

What does a negative correlation indicate?

A negative correlation indicates that as one variable increases, the other variable tends to decrease.

Which scenario best represents a violation of regression assumptions?

Variability of errors increases as x increases.

If the correlation coefficient (r) is close to zero, what does this indicate?

Weak or no linear relationship.

What does a high R² value indicate?

A large portion of variation in y is explained by x.

How does correlation differ from causation?

Correlation measures association but does not prove cause-and-effect.

What does a very small p-value for b₁ suggest in regression output?

The independent variable significantly affects the dependent variable.

What does the standard error of the regression measure?

The overall variability of prediction errors.

What is a Type II error?

Failing to reject a false null hypothesis.

In a two-tailed hypothesis test, where is the rejection region?

Is split between both tails of the distribution.

What does a significant F-test in regression indicate?

The model explains variation in the dependent variable.

What is the purpose of a sampling distribution?

To show how a sample statistic varies across repeated samples.

Why is the conclusion that increasing advertising causes higher sales flawed?

Correlation alone does not establish causation.

Which Excel function calculates a sample mean?

AVERAGE.

Which Excel function computes a sample standard deviation?

STDEV.S.

How can a manager find the proportion of customers who answered 'Yes'?

COUNTIF(range, 'Yes') divided by total observations.

Which Excel function finds a z-value from a probability?

NORM.S.INV.

Which Excel function calculates a probability from a z-value?

NORM.S.DIST.

What represents the strength of the linear relationship in Excel regression output?

Multiple R.

What does the 'Significance F' value in Excel regression output correspond to?

p-value for the overall model (F-test).

What should you do if the p-value for the independent variable is less than 0.05?

Reject the null hypothesis and conclude the variable is significant.

Which Excel tool runs a linear regression analysis?

Data Analysis ToolPak → Regression.

What does the coefficient for x (b₁) represent in Excel regression output?

The change in y for a one-unit increase in x.

What represents the proportion of variation explained by the model in Excel?

R Square.

What does the CONFIDENCE.NORM function calculate?

Margin of error for a confidence interval.

Which function computes a t-distribution probability in Excel?

T.DIST.

How is the t Stat calculated in Excel regression output?

Coefficient divided by standard error.

What type of sampling is created using RAND() in Excel?

Simple random sampling.

What is necessary after using RAND() to create a random sample?

Copy and paste values to stop numbers from changing.

What does the standard error of the regression represent?

The average size of prediction errors.

Which output value tells you how many data points were used in Excel?

Observations (n).

What does a high R² but an insignificant p-value indicate?

The model may explain variation, but the relationship is not statistically significant.

Which concept best supports hypothesis testing for proportions in Excel?

COUNTIF combined with probability functions.

What is a pivot table?

A data processing tool in Excel that allows users to summarize and analyze data from a larger dataset.

What is the independent variable in a study about employee training hours and productivity?

Employee training hours.

What is the dependent variable in a study analyzing price changes and demand?

Demand for the product.

What type of relationship is indicated by a regression model showing increased sales with increased social media spending?

Positive relationship.

What type of sample is used when measuring blood pressure before and after medication?

Matched sample.

What type of analysis compares the percentage of customers purchasing from two different ads?

Two population proportions.

What does it mean when ice cream sales and drowning incidents both increase in summer?

The variables are correlated but not necessarily causal.

What concept applies when estimating the average spending of all customers?

Confidence interval.

What concept applies when estimating how much a specific customer will spend next time?

Prediction interval.

What does a very small p-value in a hypothesis test indicate?

There is strong evidence against the null hypothesis.

What does it mean if a company does not reject the null hypothesis after testing a new strategy?

There is not enough evidence to conclude the strategy works.

What type of error occurs when a study incorrectly concludes a new drug works when it does not?

Type I error.

What type of error occurs when a study fails to detect that a new product improves performance?

Type II error.

What does it imply if a regression model shows that the slope is not statistically significant?

There is no evidence of a linear relationship.

What does a high R² value in a regression model indicate?

The model explains a large portion of variation in the dependent variable.

What can be said about correlation if a dataset shows no clear pattern between x and y values?

Weak or no linear relationship.

What does it mean when a researcher assumes that errors in a regression model are independent?

One observation does not influence another.

What does it indicate if a regression model shows that prediction errors increase as x increases?

Constant variance assumption is violated.

What type of sampling is used when a company randomly selects survey participants?

Simple random sampling.

What concept is illustrated when a study repeats sampling many times and observes how the sample mean changes?

Sampling distribution.

What explains why a larger sample size leads to more consistent results?

Standard error decreases.

What is the null hypothesis (H₀) when a company claims its delivery time is less than 2 days?

H₀: μ ≥ 2.

What is the alternative hypothesis (Hₐ) when a manager tests if customer satisfaction has changed?

Hₐ: μ ≠ old satisfaction.

What is the null hypothesis (H₀) when a company claims that at least 90% of orders are delivered on time?

H₀: p ≥ 0.90.

What is the alternative hypothesis (Hₐ) when a researcher tests if a new method increases test scores?

Hₐ: μ > old score.

What is always true about the null hypothesis (H₀)?

It includes equality (=, ≤, or ≥).

What is the correct alternative hypothesis when a company wants to prove its new system is faster?

Hₐ: μ < old time.

What situation requires a two-tailed test?

Testing if something is different.