Statistical Inference: Master Hypothesis Testing, Confidence Intervals, and Regression Analysis

Question 1

In a two-sample t-test, the null hypothesis assumes that:

Accepted Answer

The means of the two populations are equal.

Answer

The means of the two populations are not equal.

Question 2

For a two-tailed test with a significance level of 0.05 and 20 degrees of freedom, the critical value is:

Accepted Answer

2.09

Answer

1.96

Question 3

Which of the following is NOT a type of hypothesis in hypothesis testing?

Accepted Answer

Confidence interval

Answer

Null hypothesis

Answer

Alternative hypothesis

Answer

One-tailed test

Question 4

A confidence interval for the mean of a population is calculated as:

Accepted Answer

Sample mean +/- Margin of error

Answer

Sample standard deviation / Sample size

Answer

Sample mean * Margin of error

Answer

Sample size / Margin of error

Question 5

In a regression analysis, the dependent variable is the variable that:

Accepted Answer

Is predicted by the independent variable

Answer

Predicts the independent variable

Answer

Is not affected by the independent variable

Answer

Is always constant

Question 6

In a two-tailed test, the critical values are:

Accepted Answer

At the ends of the distribution

Answer

In the middle of the distribution

Answer

Always equal to zero

Answer

Always equal to one

Question 7

Which of the following is a key underlying assumption of hypothesis testing?

Accepted Answer

The sample is random and representative of the population.

Answer

The population distribution is perfectly known.

Answer

The null hypothesis is accurate.

Answer

The sample size is adequate.

Question 8

What is the main purpose of a confidence interval?

Accepted Answer

To approximate the actual population mean.

Answer

To test whether a given hypothesis is correct.

Answer

To forecast future values.

Answer

To contrast two distinct populations.

Question 9

What is the implication of failing to reject the null hypothesis in a hypothesis test?

Accepted Answer

Insufficient evidence exists to draw any conclusion.

Answer

The null hypothesis is certainly true.

Answer

The null hypothesis is likely true.

Answer

The alternative hypothesis is true.

Question 10

The critical value in a hypothesis test is primarily determined by:

Accepted Answer

The significance level

Answer

The sample size

Answer

The population mean

Answer

The sample standard deviation

Question 11

A confidence interval provides an estimate of the population parameter with a specified level of:

Accepted Answer

Confidence

Answer

Significance

Answer

Precision

Answer

Reliability

Question 12

The coefficient of determination (R-squared) in regression analysis represents:

Accepted Answer

The proportion of variance in the dependent variable explained by the independent variables

Answer

The slope of the regression line

Answer

The intercept of the regression line

Answer

The number of observations in the sample

Question 13

Which of the following statistical tests is used to compare the means of two independent groups?

Accepted Answer

Two-sample t-test

Answer

One-way ANOVA

Answer

Chi-square test

Answer

Wilcoxon rank-sum test

Question 14

The probability of a Type I error is controlled by:

Accepted Answer

The alpha level

Answer

The sample size

Answer

The population variance

Answer

The mean of the sample

Question 15

A high p-value in a hypothesis test typically indicates:

Accepted Answer

Insufficient evidence to reject the null hypothesis

Answer

Strong evidence against the null hypothesis

Answer

Strong evidence in favour of the null hypothesis

Answer

A need to collect more data

Question 16

The central limit theorem states that as the sample size increases, the distribution of sample means approaches a normal distribution, regardless of the shape of the population distribution.

Accepted Answer

True

Answer

False

Question 17

Which of the following is NOT a crucial stage in hypothesis testing?

Accepted Answer

Computing the precision of the hypothesis test

Answer

Formulating clear null and alternative hypotheses

Answer

Setting the significance level

Answer

Conducting a statistical test

Question 18

Interpret the implication of a p-value below the significance level in hypothesis testing.

Accepted Answer

Reject the null hypothesis.

Answer

Accept the alternative hypothesis.

Answer

The sample lacks statistical significance.

Answer

The p-value is insufficient to draw a conclusion.

Question 19

Explain the distinction between descriptive and inferential statistics.

Accepted Answer

Descriptive statistics summarize data, while inferential statistics draw conclusions about the population based on the sample.

Answer

Inferential statistics summarize data, while descriptive statistics draw conclusions about the population based on the sample.

Answer

Both statements are correct.

Answer

Neither statement is correct.

Question 20

Which of the following is NOT a recognized sampling method?

Accepted Answer

Quota sampling based on convenience

Answer

Simple random sampling

Answer

Stratified sampling based on known subgroups

Answer

Cluster sampling involving groups of subjects

Question 21

According to the Central Limit Theorem, which of the following is NOT a necessary condition for the sample mean to be approximately normally distributed?

Accepted Answer

The population mean is known.

Answer

The sample size is random and independent.

Answer

The sample size is large enough (n > 30).

Answer

The population distribution is approximately normal.

Question 22

What is the primary purpose of a confidence interval?

Accepted Answer

To estimate the true population mean with a specified level of confidence.

Answer

To test if the population mean is equal to a specific value.

Answer

To determine if the sample is representative of the population.

Answer

To calculate the variance of the population.

Question 23

Which of the following is not a fundamental step in hypothesis testing?

Accepted Answer

Computing the population standard deviation.

Answer

Stating the null and alternative hypotheses.

Answer

Calculating the test statistic.

Answer

Determining the critical value(s) or p-value.

Question 24

In hypothesis testing, what does the p-value represent?

Accepted Answer

The probability of observing a sample as extreme as, or more extreme than, the one obtained, assuming the null hypothesis is true.

Answer

The level of significance for the test.

Answer

The probability of rejecting the null hypothesis when it is true.

Answer

The probability of failing to reject the null hypothesis when it is false.

Question 25

What is the main purpose of creating a scatterplot in regression analysis?

Accepted Answer

To visualize the relationship between the independent and dependent variables and identify any patterns or trends.

Answer

To determine the equation of the regression line.

Answer

To calculate the correlation coefficient.

Answer

To test if the relationship between the variables is statistically significant.

Question 26

In regression analysis, what does the slope of the regression line represent?

Accepted Answer

The amount by which the dependent variable is expected to change for a one-unit increase in the independent variable, holding all other variables constant.

Answer

The correlation coefficient between the independent and dependent variables.

Answer

The y-intercept of the regression line.

Answer

The p-value for the test of significance of the regression.

Question 27

What is the function of the F-test in regression analysis?

Accepted Answer

To test the overall significance of the relationship between the independent and dependent variables.

Answer

To test the significance of individual regression coefficients.

Answer

To predict the dependent variable.

Answer

To calculate the standard error of the estimate.

Question 28

In regression analysis, what is a residual?

Accepted Answer

The difference between the observed value of the dependent variable and the predicted value based on the regression equation.

Answer

The error term in the regression equation.

Answer

The slope of the regression line.

Answer

The correlation coefficient between the independent and dependent variables.

Question 29

What is the main objective of conducting a hypothesis test?

Accepted Answer

To determine the significance of a sample statistic

Answer

To verify a hypothesis

Answer

To disprove a hypothesis

Answer

To make an educated guess about a population parameter

Question 30

In a hypothesis test, what is the purpose of the null hypothesis?

Accepted Answer

It is the hypothesis that the researcher aims to reject

Answer

It is the hypothesis that the researcher intends to prove

Answer

It is the hypothesis that the sample data supports

Answer

It is always true

Question 31

Which of the following does not influence the width of a confidence interval?

Accepted Answer

Sample mean

Answer

Level of confidence

Answer

Sample size

Answer

Population standard deviation

Question 32

What is the primary purpose of regression analysis?

Accepted Answer

To forecast a dependent variable based on one or more independent variables

Answer

To estimate the population mean of a variable

Answer

To test a hypothesis about a population parameter

Answer

To determine the significance of a sample statistic

Question 33

What does the coefficient of determination (R-squared) represent in a regression model?

Accepted Answer

The proportion of variance in the dependent variable attributed to the independent variables

Answer

The gradient of the regression line

Answer

The y-intercept of the regression line

Answer

The number of independent variables in the model

Question 34

Which of the following is a numerical characteristic that describes a population?

Accepted Answer

Parameter

Answer

Standard deviation

Answer

Sample size

Question 35

Which type of regression analysis is used when the dependent variable is continuous?

Accepted Answer

Linear regression

Answer

Logistic regression

Answer

ANOVA

Answer

Chi-square

Question 36

What is the primary distinction between one-tailed and two-tailed hypothesis tests?

Accepted Answer

A one-tailed test specifies a direction for the difference in the alternative hypothesis, while a two-tailed test does not.

Answer

One-tailed tests are more powerful than two-tailed tests.

Question 37

Which of the following violates the assumption of independence in regression analysis?

Accepted Answer

The errors in the model are correlated.

Answer

The dependent variable is normally distributed.

Answer

The independent variables are not correlated with each other.

Answer

The data points are randomly selected.

Question 38

What is the primary purpose of residual analysis in regression analysis?

Accepted Answer

To detect potential violations of the assumptions of regression analysis.

Answer

To predict the value of the dependent variable.

Answer

To calculate the confidence interval for the regression coefficients.

Question 39

In a hypothesis testing procedure, the null hypothesis (H0) represents the:

Accepted Answer

Claim of no effect or no difference.

Answer

Expected value of the test statistic.

Answer

Claim of an effect or difference.

Answer

Opposite of the alternative hypothesis.

Question 40

Which type of error occurs when you reject the null hypothesis (H0) when it is actually true?

Accepted Answer

Type I error.

Answer

Confidence interval error.

Answer

Type II error.

Answer

Sampling error.

Question 41

A 95% confidence interval for the population mean is calculated as (45, 55). This means that:

Accepted Answer

We are 95% confident that the true population mean lies between 45 and 55.

Answer

The sample mean is likely to be within the interval (45, 55).

Answer

There is a 5% chance that the true population mean is less than 45.

Question 42

Which of the following is a potential limitation of statistical inference?

Accepted Answer

Results may be biased due to sampling or measurement errors.

Answer

Cannot be applied to categorical data.

Answer

It is only relevant for small sample sizes.

Question 43

In a two-tailed hypothesis test, the significance level (α) represents the:

Accepted Answer

Maximum probability of rejecting the null hypothesis when it is true.

Answer

Probability of committing a Type II error.

Answer

Sample size required for the hypothesis test.

Question 44

What is the purpose of a chi-square test?

Accepted Answer

To determine whether there is a statistically significant association between two categorical variables.

Answer

To test the correlation between two numerical variables.

Answer

To estimate the population mean of a normally distributed variable.

Question 45

In a study testing whether a drug reduces blood pressure more effectively than a placebo, which of the following is the null hypothesis?

Accepted Answer

The new drug has no effect on blood pressure compared to the placebo.

Answer

The placebo lowers blood pressure.

Answer

The new drug lowers blood pressure.

Question 46

A 95% confidence interval for the mean height of a population is (165cm, 175cm). What is the correct interpretation of this interval?

Accepted Answer

We are 95% confident that the true mean height of the population lies between 165cm and 175cm.

Answer

There is a 95% chance that the sample mean height lies between 165cm and 175cm.

Answer

95% of the population has a height between 165cm and 175cm.

Question 47

Which of the following is NOT an assumption of linear regression analysis?

Accepted Answer

No outliers in the data.

Answer

Independence of observations.

Answer

Linearity of the relationship between variables.

Question 48

A researcher mistakenly rejects the null hypothesis when it is actually true. What type of error has been made?

Accepted Answer

Type I error

Answer

Sampling error

Answer

Type II error

Question 49

Which statistical test is most appropriate for determining if there is a significant difference in the means of two independent groups?

Accepted Answer

Two-sample t-test

Answer

Paired t-test

Answer

Chi-square test

Answer

ANOVA

Question 50

In hypothesis testing, a p-value represents the:

Accepted Answer

Probability of observing the obtained results or more extreme results, assuming the null hypothesis is true.

Answer

Probability that the null hypothesis is true.

Question 51

In simple linear regression, the coefficient of determination (R-squared) measures:

Accepted Answer

The proportion of variation in the dependent variable that is explained by the independent variable.

Answer

The strength and direction of the relationship between variables.

Answer

The slope of the regression line.

Question 52

What is the purpose of a control group in an experiment?

Accepted Answer

To provide a comparison group that does not receive the treatment.

Answer

To reduce the variability within the treatment group.

Answer

To increase the sample size of the study.

Question 53

Which of the following is an example of a non-parametric statistical test?

Accepted Answer

Median test

Answer

Independent samples t-test

Answer

One-way ANOVA

Answer

Pearson correlation