Statistical Inference for Engineering Mathematics: Master Your Data Analysis Skills

Question 1

A 95% confidence interval with a sample mean of 50 and a standard deviation of 5 suggests that:

Accepted Answer

The population mean is likely to be between 45 and 55 with 95% confidence.

Answer

The probability of the population mean being less than 50 is 2.5%.

Answer

The sample mean is significantly different from the population mean at the 5% level.

Answer

The standard deviation of the population is likely to be between 4 and 6.

Question 2

Which hypothesis test is employed to compare the means of two independent populations?

Accepted Answer

t-test for two independent samples

Answer

Z-test for a single mean

Answer

t-test for a single mean

Answer

Analysis of variance (ANOVA)

Question 3

The coefficient of determination (R²) in regression analysis represents:

Accepted Answer

The proportion of variation in the dependent variable explained by the independent variable(s).

Answer

The probability of correctly predicting the value of the dependent variable.

Answer

The slope of the regression line.

Answer

The y-intercept of the regression line.

Question 4

In regression analysis, the variable that is predicted is called:

Accepted Answer

Response variable

Answer

Predictor variable

Answer

Explanatory variable

Answer

Outcome variable

Question 5

In hypothesis testing, which of the following statements represents the null hypothesis?

Accepted Answer

The population mean is equal to 50.

Answer

The population mean is greater than 50.

Answer

The population mean is less than 50.

Answer

The population mean is not equal to 50.

Question 6

When testing the equality of two population variances, which of the following test statistics is appropriate?

Accepted Answer

F-test

Answer

Student's t-test

Answer

Chi-square test

Answer

Z-test

Question 7

Given a linear regression model specified as y = 5 + 3x, if x = 10, what is the predicted value of y?

Accepted Answer

45

Answer

25

Answer

35

Answer

55

Question 8

Which of the following is a method of non-parametric statistical inference?

Accepted Answer

Spearman's rank correlation

Answer

t-test

Answer

ANOVA

Answer

Chi-square test

Question 9

A confidence interval provides:

Accepted Answer

A range of values that is likely to contain the true population parameter

Answer

A single value that is the exact value of the true population parameter

Answer

A hypothesis about the value of the true population parameter

Answer

A statistical test that determines if there is a significant difference between two groups

Question 10

In hypothesis testing, the null hypothesis is:

Accepted Answer

The hypothesis that is assumed to be true until proven otherwise

Answer

The hypothesis that is being tested

Answer

The hypothesis that is rejected if the p-value is less than the significance level

Answer

The hypothesis that is accepted if the p-value is greater than the significance level

Question 11

In a t-test, the degrees of freedom refer to:

Accepted Answer

The sample size minus 1

Answer

The number of independent variables

Answer

The number of dependent variables

Answer

The significance level

Question 12

A non-parametric statistical test:

Accepted Answer

Makes no assumptions about the distribution of the population

Answer

Requires a large sample size

Answer

Is less powerful than parametric tests

Answer

Is used to test hypotheses about the mean of a population

Question 13

How can analyzing residuals aid in evaluating the accuracy and precision of a regression model?

Accepted Answer

Residuals can help identify outliers and influential points that may affect the model's accuracy.

Answer

Residuals are used to calculate the coefficient of determination (R-squared).

Answer

Residuals can be used to assess the significance of regression coefficients.

Question 14

In regression analysis, which of the following measures the strength and direction of the linear relationship between the dependent and independent variables?

Accepted Answer

Correlation coefficient

Answer

Mean square error

Answer

Coefficient of determination

Question 15

Which of the following is a potential benefit of using a large sample size in statistical inference?

Accepted Answer

Increased statistical power

Answer

Lower cost of data collection

Answer

Reduced risk of Type I error

Question 16

In the context of statistical inference, what does the term 'alternative hypothesis' refer to?

Accepted Answer

Statement that there is an effect or relationship

Answer

Statement that the effect is not significant

Answer

Statement that the sample is not representative

Answer

Statement that the data is not normally distributed

Question 17

Which of the following is a key feature of a confidence interval?

Accepted Answer

It has a specified level of confidence associated with it

Answer

It provides a single estimate of the parameter

Answer

It is always narrower than the range of the data

Question 18

Which of the following is NOT a type of point estimator for a population parameter?

Accepted Answer

Hypothesis

Answer

Mode

Answer

Mean

Answer

Median

Question 19

A 95% confidence interval for a population mean is (10, 20). What is the margin of error?

Accepted Answer

5

Answer

15

Answer

20

Answer

10

Question 20

In a hypothesis test with a 5% significance level, a p-value of 0.06 would lead to which conclusion?

Accepted Answer

Fail to reject the null hypothesis

Answer

The test is inconclusive

Answer

More data is needed

Answer

Reject the null hypothesis

Question 21

Which sampling method would ensure that every member of a population has an equal chance of being selected?

Accepted Answer

Simple random sampling

Answer

Cluster sampling

Answer

Stratified sampling

Question 22

What is a characteristic of a statistical test that produces reliable results even when its assumptions are not fully met?

Accepted Answer

Robustness

Answer

Applicability to all types of data

Answer

Simplicity to perform