Unit 4 - Practice Quiz

MGN206 50 Questions
0 Correct 0 Wrong 50 Left
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1 What is the primary purpose of the Null Hypothesis () in statistical testing?

A. To calculate the standard deviation of the population
B. To determine the sample size required
C. To prove that a relationship exists between variables
D. To state that there is no significant difference or relationship

2 Which of the following errors occurs when the Null Hypothesis is rejected when it is actually true?

A. Standard Error
B. Type I Error
C. Type II Error
D. Sampling Error

3 The probability of committing a Type II Error is denoted by which Greek letter?

A. (Chi)
B. (Beta)
C. (Sigma)
D. (Alpha)

4 What does the Power of a Test represent?

A. The probability of making a Type I error
B. The probability of making a Type II error
C. The probability of correctly rejecting a false Null Hypothesis
D. The probability of accepting a true Null Hypothesis

5 Which of the following conditions implies a Two-tailed Test?

A.
B.
C.
D.

6 In a hypothesis test, if the p-value is less than the level of significance (), what is the conclusion?

A. Change the level of significance
B. Reject the Null Hypothesis
C. The test is inconclusive
D. Accept the Null Hypothesis

7 Which of the following is a fundamental assumption of Parametric Tests?

A. No assumption about population parameters is made
B. The sample size must be small
C. The data is always qualitative
D. The data follows a normal distribution

8 The Z-test is generally used when the sample size () is:

A.
B.
C.
D.

9 What is the formula for the Z-statistic when testing a sample mean against a population mean?

A.
B.
C.
D.

10 Student's t-test was developed by whom?

A. Karl Pearson
B. Wilcoxon
C. R.A. Fisher
D. William Sealy Gosset

11 What is the shape of the t-distribution compared to the standard normal distribution?

A. It is flatter and has thicker tails (leptokurtic)
B. It is positively skewed
C. It is negatively skewed
D. It is identical to the normal distribution

12 Degrees of freedom () for a single sample t-test is calculated as:

A.
B.
C.
D.

13 Which test is most appropriate to compare the means of two independent small samples () taken from normal populations with unknown variances?

A. Chi-Square test
B. Z-test
C. Independent samples t-test
D. F-test

14 In a Paired t-test, the samples are:

A. Always larger than 30
B. Related or matched pairs
C. Independent of each other
D. Categorical data only

15 The F-test is primarily used to test the equality of:

A. Two Means
B. Two Variances
C. Two Proportions
D. Two Medians

16 The statistic is defined as the ratio of:

A. Smaller Variance / Greater Variance
B. Greater Variance / Smaller Variance
C. Sum of Squares / Degrees of Freedom
D. Mean / Standard Deviation

17 The Chi-Square () test is a:

A. Non-parametric test
B. Test for Standard Deviation
C. Parametric test
D. Test for Means

18 What is the formula for the Chi-Square statistic?

A.
B.
C.
D.

19 In a Chi-Square test of independence for a contingency table with rows and columns, the degrees of freedom is:

A.
B.
C.
D.

20 The Kruskal-Wallis test is a non-parametric alternative to which parametric test?

A. One-way ANOVA
B. Independent t-test
C. Z-test
D. Paired t-test

21 What type of data is primarily used in the Kruskal-Wallis test?

A. Ranked (Ordinal) data
B. Nominal data only
C. Ratio data
D. Interval data

22 Which of the following values represents the critical Z-score for a 95% Confidence Level (Two-tailed)?

A. 1.645
B. 2.33
C. 1.96
D. 2.58

23 In hypothesis testing, the Significance Level () is typically set at:

A. 0.95 or 0.99
B. 1.00
C. 0.50 or 0.10
D. 0.05 or 0.01

24 Which test statistic follows a distribution that is strictly non-negative (from 0 to positive infinity)?

A. Z-distribution
B. t-distribution
C. Normal distribution
D. Chi-Square distribution

25 When testing for Goodness of Fit, which test is applied?

A. t-test
B. Z-test
C. Chi-Square test
D. F-test

26 If the calculated value of a test statistic is greater than the critical table value, we should:

A. Reject
B. Reject
C. Accept
D. Retest with more data

27 For a One-Way ANOVA (Analysis of Variance), what is the appropriate test statistic?

A. F-statistic
B. t-statistic
C. Z-statistic
D. -statistic

28 In the Kruskal-Wallis test, the test statistic is usually denoted by:

A. H
B. K
C. W
D. U

29 Standard Error (SE) of the mean decreases when:

A. The population standard deviation increases
B. The sample mean increases
C. The sample size decreases
D. The sample size increases

30 Which assumption is NOT required for the Chi-Square Test?

A. Data must be in the form of frequencies
B. Population must be normally distributed
C. Expected frequency in any cell should not be less than 5
D. Observations must be independent

31 When , the Student’s t-distribution approaches which distribution?

A. Chi-Square distribution
B. Standard Normal (Z) distribution
C. Binomial distribution
D. F-distribution

32 In an F-test, if and , what is the calculated F-value?

A. 4.0
B. 0.25
C. 75
D. 5.0

33 A researcher wants to test if the variance of Machine A is significantly different from Machine B. Which test should be used?

A. F-test
B. Chi-Square test
C. Z-test
D. t-test

34 The degrees of freedom for the Kruskal-Wallis test with groups is:

A.
B.
C.
D.

35 Which of the following is true regarding Non-parametric tests?

A. They are more powerful than parametric tests when assumptions are met
B. They rely on strict assumptions about population parameters
C. They can only be used for small samples
D. They are also known as distribution-free tests

36 What is the Alternative Hypothesis () for a Chi-Square test of independence?

A. The variables are not independent (there is an association)
B. The means are equal
C. The variances are equal
D. The variables are independent

37 The Mann-Whitney U Test is the non-parametric equivalent of which parametric test?

A. One-way ANOVA
B. Independent samples t-test
C. Paired t-test
D. Pearson Correlation

38 If the Standard Deviation of a population is unknown and , we calculate the standard error using:

A. Variance
B. Range
C. Population standard deviation ()
D. Sample standard deviation ()

39 Which of the following symbols represents the sample mean?

A.
B.
C.
D.

40 In an F-test, the degrees of freedom are denoted as . What does represent?

A. Degrees of freedom of the numerator (larger variance)
B. Number of groups
C. Total sample size
D. Degrees of freedom of the denominator (smaller variance)

41 What is the minimum expected frequency typically recommended for each cell in a Chi-Square contingency table?

A. 5
B. 10
C. 1
D. 30

42 A Type I Error is also known as:

A. Confidence Level
B. False Positive
C. Power of the Test
D. False Negative

43 The relationship between the t-statistic and F-statistic (when comparing two groups) is:

A.
B.
C.
D.

44 Which of the following is NOT a step in Hypothesis Testing?

A. Selecting the level of significance
B. Eliminating outliers before data collection
C. Calculating the test statistic
D. Formulating and

45 The critical region is:

A. The area under the curve where is rejected
B. The area under the curve where is accepted
C. The value of the test statistic
D. The total area under the probability curve

46 What happens to the critical region in a Two-tailed Z-test at ?

A. It is split equally between both tails (0.025 each)
B. It is all on the left side (0.05)
C. It is disregarded
D. It is all on the right side (0.05)

47 For a Z-test of proportions, the standard error is calculated as:

A.
B.
C.
D.

48 If we want to test whether a die is unbiased (fair), which test is best?

A. Student's t-test
B. Wilcoxon Rank Sum
C. F-test
D. Chi-Square Goodness of Fit

49 Which test would you use to analyze the relationship between Gender (Male/Female) and Voting Preference (Party A/Party B/Party C)?

A. Chi-Square Test of Independence
B. t-test
C. Pearson Correlation
D. Z-test

50 In the context of the Kruskal-Wallis test, if the Null Hypothesis is true:

A. The variances are unequal
B. The mean ranks of the groups are roughly equal
C. The data is normally distributed
D. The mean ranks of the groups are significantly different