Deck 12: Univariate Statistical Analysis: a Recap of Inferential Statistics

Question 1

The median is the preferred measure of central tendency when the data is ordinal-scaled.

Answer 1

True

Question 2

In hypothesis testing, the symbol typically used to specify the significance level of the test is the Greek letter $\beta$ .

Answer 2

False

Question 3

In hypothesis testing, the values that lie within the region of rejection are called the critical values.

Answer 3

False

Question 4

The range is useful for describing the sample variability.

Question 5

The primary purpose of inferential statistics is to make a judgment about the population, or the collection of all elements about which one seeks information.

Question 6

Standard deviation is the most valuable index of dispersion.

Question 7

Standard deviation is a square of root of variance.

Question 8

Sample size can help to control both Type I and Type II errors.

Question 9

One method of calculating how far any observation is from the mean is to calculate individual deviation scores.

Question 10

In marketing problems, Type II errors are generally more serious than Type I errors.

Question 11

A set of data organised by summarising the number of times a particular value of a variable occurs is called frequency distribution.

Question 12

Reducing the probability of a Type II error decreases the probability of a Type I error.

Question 13

A Type II error occurs when you reject the null hypothesis when, in fact, it is true.

Question 14

The long-run relative frequency with which an event will occur is called central tendency.

Question 15

A way to eliminate the sign problem caused by the negative deviations cancelling out the positive deviations is to square the deviation scores.

Question 16

An alternative hypothesis is a statement about a status quo.

Question 17

A normal distribution has a mean of zero and a standard deviation of one.

Question 18

A Type I error occurs if you fail to reject the null hypothesis when the alternative hypothesis is true.

Question 19

When a researcher is studying one variable at a time, it is called univariate statistical analysis.

Question 20

The mode is determined by listing each possible value and noting number of times each value occurs.

Question 21

If the population mean is expected to be 550, the sample mean is 525, the sample standard deviation is 20, and the sample consists of 200 consumers, then the observed value of the Z-statistic is approximately:

A) 1.25.
B) 2.5.
C) -1.25.
D) -2.5.

Question 22

In a normal distribution, almost all (99 per cent) of its values are within how many standard deviations from its mean?

A) ± 1
B) ± 2
C) ± 3
D) ± 4

Question 23

Making the assumption that the population distribution is normal is generally appropriate when data are ordinal.

Question 24

Nonparametric statistical tests are frequently referred to as distribution free.

Question 25

Which of the following is not a measure of dispersion?

A) Range
B) Mode
C) Standard deviation
D) Variance

Question 26

The standardised normal distribution:

A) has a mean of one and a standard deviation of two.
B) has a mean higher than the mode.
C) has a mean lower than the mode.
D) has a mean of zero and a standard deviation of one.

Question 27

The number of variables that will be simultaneously investigated is a key consideration in the choice of statistical technique.

Question 28

Which of the following descriptive statistics identifies the value that occurs most often?

A) Mean
B) Median
C) Mode
D) Range

Question 29

The choice of measurement scales used in data collection will determine the allowable statistical techniques in the data analysis.

Question 30

All of the following descriptive statistics are measures of central tendency, except:

A) mean.
B) range.
C) median.
D) mode.

Question 31

If the standard deviation for a sample of 225 consumers is 20, then the standard error of the mean for this sample is approximately:

A) 0.09.
B) 0.75.
C) 1.33.
D) 1.78.

Question 32

The central-limit theorem states that as the sample size increases, the distribution of the sample mean from a nonprobability selected sample approaches a normal distribution.

Question 33

A frequency distribution table is an efficient means to organise and summarise a set of data.

Question 34

Testing a hypothesis about a mean requires nominal- or ordinal-scaled data.

Question 35

Respondents are asked to select their preference between brand A and brand
B. If we want to test the null hypothesis that the number of people who prefer brand A is equal to the number of people who prefer brand B, we would conduct an independent-sample t-test.

Question 36

A symmetrical bell-shaped distribution that describes the expected probability distribution of many chance occurrences is called:

A) normal distribution
B) standardised normal distribution
C) sampling distribution
D) randomised distribution

Question 37

The expected value of the statistic is also known as the:

A) point estimate.
B) Z-statistic.
C) standard error of the mean.
D) sampling distribution's mean.

Question 38

Which of the following is calculated to be as square root of standard deviation:

A) variance.
B) average deviation.
C) mode.
D) mean squared deviation.

Question 39

Parametric statistical procedures are most appropriate when the data are nominal-scaled.

Question 40

The t-distribution should be used when the sample size is large (n > 30) and the population standard deviation is unknown.

Question 41

The Chi-square test for goodness of fit allows us to:

A) test for differences between two mean scores.
B) test the strength of relationship between interval data.
C) test if significance exists across categorical data.
D) test if a sample mean is statistically different from a known value.

Question 42

Suppose you wish to test whether mean attitudes towards an advertisement are higher than some set value (for example, 4) on a 7-point scale. The null hypothesis should be written as:

A) Ho: µ = 4.
B) Ho: µ = 7.
C) Ho: µ > 4.
D) Ho: µ = 0.

Question 43

Which of the following test allows to test for significance in the analysis of frequency distribution?

A) Chi-square test
B) one-sample t-test
C) paired-samples t-test
D) independent samples t-test

Question 44

Suppose that a group of 100 consumers are asked to rate how much they liked the taste of a new soft drink on a 5-point scale (where 5 = good taste and 1 = poor taste). The mean rating was 4.6, with a standard deviation of 1.25. Suppose, further, that the standard error of the mean for this study was 0.15. If you wanted to find the 95 per cent confidence interval (two-tailed test), and if the Z-value at the .05 level of significance is 1.96, then the confidence interval lies between approximately:

A) 4.45 and 4.75.
B) 4.31 and 4.89.
C) 4.36 and 4.85.
D) 4.57 and 4.63.

Question 45

The idea that, in a research study, any change from what has been observed in the past will be entirely due to random error is a basic assumption of the:

A) null hypothesis.
B) confidence interval.
C) critical value.
D) significance level.

Question 46

The values that lie exactly on the boundary of the region of rejection for hypothesis testing are called the:

A) degrees of freedom.
B) critical values.
C) significance level.
D) confidence interval.

Question 47

Variables or measured characteristics of the population are known as:

A) sample statistics.
B) population parameters.
C) statistical parameters.
D) inferential parameters.

Question 48

Which of the following statements about the t-distribution is not true?

A) Its shape is influenced by its degrees of freedom.
B) It is a symmetrical, bell-shaped distribution.
C) It has a mean of one and a standard deviation of one.
D) It is contingent on sample size.

Question 49

The critical (Z) value at the 99 per cent confidence level equals:

A) 0.01.
B) 1.65.
C) 1.96.
D) 2.57.

Question 50

When a researcher would like to test if mean attitudes are higher than 5 on a 7-point scale, which of the following statistical procedures is appropriate?

A) Chi-square test
B) One-sample t-test
C) Independent samples t-test
D) Paired-samples t-test

Question 51

The critical probability of choosing between the null hypothesis and the alternative hypothesis is called the:

A) critical value.
B) significance level.
C) Chi-square test.
D) degrees of freedom.

Question 52

The decision rule used to determine whether the null hypothesis should be rejected, and the alternative hypothesis accepted is known as the:

A) point estimate.
B) confidence level.
C) significance level.
D) confidence interval estimate.

Question 53

The Chi-square statistic allows us to determine whether the difference between the observed frequency distribution and the expected frequency distribution should be attributed to:

A) sampling variation.
B) population variation.
C) random variation.
D) systematic variation.

Question 54

In a brand awareness study of 150 consumers, 60 respondents were able to identify Corolla as a type of Toyota car. The Chi-square value for a test of this brand awareness was approximately:

A) 6.00.
B) 3.00.
C) 0.60.
D) 0.20.

Question 55

When data are measured on an ordinal scale, the __________ is the most appropriate descriptive measure.

A) median
B) standard deviation
C) mean
D) mode

Question 56

Failing to reject the null hypothesis when the alternative hypothesis is true is known as a:

A) Type II error.
B) Type III error.
C) Type IV error.
D) Type I error.

Question 57

Which of the following statements is not true?

A) Type I and Type II errors can be simultaneously reduced by increasing the sample size.
B) In marketing problems, Type II errors are generally more serious than Type I errors.
C) Hypothesis testing is based on probability theory.
D) If the null hypothesis is true, it implies that there is no change to the status quo.

Question 58

The error caused by rejecting the null hypothesis when it is, in fact, true is called a:

A) Type IV error.
B) Type III error.
C) Type II error.
D) Type I error.

Question 59

Which of the following do not influence sample size?

A) Confidence interval
B) Variability in the sample.
C) Acceptable error
D) Population size

Question 60

For a t-test, the degrees of freedom are derived by:

A) n + 1
B) n(n - 1)
C) n - 1
D) n(n + 1)

Question 61

Parametric statistical tests are based on the assumption that the data is drawn from a population with a(n) ______ sampling distribution.

A) normal
B) average
C) bimodal
D) skewed

Question 62

To test a hypothesis about a mean, such as average sales between stores, our data is required to be:

A) nominal scaled or ordinal scaled.
B) ordinal scaled or interval scaled.
C) interval scaled or ratio scaled.
D) ratio scaled or ordinal scaled.

Question 63

Conducting analysis with more than two variables simultaneously is known as:

A) hypothesis analysis.
B) bivariate analysis.
C) univariate analysis.
D) multivariate analysis.