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

Question 1

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

Answer 1

True

Question 2

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

Answer 2

True

Question 3

The median is affected by extreme values, and therefore should not be used when the distribution is skewed.

Answer 3

False

Question 4

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

Question 5

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

Question 6

The variance diminishes as the observations differ increasingly from one another and from the mean.

Question 7

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

Question 8

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

Question 9

The sample consists of a large fraction of the total number of elements in the population.

Question 10

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

Question 11

The range is useful for describing the sample variability.

Question 12

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

Question 13

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

Question 14

The average deviation score is a useful measure of spread.

Question 15

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

Question 16

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

Question 17

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 18

The range takes into account all the observations in a given distribution.

Question 19

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

Question 20

An alternative hypothesis is a statement about a status quo.

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

Which of the following measures is a very good index of the degree of dispersion?

A) Variance
B) Range
C) Standard deviation
D) Mean squared deviation

Question 23

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 24

Nonparametric statistical tests are frequently referred to as distribution free.

Question 25

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

Question 26

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

Question 27

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 28

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

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

Question 29

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 30

Summing the deviation score of each observation value (that is, its difference from the mean) and then dividing by the sample size (n) computes the:

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

Question 31

Which of the following descriptive statistics is not affected by extreme values in a distribution?

A) Mean
B) Median
C) Standard deviation
D) Variance

Question 32

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

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

Question 33

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

Question 34

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

Question 35

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 36

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

Question 37

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

Question 38

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 39

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 40

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

Question 41

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 42

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 43

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 44

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 45

In statistical testing, the significance level is commonly denoted by the symbol:

A) $\beta$
B) $\alpha$
C) µ.
D) $\chi$

Question 46

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 47

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 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

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 50

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 51

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 52

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 53

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 54

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 55

The appropriate descriptive measures for a nominal scale are:

A) mean and standard deviation.
B) mode and frequency distribution.
C) median and range.
D) median and percentile.

Question 56

To test whether or not the number of customer complaints for one month is higher than usual, which of the following tests is appropriate?

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

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

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 59

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 60

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 61

Variables or measured characteristics of the population are known as:

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

Question 62

An estimate of the population mean in the form of a single value, usually the sample mean, is called a(n) _____ ________.

Question 63

The sampling distribution's mean is called the ________ _____ of the statistic.

Question 64

The square root of the variance for a distribution is known as the ________ _________.

Question 65

The midpoint of the distribution is known as the ______.

Question 66

The long-run relative frequency with which an event will occur is known as ___________.

Question 67

A(n) __________ is an unproven proposition or supposition that tentatively explains certain facts or phenomena.

Question 68

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

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

Question 69

___________ __________ uses the concept of a probability distribution, which is conceptually the same as a percentage distribution, except that the data are converted into probabilities.

Question 70

The theory that, as sample size increases, the distribution of sample means of size n, randomly selected, approaches a normal distribution is known as the _____________ _______.

Question 71

The value that occurs most often is known as the ____.

Question 72

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 73

Another term for the arithmetic average is the ____.

Question 74

A measure of variability or dispersion is known as the ________.

Question 75

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 76

A specified range of numbers within which a population mean is expected to lie is known as the __________ ________ estimate.

Question 77

A percentage or decimal value that indicates the long-run probability that the results will be correct is known as the __________ _____.

Question 78

Variables in a sample or measures computed from sample data are known as ______ __________.

Question 79

A specific normal curve that has an infinite number of cases, a mean of zero and a standard deviation of one is known as the ____________ ______ distribution.

Question 80

Variables in a population or measured characteristics of the population are known as __________ __________.