Question 1

What does it mean to label a statistical model a good fit?
A) Any predictions about the real world based on this model will be accurate
B) Any predictions about the real world based on this model will be inaccurate
C) Any predictions about the real world based on this model will be inadequate
D) Any predictions about the real world based on this model will be spurious

Accepted Answer

A statistical model is considered a good fit when predictions made from the model match observations from the real world. This means that future predictions made from the model are likely to be accurate.

Question 2

A soft drinks company developed a new fizzy drink ('Delicious Fizz'). A researcher conducted a series of 'blind tasting' trials to measure consumer response to the new drink; this involved consumers drinking 'Delicious Fizz' and a rival fizzy drink ('Rival Fizz') and then rating the products on a ten-point taste scale. The results for consumption of 'Rival Fizz' and taste was p = 0.02, while the results for consumption of 'Delicious Fizz' and taste was p = 0.015. How should the researcher interpret her findings?
A) Neither drink had significance
B) 'Delicious Fizz' had greater significance
C) 'Rival Fizz' had greater significance
D) Both drinks had equal significance

Accepted Answer

The researcher should interpret the findings to mean that 'Delicious Fizz' had greater significance, as the p-value for its taste rating was lower than that of 'Rival Fizz'. This suggests that consumers rated the taste of 'Delicious Fizz' more favorably than 'Rival Fizz' in the blind tasting trials. However, it's important to note that the researcher should also consider the sample size and potential confounding factors to ensure the results are reliable and valid.

Question 3

What does NHST stand for?
A) Null Hypothesis significance testing
B) Non Hypothesis significance testing
C) Null Hypothesis statistical testing
D) Null Hypothesis statistical trialling

Accepted Answer

NHST stands for Null Hypothesis significance testing, which is a statistical method used to test the statistical significance of results by comparing them to a null hypothesis. This method is commonly used in many fields, including psychology, medicine, and economics.

Question 4

What is the SPINE of statistics?
A) The backbone of any statistical model
B) An acronym for the five core concepts needed to understand statistical models
C) An acronym for the five core statistical tests
D) A test for statistical strength

Accepted Answer

The SPINE of statistics is an acronym for the five core concepts needed to understand statistical models: S for Study design, P for Populations, I for Inference, N for Null hypothesis testing, and E for Estimation.

Question 5

Why are large samples desirable in statistical models?
A) More likely to reflect the sample under study
B) Less likely to reflect the population under study
C) Less likely to reflect the sample under study
D) More likely to reflect the population under study

Accepted Answer

Large samples are desirable in statistical models because they are more likely to reflect the population under study. This is because as sample size increases, the sample mean, variance, and distribution become more representative of the population parameters. Therefore, the findings and conclusions drawn from a large sample are more accurate and generalizable to the population as a whole.

Question 6

A HR manager conducted a review of overtime worked by employees. Her sample size was 60 employees and there was a mean of 90 hours worked overtime per month. Her confidence interval was 95%. What would be the upper boundary confidence interval for this study?
A) 91.86 hours
B) 88.14 hours
C) 90 hours
D) 9.5 hours

Accepted Answer

Since we are looking for the upper boundary of the confidence interval, we need to use the upper limit of the interval formula. Using a 95% confidence interval, the formula is: 
Upper limit = mean + (Z-score x standard error)
The Z-score for a 95% confidence interval is 1.96. To calculate the standard error, we need to divide the standard deviation by the square root of the sample size. Assuming a standard deviation of 10 hours, the standard error would be:
Standard error = 10 / sqrt(60) = 1.29
Plugging in these values, we get:
Upper limit = 90 + (1.96 x 1.29) = 91.86 hours
Therefore, the correct choice is A.

Question 7

A financial analyst needed to calculate the mean income generated by the six most successful salespeople in her business over one month. The income figures were £1950, £3500, £4232, £4376, £2999 and £2165. What was the mean income generated?
A) £2303.76
B) £4304
C) £3203.67
D) £19222

Accepted Answer

To find the mean income, we need to add up all the incomes and divide by the number of salespeople.

(1950 + 3500 + 4232 + 4376 + 2999 + 2165) / 6 = 3203.67

Therefore, the mean income generated by the six most successful salespeople over one month is £3203.67.

Question 8

In hypothesis testing, which hypothesis do we test?
A) Experimental
B) Research
C) Alternative
D) Null

Accepted Answer

In hypothesis testing, we test the null hypothesis, which is typically the hypothesis stating that there is no significant difference or relationship between variables. The alternative hypothesis is the opposite of the null hypothesis and is only accepted if there is enough evidence to reject the null hypothesis. The other options (experimental and research) are not typically hypotheses that are tested in hypothesis testing.

Question 9

You work in a data analyst unit for a large fast food restaurant chain, planning a customer survey and a colleague informs you that a 95% confidence interval has a 95% probability of containing a population parameter. Because of this, she insists that a survey distributed at one restaurant will provide significant results. Do you agree with her?
A) No, because 95% probability is a long-run probability requiring that multiple tests to be done
B) Yes, because 95% probability is the standard level for significance testing
C) No, because 95% confidence interval requires that multiple tests to be done
D) Yes, because 95% probability is a short-run probability requiring that only one test be done

Accepted Answer

CA 95% confidence interval means that if we were to take many samples and build a confidence interval from each, about 95% of these intervals would contain the true population parameter. It's a long-run probability, not a guarantee for a single interval from one test. Multiple tests or samples are implied in the concept of confidence intervals to approximate the true parameter accurately.

Question 10

A business analyst in a software design company reviewed a series of national surveys of user satisfaction (rated on a ten-point satisfaction scale) with a new gaming interface the company had recently launched. She found that the survey mean was 8. However, her standard error was high (89.5), how should she interpret her results?
A) The sample mean is representative of the population mean
B) The sample mean might not be representative of the population mean
C) The sample mean has a low standard deviation
D) The sample has a high standard deviation

Accepted Answer

A high standard error indicates that there is a large amount of variability in the sample data and that the sample mean may not be a good representation of the population mean. Therefore, the business analyst should be cautious when interpreting the results and should consider collecting more data or investigating potential reasons for the high standard error.

Question 11

What is the power of a statistical test?
A) The probability that it will find an error when on exists
B) The probability that it will not find an effect when one exists
C) The probability that it will find an effect when one exists
D) The probability that it will not find an error when one exists

Accepted Answer

The power of a statistical test refers to its ability to correctly detect a real effect or difference. Therefore, the correct answer is the probability that it will find an effect when one exists, which is option C. Option A (finding an error when one exists) refers to the type I error rate, while option B (not finding an effect when one exists) is the type II error rate. Option D is not related to the power of a statistical test.

Question 12

What is the standard error?
A) The standard deviation of sample means
B) The square root of the sample means
C) The square root of the error in a sample
D) The standard deviation of the error in a sample

Accepted Answer

The standard error measures the dispersion or spread of the sample means around the population mean, and it is calculated as the standard deviation of the sample means.

Question 13

Your business studies lecturer has set you the following hypothesis to test, 'there will be no association between consumer socioeconomic status and level of private health insurance'. What type of hypothesis is this?
A) One tailed
B) Alternative
C) Directional
D) Two tailed

Accepted Answer

This hypothesis is a two-tailed hypothesis because it is not specifying the direction of the relationship between consumer socioeconomic status and level of private health insurance. It is simply stating that there will be no association between the two variables. A two-tailed hypothesis allows for the possibility of observing either a positive or negative correlation between the variables, or no correlation at all.

Question 14

You are the newly appointed business analyst for a large national bank (250000 customers). At a team meeting, your boss presents the results of a survey of customers regarding their opinion (measured on a ten point scale) of a new financial product. The survey sample (of 500 customers) showed a significant (p = 0.23) level of satisfaction with the new financial product. How should you interpret this result for your boss?
A) The result is significant and customers are satisfied
B) The result is not-significant but the small sample size is not important as sample size has no effect on statistical power
C) The result is not-significant but the small sample size may be missing large differences in customer satisfaction
D) The result is significant but the small sample size may be missing large differences in customer satisfaction

Accepted Answer

The result is not-significant, but the small sample size may be missing large differences in customer satisfaction. A p-value of 0.23 indicates that there is a high likelihood that the observed difference in satisfaction levels between the customers who were surveyed and the population as a whole was due to chance. While this does not necessarily mean that there is not a true difference, the small sample size means that the survey may have missed large differences in customer satisfaction. Therefore, caution should be exercised in interpreting these results as they may not accurately reflect the opinions of the entire customer base.

Question 15

What do we call the situation where we believe there is a genuine effect in our population when in fact there is not?
A) Type II error
B) Type I error
C) Standard error
D) Type III error

Accepted Answer

This is a Type I error, also known as a false positive, where we reject the null hypothesis when it is actually true. This means we believe there is a genuine effect in our population when in fact there is not.

Question 16

A member of your market research team conducted tests of a new television advert with twenty different groups of consumers, in which they rated their satisfaction (on a ten point scale) with the advert and likelihood of purchasing the advertised product (on a five point scale). He is worried about the familywise error rate across the tests, what advice would you give him.
A) Use a Cramer's V test
B) Use a Olive Dunn test
C) Use a Bonferroni Correction
D) Use a Field Correction

Accepted Answer

The best choice for controlling familywise error rate in this scenario would be to use a Bonferroni correction, which adjusts the alpha level of individual tests to account for the increased likelihood of making a Type I error across multiple tests. This is a simple and widely used method for controlling familywise error rate. The other options, such as Cramer's V test, Olive Dunn test, and Field Correction, are not appropriate for controlling familywise error rate in this context.

Quiz 2: The Spine of Statistics

What does it mean to label a statistical model a good fit?

What does NHST stand for?

What is the SPINE of statistics?

Why are large samples desirable in statistical models?

A HR manager conducted a review of overtime worked by employees. Her sample size was 60 employees and there was a mean of 90 hours worked overtime per month. Her confidence interval was 95%. What would be the upper boundary confidence interval for this study?

A financial analyst needed to calculate the mean income generated by the six most successful salespeople in her business over one month. The income figures were £1950, £3500, £4232, £4376, £2999 and £2165. What was the mean income generated?

In hypothesis testing, which hypothesis do we test?

What is the power of a statistical test?

What is the standard error?

Your business studies lecturer has set you the following hypothesis to test, 'there will be no association between consumer socioeconomic status and level of private health insurance'. What type of hypothesis is this?

What do we call the situation where we believe there is a genuine effect in our population when in fact there is not?