Question 1

In making an active prediction it is advantageous for the relationship being predicted to be of what sort?

Accepted Answer

Making an active prediction is most advantageous when the relationship being predicted is causal. This means that changes in one variable can be attributed to changes in another variable, allowing for more accurate and reliable predictions. Unbiased, efficient, and confounding relationships may still be predicted, but they may be more difficult to accurately forecast.

Question 2

The step that requires the use of inductive reasoning when making an active prediction from a sample of data is:

Accepted Answer

Inductive reasoning involves making generalized conclusions based on specific observations, and determining the population parameter from a sample requires this type of reasoning. The other choices involve the use of statistical tools and hypothesis testing, but not necessarily inductive reasoning.

Question 3

In making active predictions based on sample data it requires the use of what sort of reasoning?

Accepted Answer

The answer of In making active predictions based on sample...

Question 4

Can a t-stat be negative for the hypothesis test of the population mean of the heights of econometrics students (which will always be positive)?

Accepted Answer

The t-statistic can be negative if the sample mean is less than the hypothesized population mean, regardless of whether the hypothesized mean is positive or negative.

Question 5

To use the normal distribution to calculate the p-value of a hypothesis test involving the population mean, which assumption is not necessary?

Accepted Answer

Assuming a normal distribution for the sample mean requires the sample to be random and for the sample size to be large enough. However, the null hypothesis does not have to be zero for a hypothesis test involving the population mean.

Question 6

In making an active prediction that using a large banner advertisement will increase click-through rates based on a sample of data, what is not an appropriate criticism that someone might have for your prediction?

Accepted Answer

The normality of the underlying population distribution is not relevant to this prediction. The other three criticisms are valid concerns and could affect the accuracy of the prediction.

Question 7

If one is attempting to make a prediction on how much sales will increase in the event of a price discount of 10%, which step will not use deductive reasoning in conducting the prediction?

Accepted Answer

Deductive reasoning is used in all the steps mentioned (calculating the p-value, calculating the test statistic, determining the test statistic's distribution) as part of statistical analysis to make predictions or inferences.

Question 8

For a given set of sample statistics, changing the null hypothesized value (K) for a population mean changes everything except for what?

Accepted Answer

The sample standard deviation is a characteristic of the sample data itself and does not change with the null hypothesized value.

Question 9

Suppose you have a random sample of employees in your company and their tenure. The sample mean of this sample is 4.2 years and the sample standard deviation is 4.5 years. How would knowing that the random sample was of size 100 instead of 60 change the p-value of the hypothesis test?

Accepted Answer

Increasing the sample size from 60 to 100 decreases the standard error of the mean, leading to a tighter confidence interval around the sample mean. This generally results in a smaller p-value if the null hypothesis is being tested against an alternative, assuming the mean difference remains constant.

Question 10

If you conduct a hypothesis test under the scenario in which you know the population standard deviation, which of the following will not affect the size of the p-value of the hypothesis test?

Accepted Answer

The p-value in a hypothesis test is not affected by the sample standard deviation when the population standard deviation is known. In such cases, the test typically uses the population standard deviation for calculations, making the sample standard deviation irrelevant to the p-value.

Quiz 3: Reasoning From Sample to Population