Question 1

In evaluating the hypothesis test on experimental data, all the following will change the resulting p-value except for what?

Accepted Answer

The confidence level is predetermined before conducting the hypothesis test and does not change based on the experimental data. A, B, and C can all impact the results of the test and therefore the resulting p-value.

Question 2

Suppose you wanted to determine if you should reject the null hypothesis that running a playing fast tempo (as opposed to slow) music in your store has no effect on sales. On 65 randomly selected days with fast tempo music on the average store sales is $2,345 with a sample standard deviation of 45, while on 75 randomly selected days with slow tempo music on the average store sales is $2,555, with a sample standard deviation of 65. What would be the proper t-stat for this hypothesis test?

Accepted Answer

The proper t-stat for a two-sample t-test with unequal variances is given by the formula (x1 - x2)/sqrt(s1^2/n1 + s2^2/n2), where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes. Therefore, the correct formula would be (2345 - 2555)/sqrt((45^2/65)+(65^2/75)). Option A is the correct formula with correct values plugged in.

Question 3

If you have a sufficiently large random sample from the population, but do not know how treatment was assigned, what object will a confidence interval centered on the difference in average outcomes for the treated and control groups be describing?

Accepted Answer

A confidence interval centered on the difference in average outcomes for the treated and control groups, without knowing how treatment was assigned, describes the Estimated Treatment Effect on the Treated (ETT) plus any Selection Bias. This is because without knowing the assignment mechanism, we cannot distinguish between the effect of the treatment itself and the effect of the factors that led to receiving the treatment.

Question 4

In evaluating the hypothesis test on experimental data, all the following will change the resulting test statistic except for what?

Accepted Answer

The test statistic itself is calculated based on the data and the hypothesized value in the null hypothesis, so changing the number of subjects in either group or the hypothesized value will affect the test statistic. However, the confidence level determines the critical value for the test statistic, which in turn affects the determination of statistical significance but does not change the test statistic itself.

Question 5

In building a confidence interval for ATE in experimental data, which of the following is not required?

Accepted Answer

The null hypothesis proposed value of the ATE is not required to build a confidence interval for the Average Treatment Effect (ATE) in experimental data. Confidence intervals are constructed to estimate the range within which the true ATE is likely to lie, based on the observed data, without assuming a specific value for the ATE under the null hypothesis.

Question 6

In building a confidence interval for the ATE of an experiment, all the following objects will influence the spread of the confidence interval except what?

Accepted Answer

The objects that influence the spread of a confidence interval are the confidence level, the sample size of both the treated and control groups, the variance in the outcome, and the sample average outcome for the treated group. The sample average outcome for the control group does not directly influence the spread of the confidence interval.

Question 7

Given the average outcomes for the treated and control groups, and their respective sample standard deviations how does the number of observations impact the p-value of a hypothesis test?

Accepted Answer

Increasing the number of observations in either the treated or control groups generally leads to a more precise estimate of the mean outcomes, which can lower the p-value if there is a true effect, making it easier to detect statistically significant differences. The statement does not specify that increasing observations in one group over the other would have a unique effect on the p-value without considering the effect size and variance in both groups.

Question 8

If you have a sufficiently large sample that was randomly drawn from your target population with a randomly assigned treatment then all of the following conditions hold except for what?

Accepted Answer

None of the answers are correct. A large randomly drawn sample with a randomly assigned treatment would not necessarily guarantee that the distribution of the difference in average outcomes for treated and control groups will be normal, as it would depend on the characteristics of the population and treatment.

Question 9

Which of the following departments is likely to experience experimental data more frequently than nonexperimental data?

Accepted Answer

R&D (Research and Development) is a department that is primarily focused on conducting experiments to develop new products or improve existing ones. Therefore, it is likely to encounter experimental data more frequently than nonexperimental data. The other departments may also encounter some experimental data but it is not their primary focus.

Question 10

Suppose you wanted to determine if you should reject the null hypothesis that running a playing fast tempo (as opposed to slow) music in your store decreases sales by $100 on average. On 65 randomly selected days with fast tempo music on the average store sales is $2,345 with a sample standard deviation of 45, while on 75 randomly selected days with slow tempo music on the average store sales is $2,555, with a sample standard deviation of 65. What would be the proper t-stat for this hypothesis test?

Accepted Answer

The correct formula for the t-statistic is:t = (x̄1 - x̄2 - μ0) / √(s1^2/n1 + s2^2/n2)where x̄1 and x̄2 are the sample means, μ0 is the hypothesized difference in means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.In this case, we have:x̄1 = 2,345x̄2 = 2,555μ0 = -100s1 = 45s2 = 65n1 = 65n2 = 75Plugging these values into the formula, we get:t = (2,345 - 2,555 - (-100)) / √(45^2/65 + 65^2/75)= (2,345 - 2,555 + 100) / √(45^2/65 + 65^2/75)= (2,345 - 2,555 + 100) / √(2,025/65 + 4,225/75)= (2,345 - 2,555 + 100) / √(31.1538 + 56.3333)= (2,345 - 2,555 + 100) / √(87.4871)= (2,345 - 2,555 + 100) / 9.3538= (-210 + 100) / 9.3538= -110 / 9.3538= -11.7674Therefore, the correct answer is C.

Question 11

Given the average outcomes for the treated and control groups, and their respective sample standard deviations, how does the number of observations impact the spread of a confidence interval?

Accepted Answer

The spread of a confidence interval is influenced by the sample size of both the treated and control groups, not just one or the other. Increasing the number of observations in either group generally decreases the spread of the confidence interval by reducing the standard error.

Question 12

Suppose you want to build a 95% confidence interval for the ATE when the average outcome for the treated (55 subjects) is 12, with a sample standard deviation of 4, while the average outcome for the control (65 subjects) is 10, with a sample standard deviation of 6. Which of the following would be the proper confidence interval?

Accepted Answer

The correct confidence interval for the ATE (Average Treatment Effect) is calculated by taking the difference between the average outcomes of the treated and control groups, which is $12 - 10 = 2$, and then adding and subtracting the margin of error. The margin of error is calculated using the formula for the standard error of the difference between two means, which involves the sample standard deviations and sizes of both groups. Choice C correctly applies the 1.96 multiplier for a 95% confidence interval and the formula for the standard error of the difference between two means.

Question 13

Which of the following fields is likely to experience nonexperimental data more frequently than experimental data?

Accepted Answer

Business is a field that frequently relies on nonexperimental data such as surveys, observational studies, and case studies to study consumer behavior, market trends, and other related topics. On the other hand, fields like Chemistry, Pharma, and Psychology may rely more heavily on experimental methods.

Question 14

In building a confidence interval for the ATE of an experiment, what object will determine the center of the confidence interval?

Accepted Answer

The center of the confidence interval for the ATE is determined by the difference between the average outcome for the treated group and the average outcome for the control group. This is because we are interested in the average treatment effect, which is the difference in outcomes between the treated and control groups. Therefore, the center of the confidence interval should reflect this difference.

Question 15

Suppose you want to build a 90% confidence interval for the ATE when the average outcome for the treated (55 subjects) is 12, with a sample standard deviation of 4, while the average outcome for the control (65 subjects) is 10, with a sample standard deviation of 6. Which of the following would be the proper confidence interval?

Accepted Answer

The correct confidence interval accounts for the difference in means (12 - 10 = 2) and uses the 1.65 z-score for a 90% confidence interval, along with the correct formula for the standard error of the difference in means.

Question 16

Which of the following is not an assumption required to build a confidence level for an ATE in an experimental design?

Accepted Answer

The assumption that the outcomes for the treated group and control group are the same is not necessary to build a confidence level for an ATE in an experimental design. In fact, the purpose of conducting an experiment is to see if there is any difference in outcomes between the treatment and control groups. The assumptions required to build a confidence level include having a random sample, randomly assigning treatment, and having a large enough sample size.

Question 17

In testing if promotions (binary) P_i have an effect on sales, S_i with a null hypothesis that the average treatment effect is zero, the null hypothesis could be written as:

Accepted Answer

The null hypothesis should state that the average treatment effect is zero, which is captured by subtracting the outcome variable (sales) when the promotion is present from when it is not present and taking their expected value. Therefore, the correct formulation is E [S_i (P_i= 1) - S_i (P_i= 0)] = 0. B and C are incorrect because they do not include the outcome variable in the formulation of the null hypothesis. D is incorrect because ETT (expected treatment effect) is not equal to zero and is not a statement of the null hypothesis.

Question 18

Which of the following will yield nonexperimental data?

Accepted Answer

Investment performance over the last ten years of several portfolio managers is an example of nonexperimental data, as it is obtained through observational study rather than a controlled experiment. A clinical trial (A) would yield experimental data, and crop yields (B) could potentially be experimental if the crops were grown under controlled conditions with different types of fertilizers.

Question 19

Suppose Apple is considering increasing its advertising expenditures to promote the most recent iPhone. To try to assess the effect of such a move, it looks at sales in several small markets. In some of these markets Apple increased advertising expenditures by 30% and in others there was no change. When conducting this "experiment," what is the treatment?

Accepted Answer

The treatment in this experiment is the increase in advertising expenditures by 30%. This is the factor that is being manipulated to see if it has an effect on iPhone sales. The other choices are not the treatment because they are either outcomes (iPhone sales) or irrelevant factors (number of small markets).

Question 20

In building a confidence interval for the ATE of an experiment, what object will determine the spread of the confidence interval?

Accepted Answer

The spread of the confidence interval will be determined by the sample standard deviation for the treated group. This is because the standard deviation captures the variability within the group and thus affects the precision of the estimate of the ATE. The null hypothesis value, average outcome for the treated group, and average outcome for the control group may be used in calculating the confidence interval, but they do not determine the spread of the interval.

Quiz 4: The Scientific Method: The Gold Standard for Establishing Causality