Question 1

Statistical tools allow us to prove the null hypothesis is wrong.

Accepted Answer

Statistical tools can only provide evidence against the null hypothesis, but they cannot prove it to be wrong with absolute certainty. The null hypothesis can only be rejected or failed to be rejected based on the evidence provided by the statistical analysis.

Question 2

Type I errors occur when we fail to reject a null hypothesis even when it is false.

Accepted Answer

Type I errors occur when we reject a null hypothesis that is actually true.

Question 3

Type II errors occur when we fail to reject a null hypothesis even when it is false.

Accepted Answer

Type II errors occur when we fail to reject a null hypothesis even when it is false, meaning we incorrectly accept the null hypothesis when it should have been rejected.

Question 4

In hypothesis testing, what we really care about is the size of the ₁ coefficient.

Accepted Answer

The statement is incorrect. In hypothesis testing, we are concerned with the significance level or p-value, which helps us determine the strength of evidence against the null hypothesis. The ₁ coefficient may be relevant in the context of a regression analysis, but not necessarily in hypothesis testing.

Question 5

We fail to reject the null hypothesis if the test statistic is greater than the critical value.

Accepted Answer

We fail to reject the null hypothesis if the test statistic is less than the critical value, indicating that the observed data do not provide sufficient evidence to conclude that the effect exists at the specified level of significance.

Question 6

A large sample will tend to produce high-power statistical tests while small samples will tend to produce low power statistical tests.

Accepted Answer

This is true because with a larger sample size, the test will have more data points and be less susceptible to random variation. This reduces the probability of a Type II error, which increases the power of the test. On the other hand, with a smaller sample size, there may not be enough data points to detect a significant difference even if one exists, leading to a higher probability of a Type II error and resulting in a lower power statistical test.

Question 7

Reducing the significance level (alpha) will:&#10;A) Will increase the probability of making a Type I Error&#10;B) Will increase the probability of making a Type II Error&#10;C) Will not affect the probability of making either error&#10;D) Will decrease the probability of making a Type II Error

Accepted Answer

Reducing the significance level (alpha) decreases the probability of making a Type I error (rejecting a true null hypothesis) but increases the probability of making a Type II error (failing to reject a false null hypothesis), as it makes the criteria for rejecting the null hypothesis more stringent.

Question 8

In which case would we choose to a one-sided alternative hypothesis over a two-sided alternative hypothesis?&#10;A) It does not matter what type of alternative hypothesis we specify.&#10;B) Choose a one sided alternative hypothesis when the theory and literature suggests either that the coefficient should be greater than zero or that the coefficient should be less than zero.&#10;C) We choose a one sided alternative hypothesis when we have a large sample size.&#10;D) We choose a one sided alternative hypothesis when we specify a low (0.01) alpha.

Accepted Answer

We choose a one-sided alternative hypothesis when the theory and literature suggest either that the coefficient should be greater than zero or that the coefficient should be less than zero. This is because a two-sided alternative hypothesis assumes that the coefficient could be either positive or negative, while a one-sided alternative hypothesis specifies the direction of the effect that we are interested in testing.

Question 9

Assume that the two-sided 95% confidence interval for the effect of a price on amount of beef purchased is between 0.30 and 0.38. Which of the following statements is incorrect?&#10;A) We will reject the null hypothesis that this coefficient equals zero.&#10;B) There is less than a 2.5% chance that a coefficient higher than 0.38 would produce the coefficient we actually observe.&#10;C) There is a 95% chance that the true coefficient is between 0.30 and 0.38.&#10;D) There is a 95% chance that a random sample will produce a confidence interval that includes the true coefficient.

Accepted Answer

A confidence interval indicates the range within which we can be confident that the true parameter lies, given our sample data. It does not imply that the true coefficient has a specific probability of being within that range. Instead, it means that if we were to repeat the experiment many times, 95% of the confidence intervals calculated from those experiments would contain the true coefficient.

Question 10

A null and alternative hypothesis are statements pertaining to:&#10;A) Sample parameters&#10;B) Sample statistics&#10;C) Population parameters&#10;D) It depends - In some cases it is population parameters, in others it is the sample statistics.

Accepted Answer

A null and alternative hypothesis are statements pertaining to the population parameters. It is important to note that the sample statistics are used to make inferences about the population parameters.

Question 11

A statistical significance test that is based on a small sample may not produce a result that is statistically significant even if the true value of the coefficient is different from the value in the null hypothesis. Such a situation is:

A) Power of the test
B) Type I Error
C) Type II Error
D) Significance level of the test

Accepted Answer

The answer of A statistical significance test that is based...

Question 12

A null hypothesis of H₀: \beta = 0 can be rejected at the 95% confidence interval if and only if: A) The 95% confidence interval contains zero B) The 95% confidence interval does not contain zero C) The null hypothesis is in the middle of the 95% confidence interval D) The sample size is sufficiently large (n>=30)

Accepted Answer

The answer of A null hypothesis of H₀: \beta =...

Question 13

Which of the following will tend to reduce the size of a confidence interval?&#10;A) Decrease the significance level (alpha).&#10;B) Increase the sample size&#10;C) Decrease the standard deviation of the population&#10;D) You can't do anything to reduce the interval

Accepted Answer

The answer of Which of the following will tend to...

Question 14

If we decrease the significance level (alpha) all else being equal, the power of the test will:&#10;A) Decrease&#10;B) Increase&#10;C) Won't change&#10;D) It depends - need more information

Accepted Answer

The answer of If we decrease the significance level (alpha)...

Question 15

Explain what the distribution of B̂₁ is under the null hypothesis H₀: \beta = 0 and why.

Accepted Answer

The answer of Explain what the distribution of B̂₁ is...

Question 16

Explain the t distribution and explain what its tails are like and why?

Accepted Answer

The answer of Explain the t distribution and explain what...

Question 17

Describe the relationship between sample size and statistical significance.

Accepted Answer

The answer of Describe the relationship between sample size and...

Question 18

Describe what a power curve is, and provide a rough sketch of a power curve, and accurately label the x-axis and the y-axis.

Accepted Answer

The answer of Describe what a power curve is, and...

Question 19

Explain the difference between statistical significance and substantive significance.

Accepted Answer

The answer of Explain the difference between statistical significance and...

Question 20

Show the full equation to calculate the t-statistic.

Accepted Answer

The answer of Show the full equation to calculate the...

Deck 4: Hypothesis Testing and Interval Estimation: Answering Research Questions