Question 1

In general, if N ≥ 30, the sampling distribution of the mean will be normally shaped.

Accepted Answer

According to the central limit theorem, if the sample size is 30 or greater, the sampling distribution of the mean will be approximately normally distributed, regardless of the shape of the population distribution.

Question 2

Increasing N usually results in an increase of power.

Accepted Answer

Increasing N (sample size) usually results in a more representative sample and a larger sample size can increase the probability of finding statistically significant results. This can translate into an increase in statistical power.

Question 3

If a = 0.05 2 tail, the critical value of z is ±1.96.

Accepted Answer

This statement is true. A significance level (or alpha level) of 0.05 for a two-tailed test corresponds to a critical value (or cutoff point) of ±1.96 standard deviations from the mean, assuming a normal distribution. This means that if the calculated test statistic falls outside this range, then it is considered statistically significant at the 0.05 level.

Question 4

For the population 2, 4, 6, 8, 10,  .

Accepted Answer

The answer of For the population 2, 4, 6, 8,...

Question 5

The formula for z obt for the sampling distribution of the mean is  .

Accepted Answer

The answer of The formula for z obt for the...

Question 6

If z obt falls within the critical region for rejection of H₀ , one can be certain H₀ is in reality false.

Accepted Answer

It is not certain that H₀ is false if z obt falls within the critical region for rejection. It only suggests that there is sufficient evidence to reject H₀, but there could still be a possibility that it is true.

Question 7

If there is a real effect, the higher the power, the more likely H₀ will be rejected.

Accepted Answer

This is because a higher power means a lower probability of making a type II error, which in turn increases the likelihood of rejecting the null hypothesis (H₀) when there is a real effect.

Question 8

To use the normal deviate one must know the population parameters of the Null Hypothesis Population.

Accepted Answer

The normal deviate (z-score) requires knowledge of the population parameters, specifically the mean and standard deviation of the null hypothesis population, to calculate how many standard deviations a sample statistic is from the population mean.

Question 9

The z test is used to test whether or not it is reasonable to assume a sample of size N was likely to have been drawn from a population with known parameters µ and s .

Accepted Answer

The z-test is used when the population parameters (mean µ and standard deviation s) are known, and it helps determine if a sample mean significantly differs from the population mean.

Question 10

is sometimes called the standard error of the mean because each sample can be considered an estimate of the mean of the raw score population and variability between sample means occur due to errors in estimation.

Accepted Answer

This statement is true, as the standard error of the mean measures the variability between sample means which can occur due to errors in estimation. Each sample can be considered an estimate of the mean of the raw score population, therefore the term "standard error of the mean" is used.

Question 11

By using a stringent alpha level, and designing the experiment for high power, we maximize the probability of correctly concluding regardless of whether H₀ is true or false.

Accepted Answer

Using a stringent alpha level and designing the experiment for high power ensures that we have a low probability of making a Type I error (incorrectly rejecting a true null hypothesis) and a high probability of detecting a true effect (Type II error). This maximizes the probability of correctly concluding regardless of whether the alternative hypothesis (H₀) is true or false.

Question 12

If H₀ is false, but power is low, there is a high probability we will err in our conclusion.

Accepted Answer

Since H₀ being false does not necessarily mean that the conclusion is false, but with low power, the sample size may not be large enough to give a representative result, increasing the likelihood of Type I or Type II errors. Therefore, there is a high probability of erring in our conclusion.

Question 13

For sampling distribution of the mean,  =  .

Accepted Answer

The statement "For sampling distribution of the mean, 11ec1b7e_f91f_e9ae_bbf8_3f6827702e00_TBX9373_11 = 11ec1b7e_f91f_e9af_bbf8_c703a9e5c5a7_TBX9373_11" means that the sampling distributions of the mean for two different datasets (with IDs TBX9373_11) are the same. This is possible if the datasets have the same sample size, population standard deviation, and underlying population distribution. Therefore, the statement is true.

Question 14

The sampling distribution of the mean changes as sample size changes.

Accepted Answer

As sample size increases, the standard error of the mean decreases and the shape of the sampling distribution becomes more normal. This means that the distribution of sample means becomes more precise and closer to the population mean. Therefore, the sampling distribution of the mean changes as sample size changes.

Question 15

If the sample mean is different from the population mean, H₀ must be false.

Accepted Answer

H₀ states that the sample mean is equal to the population mean. Therefore, if the sample mean is different from the population mean, H₀ must be false.

Question 16

For the sampling distribution of the mean,  .

Accepted Answer

The answer of For the sampling distribution of the mean,...

Question 17

As N increases,  decreases.

Accepted Answer

The answer of As N increases,  decreases....

Question 18

a + b = 1.00.

Accepted Answer

The equation a + b = 1.00 is not necessarily true without knowing the specific values of a and b.

Question 19

Power is independent of the magnitude of the independent variable's effect.

Accepted Answer

Power is, by definition, the probability of rejecting a null hypothesis when it is false. This probability is influenced by the magnitude of the independent variable's effect. Therefore, power is not independent of the magnitude of the independent variable's effect.

Question 20

A sampling distribution gives one the values a statistic can take, along with the probability of getting each value if sampling is random from the H₁ population.

Accepted Answer

A sampling distribution gives the values a statistic can take, but the probabilities associated with each value depend on the specific sample taken and are not predetermined by the population. Therefore, the statement is false.

Quiz 12: Sampling Distributions, Sampling Distribution of the Mean: the Normal Deviate Z Test

In general, if N ≥ 30, the sampling distribution of the mean will be normally shaped.

Increasing N usually results in an increase of power.

If a = 0.05 2 tail, the critical value of z is ±1.96.

For the population 2, 4, 6, 8, 10, .

The formula for z obt for the sampling distribution of the mean is .

If z obt falls within the critical region for rejection of H0 , one can be certain H0 is in reality false.

If there is a real effect, the higher the power, the more likely H0 will be rejected.

To use the normal deviate one must know the population parameters of the Null Hypothesis Population.

The z test is used to test whether or not it is reasonable to assume a sample of size N was likely to have been drawn from a population with known parameters µ and s .

is sometimes called the standard error of the mean because each sample can be considered an estimate of the mean of the raw score population and variability between sample means occur due to errors in estimation.

By using a stringent alpha level, and designing the experiment for high power, we maximize the probability of correctly concluding regardless of whether H0 is true or false.

If H0 is false, but power is low, there is a high probability we will err in our conclusion.

For sampling distribution of the mean, = .

The sampling distribution of the mean changes as sample size changes.

If the sample mean is different from the population mean, H0 must be false.

For the sampling distribution of the mean, .

As N increases, decreases.