Question 1

When a sample mean is different from the mean of the sampling distribution (the population mean),two alternatives must be considered: The sample mean may represent _____,or it may represent _____.
A)the central tendency of a population well;the variability of a population well
B)a well population;a poor population
C)the population poorly;the population well
D)the population poorly;a different population

Accepted Answer

If the sample mean is different from the mean of the sampling distribution, it is likely that the sample is not representative of the population. Thus, the sample mean may represent the population poorly or it may represent a different population altogether. Option D captures this possibility.

Question 2

What can we conclude about a sample mean that is found to lie in the region of rejection? It is extremely _____ to have occurred by chance,and it represents _____.
A)unlikely;the population
B)likely;the population
C)unlikely;some other population
D)likely;some other population

Accepted Answer

A sample mean in the region of rejection is unlikely to have occurred by chance, suggesting it represents some other population rather than the one being tested.

Question 3

Which of the following is correct regarding means that fall within the region of rejection when the critical values are  ?
A)It is likely they represent the population under study.
B)They have a high relative frequency.
C)They occur with a probability of 95%.
D)They occur with a probability of 5%.

Accepted Answer

The critical values indicate that the region of rejection has a probability of 5%. Therefore, any means that fall within this region have a probability of 5% or lower of occurring by chance. This means that they are unlikely to represent the population under study and are most likely due to random sampling variability.

Question 4

Which of the following is the criterion that psychologists usually use to determine the likelihood that a sample mean was obtained by chance?
A)p = 0.005
B)p = 0.05
C)p = 0.50
D)p = 0.01

Accepted Answer

Psychologists typically use a p-value of 0.05 as the criterion to determine the likelihood that a sample mean was obtained by chance, indicating a 5% probability that the observed results occurred by random chance.

Question 5

_____ occurs when random chance produces a sample statistic that is not equal to the population parameter it represents.
A)Random sampling
B)Sampling error
C)Criterion probability
D)Sampling replacement

Accepted Answer

Sampling error occurs when random chance produces a sample statistic that is not equal to the population parameter it represents. This can happen due to various reasons such as sampling bias, measurement error, or simply due to the natural variation present in any sample. Random sampling (A) refers to the process of selecting a sample from a population randomly and without any bias, while sampling replacement (D) refers to the process of placing the selected unit back into the population before selecting the next one, which can affect the representativeness of the sample. Criterion probability (C) is not a relevant term in this context.

Question 6

What do we call that portion of the sampling distribution in which values are considered too unlikely to have occurred by chance?
A)Region of criterion value
B)Region of critical value
C)Region of rejection
D)Critical value

Accepted Answer

This portion of the sampling distribution is called the region of rejection, as it is rejecting the null hypothesis. This region is determined by a critical value, which is the point beyond which values are too unlikely to have occurred by chance. Therefore, option C (Region of rejection) is the correct choice. Option A (Region of criterion value) is not a commonly used phrase in statistics, while option B (Region of critical value) is a similar concept but not specific to rejecting a null hypothesis. Option D (Critical value) is only a part of the region of rejection but is not exclusive to it.

Question 7

An advertising executive wanted to know whether a new ad campaign designed to deter children from smoking was working.After seeing the ads,a randomly selected sample of 36 teenagers rated what they thought of smoking on a -5 (it's terrible)to +5 (it's fantastic).The mean rating for the sample was -0.70.The population mean is 0,with a population standard deviation of 2.00.What is the probability of obtaining a sample mean of -0.70 or lower (more negative)?
A)0.0179
B)0.1368
C)0.3632
D)0.4821

Accepted Answer

We need to calculate the z-score for the sample mean:

z = (x̄ - μ) / (σ / √n) = (0.70 - 0) / (2 / √36) = 1.5

Then, we need to find the probability of obtaining a z-score of -1.5 or lower:

P(z ≤ -1.5) = 0.0668

Using a standard normal distribution table or calculator, we can find that the probability is 0.0179 (rounded to four decimal places). Therefore, the best choice is A, with a probability of 0.0179.

Question 8

A student wanted to know whether memory for items on a grocery list was better when a bizarre image was created for each item,compared with a strategy of simply trying to remember the items.The student had a randomly selected sample use bizarre imagery to remember a list of 15 items;the mean number of items remembered was 10.The student compared this mean to a population mean of 7 and a standard error of 1.20.What is the probability of obtaining a sample mean of 10 or higher?
A)0.0062
B)0.1151
C)0.4938
D)0.9938

Accepted Answer

The probability can be found using a z-score calculation. The z-score is (10 - 7) / 1.20 = 2.5. Using a standard normal distribution table, the probability of obtaining a z-score of 2.5 or higher is approximately 0.0062.

Question 9

When rolling a pair of fair dice,the probability of rolling a total point value of "7" is 0.17.If you rolled a pair of dice 1,000 times and the point value of "7" appeared 723 times,what would you probably conclude?
A)This is not so unlikely as to make you doubt the fairness of the dice.
B)Although not impossible,this outcome is so unlikely that the fairness of these dice is questionable.
C)Since the total point value of "7" has the highest probability of any event in the sampling distribution,this is an extremely likely outcome.
D)It is impossible for this to happen if the dice are fair.

Accepted Answer

The probability of rolling a 7 with a pair of fair dice is actually 6/36 or 1/6, which is approximately 0.1667, not 0.17. However, getting a total of 723 occurrences of 7 out of 1000 rolls significantly exceeds the expected number of occurrences (which would be around 166.67 if we use the 1/6 probability). This deviation suggests that the outcome is so unlikely that it casts doubt on the fairness of the dice.

Question 10

What is the purpose of the critical value?
A)To determine the size of the region of rejection.
B)To determine the maximum allowable population standard deviation
C)To determine the likelihood that the population mean was obtained by chance
D)To determine the value of z needed to conclude that the population mean was obtained by chance

Accepted Answer

The critical value is used to determine the size of the region of rejection in hypothesis testing. This region is used to determine whether a sample result is statistically significant and supports rejecting the null hypothesis in favor of the alternative hypothesis. The critical value is typically based on the desired level of significance, alpha, and the degrees of freedom in the test.

Question 11

The criterion determines
A)the critical value of the sample mean.
B)the probability of the sample mean.
C)the standard deviation (standard error)of the sampling distribution of means.
D)the size of the region of rejection.

Accepted Answer

The criterion for hypothesis testing determines the size of the region of rejection, which is the range of values for which the null hypothesis is rejected. This is often determined by the significance level (alpha) chosen for the test.

Question 12

What is the critical value?
A)The outer end of the region of rejection
B)The inner edge of the region of rejection
C)The absolute value of the entire region of rejection
D)The value of z needed to conclude that the population mean occurred by chance

Accepted Answer

The critical value is the inner edge of the region of rejection, marking the boundary beyond which we reject the null hypothesis.

Question 13

The scores that lie in the tails of a normal distribution have a _____ frequency and a _____ probability of occurring.
A)high;high
B)low;high
C)high;low
D)low;low

Accepted Answer

Scores in the tails of a normal distribution are less frequent and thus have a lower probability of occurring, reflecting the characteristics of a normal distribution where most scores cluster around the mean.

Question 14

Why can we never be sure that a sample represents a population?
A)Random selection never works the way it is supposed to work.
B)Samples created by random selection are almost never perfectly representative.
C)A random sample may poorly represent a population,or it may accurately represent a different population.
D)If selection is conducted correctly,samples always accurately represent the populations they are supposed to represent.

Accepted Answer

A random sample may be subject to sampling error and may not perfectly represent the population from which it was drawn. Additionally, the chosen sample may be representative of a different population than the one of interest, leading to incorrect conclusions being drawn. Therefore, we can never be sure that a sample completely represents a population.

Question 15

What is the probability of getting a sample mean between 500 and 520 if the population mean is 500 and the standard deviation of the sampling distribution (the standard error of the mean)is 20?
A)0.5000
B)0.4332
C)0.3413
D)0.1915

Accepted Answer

First, we need to find the z-scores for both the upper and lower limits:

Lower limit: (500-500)/20 = 0 
Upper limit: (520-500)/20 = 1

Using a z-table, we can find the probabilities associated with these z-scores:

Lower limit: 0.5000 
Upper limit: 0.8413

To find the probability of the sample mean falling between these two limits, we subtract the lower probability from the upper probability:

0.8413 - 0.5000 = 0.3413

Therefore, the answer is C.

Question 16

If the probability of getting a z-score between the mean and +1 standard deviation is 0.3413,what is the probability of getting a z-score lower than -1 standard deviation?
A)0.3413
B)0.1587
C)0.6587
D)0.8413

Accepted Answer

Since the area between the mean and +1 standard deviation is 0.3413, the area to the left of the mean (which is the same as the area to the left of F1F1F1S1F1F1F101 standard deviation) is 0.5-0.3413=0.1587. Therefore, the probability of getting a z-score lower than F1F1F1S1F1F1F101 standard deviation is 0.1587.

Question 17

We create the sampling distribution of means from
A)a random sample of all possible means.
B)the region of rejection.
C)the z-distribution.
D)the underlying raw score population.

Accepted Answer

The sampling distribution of means is created from multiple random samples of the underlying raw score population. This allows us to estimate the population mean and standard deviation using the means and standard deviations of the random samples. Therefore, option D, which refers to the underlying raw score population, is the best choice. The other options (A, B, and C) do not accurately reflect the creation process of the sampling distribution of means.

Question 18

Which of the following is not true of the criterion?
A)The criterion is the probability that defines samples as unlikely.
B)Samples that meet the criterion occur more than 5% of the time.
C)Behavioral researchers usually use 0.05 as their criterion probability.
D)Sample means that occur with a probability less than that of the criterion probability are likely to represent some other population.

Accepted Answer

The criterion is the probability level at which we decide to reject the null hypothesis. Usually, behavioral researchers use a criterion of 0.05 or 0.01, meaning that they consider a result statistically significant if the probability of obtaining that result by chance is less than or equal to 5% or 1%. Therefore, samples that meet the criterion occur less than 5% of the time.

Question 19

If the probability of getting a z-score between the mean and +1 standard deviation is 0.3413,what is the probability of getting a z-score of +1 standard deviation or less?
A)0.3413
B)0.1587
C)0.6587
D)0.8413

Accepted Answer

The probability of getting a z-score of +1 standard deviation or less includes the probability from the mean to +1 standard deviation (0.3413) plus the probability from the mean to the left tail (0.5), totaling 0.8413.

Question 20

Your professor told the class that,typically,20% of the class receives As,20% Bs,35% Cs,10% Ds,and 15% Fs.What is the probability that the student sitting next to you will receive an A or an F?
A)0.35
B)0.50
C)35%
D)65%

Accepted Answer

The probability of receiving an A is 20% and an F is 15%, so the total probability of receiving an A or an F is 20% + 15% = 35% or 0.35.

Quiz 9: Using Probability to Make Decisions About Data

When a sample mean is different from the mean of the sampling distribution (the population mean) ,two alternatives must be considered: The sample mean may represent _,or it may represent _.

What can we conclude about a sample mean that is found to lie in the region of rejection? It is extremely _ to have occurred by chance,and it represents _.

Which of the following is correct regarding means that fall within the region of rejection when the critical values are ?

Which of the following is the criterion that psychologists usually use to determine the likelihood that a sample mean was obtained by chance?

_____ occurs when random chance produces a sample statistic that is not equal to the population parameter it represents.

What do we call that portion of the sampling distribution in which values are considered too unlikely to have occurred by chance?

When rolling a pair of fair dice,the probability of rolling a total point value of "7" is 0.17.If you rolled a pair of dice 1,000 times and the point value of "7" appeared 723 times,what would you probably conclude?

What is the purpose of the critical value?

The criterion determines

What is the critical value?

The scores that lie in the tails of a normal distribution have a _ frequency and a _ probability of occurring.

Why can we never be sure that a sample represents a population?

What is the probability of getting a sample mean between 500 and 520 if the population mean is 500 and the standard deviation of the sampling distribution (the standard error of the mean) is 20?

If the probability of getting a z-score between the mean and +1 standard deviation is 0.3413,what is the probability of getting a z-score lower than -1 standard deviation?

We create the sampling distribution of means from

Which of the following is not true of the criterion?

If the probability of getting a z-score between the mean and +1 standard deviation is 0.3413,what is the probability of getting a z-score of +1 standard deviation or less?

Your professor told the class that,typically,20% of the class receives As,20% Bs,35% Cs,10% Ds,and 15% Fs.What is the probability that the student sitting next to you will receive an A or an F?