Question 1

Given that on one section of the SAT the mean is 500 and the standard deviation is 100,what is the approximate probability of selecting a student whose score is 400 or lower followed by selecting a student whose score is 500 or higher on the test?

Accepted Answer

The answer of Given that on one section of the...

Question 2

H₀ is to H_a as _____ hypothesis is to _____ hypothesis.

Accepted Answer

H₀ represents the null hypothesis, while H_a represents the alternative hypothesis in hypothesis testing.

Question 3

Given that on one section of the SAT the mean is 500 and the standard deviation is 100,what is the approximate probability of a student scoring 700 or higher on the test?

Accepted Answer

Since we want to find the probability of a student scoring 700 or higher, we need to find the z-score associated with this score.

z = (x - μ) / σ

z = (700 - 500) / 100

z = 2

Using a z-table or calculator, we can find that the probability of a z-score of 2 or higher is approximately 0.0228. This means that the probability of a student scoring 700 or higher is approximately 0.0228 or 2.28%.

Therefore, the best choice is B) 0.02.

Question 4

Given that on one section of the SAT the mean is 500 and the standard deviation is 100,what is the approximate probability of a student scoring 300 or lower or 700 or higher on the test?

Accepted Answer

To solve this, we need to find the z-scores for both 300 and 700.

Z-score for 300: 
z = (300-500)/100 = -2

Z-score for 700: 
z = (700-500)/100 = 2

Now, we need to find the area to the left of -2 and the area to the right of 2 on a standard normal distribution table (or using a calculator).

The area to the left of -2 is approximately 0.0228, and the area to the right of 2 is also approximately 0.0228.

Therefore, the approximate probability of scoring 300 or lower or 700 or higher is the sum of these two probabilities:

P(Z ≤ -2) + P(Z ≥ 2) = 0.0228 + 0.0228 = 0.0456

Rounded to the nearest thousandth, the answer is 0.045, which corresponds to choice C.

Question 5

Directional hypothesis is to non-directional hypothesis as _____ hypothesis is to _____ hypothesis.

Accepted Answer

A directional hypothesis only predicts the direction of the effect while a non-directional hypothesis predicts the presence or absence of an effect. Similarly, a one-tailed hypothesis predicts the direction of the effect while a two-tailed hypothesis predicts the presence or absence of an effect.

Question 6

When using a _____ hypothesis the researcher predicts the direction of the expected difference between the groups.

Accepted Answer

In a one-tailed hypothesis, the researcher predicts the direction of the expected difference between the groups. For example, if the hypothesis is that Group A will perform better than Group B, this would be a one-tailed hypothesis. The other options (A, B, and D) do not involve predicting the direction of the expected difference between the groups.

Question 7

In a study of the effects of exercise on stress,researchers predict simply that there will be a difference in stress level between the exercise and no exercise groups.The researchers are using a _____ hypothesis.

Accepted Answer

A two-tailed hypothesis predicts that there will be a difference between groups but does not specify the direction of the difference.

Question 8

One- and two-tailed hypotheses are both types of _____ hypotheses.

Accepted Answer

One- and two-tailed hypotheses are types of alternative hypotheses, which specify the nature of the effect or relationship being tested.

Question 9

Given that on one section of the SAT the mean is 500 and the standard deviation is 100,what is the approximate probability of selecting a student whose score is 400 or lower followed by selecting a student whose score is 600 or higher on the test?

Accepted Answer

To solve this problem, we will use the standard normal distribution, which has a mean of 0 and a standard deviation of 1. First, we need to standardize the two scores we are interested in:

For a score of 400 or lower: Z = (400 - 500) / 100 = -1

For a score of 600 or higher: Z = (600 - 500) / 100 = 1

We can use a standard normal distribution table or a calculator to find the probabilities associated with these two Z-scores. For a Z-score of -1, the probability of getting a score of 400 or lower is about 0.16. For a Z-score of 1, the probability of getting a score of 600 or higher is also about 0.16.

To find the probability of both events happening, we need to multiply their probabilities together:

P(400 or lower AND 600 or higher) = P(400 or lower) x P(600 or higher)

P(400 or lower AND 600 or higher) = 0.16 x 0.16

P(400 or lower AND 600 or higher) = 0.0256

Therefore, the approximate probability of selecting a student whose score is 400 or lower followed by selecting a student whose score is 600 or higher on the test is 0.0256, which is closest to choice C (0.025).

Question 10

Given that on one section of the SAT the mean is 500 and the standard deviation is 100,what is the approximate probability of selecting a student whose score is 300 or lower followed by selecting a student whose score is 700 or higher on the test?

Accepted Answer

The probability of selecting a student whose score is 300 or lower is approximately 0.0005. The probability of selecting a student whose score is 700 or higher is approximately 0.0005. The probability of selecting a student whose score is 300 or lower followed by selecting a student whose score is 700 or higher is approximately 0.0005 * 0.0005 = 0.00000025.

Question 11

No effect is to _____ hypothesis as effect is to _____ hypothesis.

Accepted Answer

The null hypothesis typically states that there is no effect or no difference, while the alternative hypothesis states that there is an effect or a difference.

Question 12

Given that on one section of the SAT the mean is 500 and the standard deviation is 100,what is the approximate probability of a student scoring 300 or higher on the test?

Accepted Answer

The score of 300 is 2 standard deviations below the mean (500 - 2*100 = 300). Using the empirical rule, approximately 95% of data falls within 2 standard deviations of the mean, so about 2.5% is below 300. Therefore, the probability of scoring 300 or higher is approximately 1 - 0.025 = 0.975, which is closest to 0.98.

Question 13

A liberal statistical test is one that

Accepted Answer

A liberal statistical test is one that minimizes type II errors but increases the likelihood of type I errors, meaning it is more likely to detect an effect when there is one, but also more likely to detect an effect when there is none.

Question 14

Given that on one section of the SAT the mean is 500 and the standard deviation is 100,what is the approximate probability of a student scoring 400 or lower or 500 or higher on the test?

Accepted Answer

The answer of Given that on one section of the...

Question 15

The hypothesis predicting that differences exist between the groups being compared is to the hypothesis predicting that no differences exist between the groups being compared as _____ hypothesis is to _____ hypothesis.

Accepted Answer

The alternative hypothesis predicts that differences exist between groups, while the null hypothesis predicts that no differences exist.

Question 16

Given that on one section of the SAT the mean is 500 and the standard deviation is 100,what is the approximate probability of a student scoring 400 or lower or 700 or higher on the test?

Accepted Answer

The score of 400 is 1 standard deviation below the mean, and the score of 700 is 2 standard deviations above the mean. Using the empirical rule (68-95-99.7 rule), approximately 16% of students score below 400, and about 2.5% score above 700. Adding these probabilities gives approximately 18%.

Question 17

When using a _____ hypothesis the researcher predicts that the groups being compared will differ,but does not predict how they will differ.

Accepted Answer

A two-tailed hypothesis predicts that the groups being compared will differ, but does not specify the direction in which they will differ. This is in contrast to a directional hypothesis (B) which predicts the direction of the difference, and a one-tailed hypothesis (C) which also predicts the direction of the difference but only in one direction. A null hypothesis (A) predicts that there will be no difference between the groups being compared.

Question 18

Inferential statistics allow us to

Accepted Answer

Inferential statistics allow us to make conclusions about the population based on the sample data. This involves using probability theory to estimate population parameters from sample statistics. In other words, we use information from a sample to infer something about the larger population.

Question 19

In a study on the effects of amount of sleep on driving performance,researchers predict that those in the group that is allowed more sleep will exhibit better driving performance.The researchers are using a _____ hypothesis.

Accepted Answer

The answer of In a study on the effects of...

Question 20

_____ statistics are used in the process of hypothesis testing.

Accepted Answer

Inferential statistics are used in the process of hypothesis testing. This involves using a sample to make inferences about a population and testing whether any differences observed in the sample are statistically significant or due to chance. Descriptive statistics summarize and describe the characteristics of a sample or population, while null and alternative hypotheses are statements about the population that are tested using inferential statistics.

Quiz 7: Probability and Hypothesis Testing

Given that on one section of the SAT the mean is 500 and the standard deviation is 100,what is the approximate probability of selecting a student whose score is 400 or lower followed by selecting a student whose score is 500 or higher on the test?

H₀ is to H_a as _ hypothesis is to _ hypothesis.

Given that on one section of the SAT the mean is 500 and the standard deviation is 100,what is the approximate probability of a student scoring 700 or higher on the test?

Given that on one section of the SAT the mean is 500 and the standard deviation is 100,what is the approximate probability of a student scoring 300 or lower or 700 or higher on the test?

Directional hypothesis is to non-directional hypothesis as _ hypothesis is to _ hypothesis.

When using a _____ hypothesis the researcher predicts the direction of the expected difference between the groups.

In a study of the effects of exercise on stress,researchers predict simply that there will be a difference in stress level between the exercise and no exercise groups.The researchers are using a _____ hypothesis.

One- and two-tailed hypotheses are both types of _____ hypotheses.

Given that on one section of the SAT the mean is 500 and the standard deviation is 100,what is the approximate probability of selecting a student whose score is 400 or lower followed by selecting a student whose score is 600 or higher on the test?

Given that on one section of the SAT the mean is 500 and the standard deviation is 100,what is the approximate probability of selecting a student whose score is 300 or lower followed by selecting a student whose score is 700 or higher on the test?

No effect is to _ hypothesis as effect is to _ hypothesis.

Given that on one section of the SAT the mean is 500 and the standard deviation is 100,what is the approximate probability of a student scoring 300 or higher on the test?

A liberal statistical test is one that

Given that on one section of the SAT the mean is 500 and the standard deviation is 100,what is the approximate probability of a student scoring 400 or lower or 500 or higher on the test?

The hypothesis predicting that differences exist between the groups being compared is to the hypothesis predicting that no differences exist between the groups being compared as _ hypothesis is to _ hypothesis.

Given that on one section of the SAT the mean is 500 and the standard deviation is 100,what is the approximate probability of a student scoring 400 or lower or 700 or higher on the test?

When using a _____ hypothesis the researcher predicts that the groups being compared will differ,but does not predict how they will differ.

Inferential statistics allow us to

In a study on the effects of amount of sleep on driving performance,researchers predict that those in the group that is allowed more sleep will exhibit better driving performance.The researchers are using a _____ hypothesis.

_____ statistics are used in the process of hypothesis testing.

Quiz 7: Probability and Hypothesis Testing

Given that on one section of the SAT the mean is 500 and the standard deviation is 100,what is the approximate probability of selecting a student whose score is 400 or lower followed by selecting a student whose score is 500 or higher on the test?

H0 is to Ha as _____ hypothesis is to _____ hypothesis.

Given that on one section of the SAT the mean is 500 and the standard deviation is 100,what is the approximate probability of a student scoring 700 or higher on the test?

Given that on one section of the SAT the mean is 500 and the standard deviation is 100,what is the approximate probability of a student scoring 300 or lower or 700 or higher on the test?

Directional hypothesis is to non-directional hypothesis as _____ hypothesis is to _____ hypothesis.

When using a _____ hypothesis the researcher predicts the direction of the expected difference between the groups.

In a study of the effects of exercise on stress,researchers predict simply that there will be a difference in stress level between the exercise and no exercise groups.The researchers are using a _____ hypothesis.

One- and two-tailed hypotheses are both types of _____ hypotheses.

Given that on one section of the SAT the mean is 500 and the standard deviation is 100,what is the approximate probability of selecting a student whose score is 400 or lower followed by selecting a student whose score is 600 or higher on the test?

Given that on one section of the SAT the mean is 500 and the standard deviation is 100,what is the approximate probability of selecting a student whose score is 300 or lower followed by selecting a student whose score is 700 or higher on the test?

No effect is to _____ hypothesis as effect is to _____ hypothesis.

Given that on one section of the SAT the mean is 500 and the standard deviation is 100,what is the approximate probability of a student scoring 300 or higher on the test?

A liberal statistical test is one that

Given that on one section of the SAT the mean is 500 and the standard deviation is 100,what is the approximate probability of a student scoring 400 or lower or 500 or higher on the test?

The hypothesis predicting that differences exist between the groups being compared is to the hypothesis predicting that no differences exist between the groups being compared as _____ hypothesis is to _____ hypothesis.

Given that on one section of the SAT the mean is 500 and the standard deviation is 100,what is the approximate probability of a student scoring 400 or lower or 700 or higher on the test?

When using a _____ hypothesis the researcher predicts that the groups being compared will differ,but does not predict how they will differ.

Inferential statistics allow us to

In a study on the effects of amount of sleep on driving performance,researchers predict that those in the group that is allowed more sleep will exhibit better driving performance.The researchers are using a _____ hypothesis.

_____ statistics are used in the process of hypothesis testing.

H₀ is to H_a as _ hypothesis is to _ hypothesis.

Directional hypothesis is to non-directional hypothesis as _ hypothesis is to _ hypothesis.

No effect is to _ hypothesis as effect is to _ hypothesis.

The hypothesis predicting that differences exist between the groups being compared is to the hypothesis predicting that no differences exist between the groups being compared as _ hypothesis is to _ hypothesis.