### Null Hypothesis, Population Mean, Z-Test, Statistic Final Exam

The key terms in these Statistic chapters include Hypothesis Test, Statistical Method, Distribution, Population Mean, Null Hypothesis, Sample Mean, Z-Score, Reject The Null Hypothesis, Z-Test, Standard Error, Two-Tailed T Test, Normal Distribution, – Statistic Final Exam

Which of the following accurately describes a hypothesis test statistical method?

An inferential statistical method that uses the data from a sample to draw inferences about a population

What is measured by the numerator of the z-score test statistic?

The actual distance between a sample mean M and a population mean µ.

What is measured by the denominator of the z-score test statistic?

The average distance between a sample mean M and the population mean µ that would be expected if H0 was true.

The statement of the null hypothesis refers to which of the following?

##### The population after treatment.

Which of the following accurately describes outcomes in the critical region of the distribution of sample means for z-test?

Sample means with a very low probability if the null hypothesis is true.

If a hypothesis test produces a z-score in the critical region, what decision should be made?

Reject the null hypothesis.

A sample of n = 25 individuals is selected from a population with µ = 80, and a treatment is administered to the sample. What is expected if the treatment has no effect?

The sample mean should be close 80 and should lead you to fail to reject the null hypothesis.

Which of the following accurately describes a hypothesis test statistical method?

An inferential statistical method that uses the data from a sample to draw inferences about a population

What is measured by the numerator of the z-score test statistic?

The actual distance between a sample mean M and a population mean µ.

Which of the following accurately describes outcomes in the critical region of the distribution of sample means for z-test?

##### Sample means with a very low probability if the null hypothesis is true.

What is measured by the denominator of the z-score test statistic?

The average distance between a sample mean M and the population mean µ that would be expected if H0 was true.

How the critical region is related to the alpha level and the decision regarding the null hypothesis.

The value of alpha level equals size of the critical region and defines a precise probability for the term “very unlikely”. If the sample after treatment falls in the critical region (i.e., z-test score falls in the critical region) than one should reject the null hypothesis.

Which of the following is the correct style of reporting the results of a hypothesis test with a t-test for a single sample and a measure of effect size using a t statistic, according to APA style

#### t(19) = 2.30, p < .05, r2 = 0.42,

The null hypothesis for z-test ________

States that the treatment has no effect (or the difference is not significant).

Rejecting the null hypothesis means that the outcome observed in the sample is very unlikely to have occurred if the statement of H0 is correct.

True

A researcher administers a treatment to a sample of participants selected from a population with µ = 50. If the researcher obtains a sample mean of M = 55, which combination of factors is most likely to result in rejecting the null hypothesis?

σ = 5 and α = .05

What is the relationship between the alpha level and the size of the critical region?

As the alpha level increases, the size of the critical region increases.

If a hypothesis test produces a z-score in the critical region, what decision should be made?

Reject the null hypothesis.

A two-tailed hypothesis test is being used to evaluate a treatment effect with α = .05. If the sample data produce a z-score of z = – 2.24, what is the correct decision?

Reject the null hypothesis and conclude that the treatment has an effect

A researcher administers a treatment to a sample of participants selected from a population with µ = 50. If the researcher obtains a sample mean of M = 55, which combination of factors is most likely to result in rejecting the null hypothesis?

#### σ = 5 and α = .05

Which of the following is a fundamental difference between the t statistic and a z-score?

The t statistic uses the sample variance in place of the population variance

On average, what value is expected for the t statistic when the null hypothesis is true?

0

What is the sample variance and the estimated standard error for a sample of n = 9 scores with SS = 72?

s2 = 9 and sM = 1

How does the shape of the t distribution compare to the normal distribution?

It is flatter and more spread out than the normal distribution

Corey scores X = 70 on his first exam, for which the entire class scored a mean of µ = 78 and standard deviation of σ = 6. The instructor wants to standardize the distribution of exam scores to have µ = 100 and σ = 15. What will Corey’s grade on the exam be in the new distribution?

##### X = 80

If other factors are held constant, what is the effect of increasing the sample size?

It will decrease the estimated standard error and increase the likelihood of rejecting H0.

A researcher is conducting an experiment to evaluate the effectiveness of treatment for individuals in a population that is known to have a mean of μ = 25. The results will be examined using a two-tailed hypothesis test. Which of the following is the correct statement of the null hypothesis?

μ = 25 (i.e., the treatment has no effect on the population mean).

Which set of scores below has the smallest standard deviation? a. 5, 11, 42, 22 b. 27, 105, 10, 80 c. 145, 143, 145, 147 d. 11, 17, 31, 53

b. 145, 143, 145, 147

A sample of n = 9 individuals is selected from a population with μ = 60 and σ = 6, and a treatment is administered to the sample. After treatment, the sample mean is M = 64. What is the size of the treatment effect evaluated by Cohen’s d for this sample?

#### d = 0.67

The null hypothesis makes a statement about

The population after treatment

The null hypothesis for z-test ________

States that the treatment has no effect (or the difference is not significant).

In hypothesis testing with the z-test, standard error measures

The amount of difference between a sample mean M and the actual population mean that could occur by chance.

The concept of critical region in hypothesis testing

The critical region consists of sample means that are very unlikely to occur if the statement about the population in the null hypothesis is true.

If a hypothesis test produces a z-score in the critical region, what decision should be made?

Reject the null hypothesis.

How the critical region is related to the alpha level and the decision regarding the null hypothesis.

The value of alpha level equals size of the critical region and defines a precise probability for the term “very unlikely”. If the sample after treatment falls in the critical region (i.e., z-test score falls in the critical region) than one should reject the null hypothesis.

A researcher selects a sample from a population with a mean of μ = 40 and administers a treatment to the individuals in the sample. Which of the following is the correct statement of the null hypothesis for a two-tailed t-test for a single sample?

#### μ = 40

Which of the following is a fundamental difference between the t statistic and a z-score?

The t statistic uses the sample variance in place of the population variance

On average, what value is expected for the t statistic when the null hypothesis is true?

#### 0

What is the sample variance and the estimated standard error for a sample of n = 9 scores with SS = 72?

s2 = 9 and sM = 1

How does the shape of the t distribution compare to the normal distribution?

It is flatter and more spread out than the normal distribution

If other factors are held constant, what is the effect of increasing the sample size?

It will decrease the estimated standard error and increase the likelihood of rejecting H0.

If other factors are held constant, what is the effect of increasing the sample variance?

It will increase the estimated standard error and decrease the likelihood of rejecting H0.

What value is estimated with a confidence interval using the t statistic?

The value for an unknown population mean

Which of the following is the correct style of reporting the results of a hypothesis test with a t-test for a single sample and a measure of effect size using a t statistic, according to APA style

t(19) = 2.30, p < .05, r2 = 0.42,

A researcher selects a sample from a population with a mean of μ = 40 and administers a treatment to the individuals in the sample. Which of the following is the correct statement of the null hypothesis for a two-tailed t-test for a single sample?

#### μ = 40

Which of the following accurately describes outcomes in the critical region of the distribution of sample means for z-test?

Sample means with a very low probability if the null hypothesis is true.

What are the values for SS and variance for the following sample of n = 4 scores? Scores: 1, 3, 0, 4

SS = 10 and variance = 3.33

Which set of scores below has the smallest standard deviation? a. 5, 11, 42, 22 b. 27, 105, 10, 80 c. 145, 143, 145, 147 d. 11, 17, 31, 53

b. 145, 143, 145, 147

The sum of the squared deviation scores is SS = 20 for a sample of n = 6 scores. What is the variance for this sample?

s2 = 4

Consider a population that has a score of X = 15 associated with a z-score of +1.50. What does this z-score indicate about the location of X = 15?

A score of X = 15 is 1.5 standard deviations above the mean.

Corey scores X = 70 on his first exam, for which the entire class scored a mean of µ = 78 and standard deviation of σ = 6. The instructor wants to standardize the distribution of exam scores to have µ = 100 and σ = 15. What will Corey’s grade on the exam be in the new distribution?

##### X = 80

A score that is 3 points lower than the sample mean has a z-score of z = -0.25, and a score of X = 44 has a z-score of -0.75. What is the sample mean?

M = 53

Which position in a distribution corresponds to a z-score of z = -1.00?

Below the mean by 1 standard deviation

Tom scores an X = 43 on an exam with a mean of µ = 52. Tom’s score is associated with a z-score of -1.80. What is the value for the exam standard deviation?

#### σ = 5

A researcher administers a treatment to a sample of participants selected from a population with µ = 50. If the researcher obtains a sample mean of M = 55, which combination of factors is most likely to result in rejecting the null hypothesis?

#### σ = 5 and α = .05

Corey scores X = 70 on his first exam, for which the entire class scored a mean of µ = 78 and standard deviation of σ = 6. The instructor wants to standardize the distribution of exam scores to have µ = 100 and σ = 15. What will Corey’s grade on the exam be in the new distribution?

X = 80

A researcher selects a sample from a population with a mean of μ = 40 and administers a treatment to the individuals in the sample. Which of the following is the correct statement of the null hypothesis for a two-tailed t-test for a single sample?

#### μ = 40

Which set of scores below has the smallest standard deviation? a. 5, 11, 42, 22 b. 27, 105, 10, 80 c. 145, 143, 145, 147 d. 11, 17, 31, 53

b. 145, 143, 145, 147

How the critical region is related to the alpha level and the decision regarding the null hypothesis.

The value of alpha level equals size of the critical region and defines a precise probability for the term “very unlikely”. If the sample after treatment falls in the critical region (i.e., z-test score falls in the critical region) than one should reject the null hypothesis.

Which of the following is the correct style of reporting the results of a hypothesis test with a t-test for a single sample and a measure of effect size using a t statistic, according to APA style

t(19) = 2.30, p < .05, r2 = 0.42,

The null hypothesis for z-test ________

States that the treatment has no effect (or the difference is not significant).

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