### 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).**