Public Health Statistics Chapter 8

The sampling distribution of the sample mean used in the single-sample z test is assumed to be ____

A) Normal

B) Exponential

C) Skewed

D) Uniform

A) Normal

The ____ is an assumption of the single-sample z test.

A) Population mean is unknown

B) Dependent variable is categorical

C) Population standard deviation is unknown

D) Sample is selected randomly

D) Sample is selected randomly

The purpose of a single-sample z test is to ____

A) Assess frequencies in categorical data

B) Determine whether a sample mean differs significantly from a known population mean

C) Evaluate the relationship between two continuous variables

D) Compare the means of two related samples

B) Determine whether a sample mean differs significantly from a known population mean

In a single-sample z test, when the sample size increases, the standard error of the mean (SEM) ____

A) Becomes zero

B) Stays the same

C) Decreases

D) Increases

C) Decreases

Under which condition is a single-sample z test appropriate?

A) You are comparing two independent sample means

B) The population mean and standard deviation are known

C) The population follows a non-normal distribution

D) The population standard deviation is unknown

B) The population mean and standard deviation are known

True or False: If the sample mean equals the population mean, the z score will be zero

True

The purpose of conducting a single-sample z test is to ____

A) Compare two independent sample means

B) Measure the correlation between two variables

C) Determine if a sample mean differs significantly from a known population mean

D) Analyze categorical data

C) Determine if a sample mean differs significantly from a known population mean

When conducting a single-sample z test, which value is compared to the z score to determine significance?

A) Population mean

B) p-value

C) Critical z value

D) Alpha level

C) Critical z value

In a single-sample z test, the z score represent the ____

A) Number of standard errors the sample mean is from the population mean

B) Proportion of the population outside the sample range

C) Percentage of variance explained

D) Probability of the sample mean

A) Number of standard errors the sample mean is from the population mean

A higher absolute z score in a single sample z test indicates ____

A) Greater evidence against the null hypothesis

B) A lower population mean

C) Less evidence against the null hypothesis

D) A smaller sample size

A) Greater evidence against the null hypothesis

True or False: SPSS reports the p-value for a single-sample t test as “Sig. (2-tailed)” by default

True

True or False: SPSS requires raw data (not summary statistics) to run a single-sample t test

True

Which SPSS output table reports the results of the single-sample t test, including the t value and p-value?

A) One-Sample Test

B) Descriptive Statistics

C) Case Summary

D) Frequencies Table

A) One-Sample Test

Where can you find the sample mean and standard deviation in SPSS output for a single-sample t test?

A) Variable View

B) One-Sample Statistics table

C) Data View

D) One-Sample Test table

B) One-Sample Statistics table

In SPSS, which menu allows you to conduct a single-sample t test?

A) Graphs

B) Data

C) Analyze

D) Transform

C) Analyze

True or False: Larger sample sizes can lead to statistically significant results even when Cohen’s d indicates a small effect

True

What is the typical interpretation of a Cohen’s d value of 0.8?

A) Small effect size

B) Large effect size

C) Medium effect size

D) No effect

B) Large effect size

What does Cohen’s d measure?

A) Variance

B) Effect size

C) Sampling error

D) Statistical significance

B) Effect size

Which two pieces of information are necessary to calculate Cohen’s d?

A) Difference between the sample mean and population mean, and the standard deviation

B) Standard errors and critical z value

C) p-value and alpha level

D) Sample size and p-value

A) Difference between the sample mean and population mean, and the standard deviation

According to Cohen’s guidelines, what d value represents a small effect?

A) 0.2

B) 0.8

C) 1.0

D) 0.5

A) 0.2

A researcher wants to test if the average test score of students differs from a national average of 80. The population standard deviation is known to be 10, and the sample size is 50. Which test is most appropriate?

A) Paired-samples t test

B) Independent t test

C) Single-sample t test

D) Single-sample z test

D) Single-sample z test

A single-sample z test inappropriate when the ____

A) Population follows a normal distribution

B) Sample size is greater than 30

C) Population standard deviation is unknown

D) Researcher is testing a single group’s mean against a known value

C) Population standard deviation is unknown

A sample of 25 students has a mean score of 75, and the population mean is 70 with a population standard deviation of 5. What is the obtained z value?

1

If the observed z-value from a single-sample z test is 2.5 and the critical z value at a = 0.05 (two-tailed) is 1.96, what should the researcher conclude?

A) Reject the null hypothesis

B) Fail to reject the null hypothesis

C) The test is inconclusive

D) Accept the null hypothesis

A) Reject the null hypothesis

A single-sample t test should be used instead of a z test when the ___

A) Population standard deviation is unknown

B) Researcher is comparing two groups

C) Population standard deviation is known

D) Sample size is large

A) Population standard deviation is unknown

A study reports an effect size of d = 0.8. How should this be interpreted?

A) An insignificant effect size

B) A small effect size

C) A medium effect size

D) A large effect size

D) A large effect size

With a sample mean of 10 and a sample standard deviation of 2, and a population mean of 9.50, what is Cohen’s d?

0.25

Which is true about the z distribution?

A) It is the normal distribution

B) It usually produces large effect sizes

C) It is used when there are three or more means to compare simultaneously

D) It varies depending on the sample size

A) It is the normal distribution

Which is true about the t distribution?

A) It varies depending on sample size

B) It is used when there are three or more means to compare simultaneously

C) It is the normal distribution

D) It usually produces large effect sizes

A) It varies depending on sample size

How many sample means are used in a z test?

1

Compare the advantages of using effect sizes (e.g., Cohen’s d) alongside p-values in reporting the results of a single-sample z test. Which statement is most accurate?

A) p-value reflect clinical importance

B) Effect size provide context on the magnitude of difference, whereas p-values indicate whether the results occurred by chance

C) Effect sizes are useful mainly when p-values are not significant

D) p-values and effect sizes provide the same information in different ways

B) Effect size provide context on the magnitude of difference, whereas p-values indicate whether the results occurred by chance

The z values most likely to be statistically significant are those closest to __

A) 1

B) 2

C) 3

D) 0

C) 3