stats exam 2

it can be impractical or even impossible to study populations

One reason that researchers nearly always gather data from samples of participants instead of entire populations is because

the mean of the original population

According to the Central Limit Theorem, the mean of the sampling distribution of means –μₓ̄  – will equal...

3

If a test has a population mean of 70 and standard deviation of 6, then what is the z-score for a sample of n = 9 scores with a mean of 76?

normally distributed.

The central limit theorem says that when all possible samples of a sufficient size are taken from a population and their means are charted, that distribution of means will be...

the sampling distribution of means.

The distribution of all possible samples of a given size (e.g., n = 54 or n = 117) are taken from a population and their means are charted, that distribution is known as..

be normal.

If a distribution of raw scores has a strong negative skew, then, given a sufficiently large n, the sampling distribution of means for that distribution will...

the standard deviation of the sampling distribution

The standard error is...

the sampling distribution of means

The distribution of all possible sample means (of a given size) is called...

1

If a distribution has a mean of 100 and a standard deviation of 15, then what is the standard error for a sample of 225 scores?

-2

If a distribution has a mean of 30 and a standard deviation of 3, then what is the z-score for a sample of 4 scores with a mean of 27?

Normal

The Central Limit Theorem states that the shape of a sampling distribution becomes closer to what shape as the number of sample means in the distribution increases?

1.5

If the population mean for a distribution is 150 and the standard deviation is 20, then what is the z-score for a sample of 100 people with an average score of 153?

the standard deviation of the original distribution.

If a person were to create a sampling distribution for sample standard deviations, then the mean of that distribution would be equal to...

σ/√n

The equation for the standard error of a sampling distribution is...

3

If a population has a mean of 40 and a standard deviation of 8, what would the z-score be for a sample of 16 people with a mean of 46?

  any sample statistic

A sampling distribution can be calculated for...

4

What is the standard error of a distribution if o= 20 and n = 25?

-1

If a population has a mean of 60 and a standard deviation of 15, what is the z-score for a sample of 9 people with an average of 55?

σxˉ

What is the symbol for the standard error?

Normal

As the size of samples (n) in a sampling distribution increases, the shape of that distribution becomes more...

The mean of the sampling distribution of mean

What does the symbol μₓ̄ refer to

+3

What is the z-score for a sample with n = 100 and M = 103 if the population parameters are =100 and =10?

20

What is the standard error for a distribution with = 40 when n = 4?

Mean

If a distribution of raw scores has a strong positive skew, then, given a sufficiently large n, the mean of the sampling distribution will be equal to the _____ of the raw score distribution.

it is easier to gather data from samples than populations.

One reason that researchers nearly always gather data from samples of participants instead of populations is because..

unimodal

According to the Central Limit Theorem, if a research takes sufficiently large samples (e.g., n > 30) from a bimodal distribution, then the resulting sampling distribution will be..

the sampling distribution of variances.

The distribution of all possible sample variances (of a given sample size) is called...

mesokurtic.

The distribution of all possible sample variances – if n is sufficiently large (e.g., n > 30) – will be...

The population standard deviation and the sample size

The standard error of a sampling distribution is a function of two things:

narrower

As the size of samples in a sampling distribution increases (i.e., as n get bigger), then that distribution becomes...

A population parameter

When we talk about “estimation” in statistics, what is it that is being estimated?

The confidence interval gives two numbers instead of one

What is one important difference between a point estimate and a confidence interval?

It does not change

How is a point estimate affected when the sample size increases?

(51.08, 58.92)

Imagine a sample with n = 25 and a mean of 55 that comes from a population with a standard deviation of 10. Based on these data, what would be the 95% confidence interval for the population mean? (Use z-scores of ±1.96 for the 95% confidence level.)

Sample B

Imagine that two samples – Sample A with n = 20 and Sample B with n = 200 – are drawn from the same population and confidence intervals are computed for the same variables, which sample will have the narrower confidence interval?

point estimate.

If you can use only one number to estimate a population parameter, then the best value is a...

It becomes narrower

How is a confidence interval affected when the sample size increases?

Sample B

Imagine two samples that are drawn from the same population and measure the same variables in the same way. Sample A has a larger confidence interval than Sample B does. Which sample likely has the larger n?

become wider.

When the range of confidence for a confidence interval becomes higher – from 80% to 99%, for example – then the confidence interval will

(118.44, 123.56)

Imagine a sample with n = 64 and a mean of 121 that comes from a population with a standard deviation of 16. Based on these data, what would be the 80% confidence interval for the population mean? (Use z-scores of ±1.28 for the 80% confidence level.)

80

What is the point estimate for the population mean if the population standard deviation is 10, the sample size is 100, and the sample mean is 80?

Any population parameter

For which measures is it possible to compute a confidence interval?

become wider.

As the standard deviation for a distribution increases, then the corresponding confidence interval will...

stay the same

As the mean for a sample becomes greater, the width of the corresponding confidence interval will...

(173.13, 192.87)

Imagine a sample with n = 49 and a mean of 183 that comes from a population with a standard deviation of 21. Based on these data, what would be the 99.9% confidence interval for the population mean? (Use z-scores of ±3.29 for the 99.9% confidence level.)

(66.36, 69.64)

Imagine a sample with n = 400 and a mean of 68 that comes from a population with a standard deviation of 20. Based on these data, what would be the 90% confidence interval for the population mean? (Use z-scores of ±1.64 for the 90% confidence level.)

point estimate

A confidence interval specifies a range of values for a parameter estimate, whereas a(n) _____ specifies just a single value for that parameter.

A point estimate

Which is generally more precise (in the statistical sense): a point estimate or a confidence interval?

A confidence interval

Which is generally more accurate (in the statistical sense): a point estimate or a confidence interval?

The sample mean

A point estimate for the population mean is based on..

inferential statistics.

"Estimation" refers to a class of...

It does not change

How is the point estimate affected when the sample standard deviation increases?

Sample B

Imagine that samples – Sample A with n = 20 and Sample B with n = 200 – are drawn from the same population and confidence intervals are computed for the same variables, which sample will likely have the more precise confidence interval?

It becomes narrower

How is a confidence interval affected when the sample standard deviation decreases?

become narrower.

When the range of confidence for a confidence interval becomes lower - from 90% to 80%, for example - then the confidence interval will...

110

What is the point estimate for the population mean if the population standard deviation is 24, the sample size is 36, and the sample mean is 110?

stay the same

As the mean for a distribution increases, then the width of the corresponding confidence interval will...

(56.71, 63.29)

Imagine a sample with n = 49 and a mean of 60 that comes from a population with a standard deviation of 7. Based on these data, what would be the 99.9% confidence interval for the population mean? (Use z-score of 3.29 for the 99.9% confidence level.)

a descriptive statistic; an inferential statistic

The sample mean is ________ and a confidence interval for the mean is _______.

A point estimate

Which is more precise (in the statistical sense): a point estimate or a confidence interval?

the researcher knows the population mean and variance/standard deviation

The z-test is appropriate when...

the null hypothesis of no difference between the group and the population.

If a researcher wants to test whether an experimental group is different from the general population, the she would test...

is not rejected (i.e., retained).

In a two-tailed or non-directional test, if the critical value has a greater absolute value than the observed (or test) value does, the the null hypothesis...

the sample size is irrelevant.

When calculating an effect size for the z-test...

The alpha value was greater than the p-value

What does it mean when the result of a z-test is called "statistically significant"?

the sample data lead us to reject a null hypothesis that is true.

A Type I error occurs when..

the sample data lead us to retain (i.e., fail to reject) a null hypothesis that is false.

A Type II error occurs when...

.05

When choosing a level of alpha for a hypothesis test, unless you have a compelling reason to do otherwise, you should use.

 retain (i.e., fail to reject) the null hypothesis.

If a researcher is using an alpha of .05 for a z-test and gets an observed (or test) p-value of .23, then the researcher should...

 retain (i.e., fail to reject) the null hypothesis.

If a researcher is using an critical value of ±1.96 for a z-test and gets an observed (or test) z of -1.73, then the researcher should...

local residents average > national average

Imagine that a researcher is interested in whether residents in his local area have higher levels of well-being than the national average. What would be an appropriate alternate hypothesis for a one-tailed or directional z-test for this test?

Sample A

Imagine two studies that are identical in every respect except the size of their samples. Sample A has an effect size of d = .20 and a p-value of .03. Sample B has an effect size of d = .20 and a p-value of .005. Which sample likely had the smaller sample size?

Sample A

Imagine two studies that are identical in every respect except their effect sizes. Sample A has a sample size of n = 80 and a p-value of .01. Sample B has a sample size of n = 80 and a p-value of .10. Which sample likely had the larger effect size?

a Type I error has occurred.

When the mean of the population that a sample comes from does not differ from the general population but the sample mean is nonetheless significantly different from the general population, then...

the sample mean is two standard deviations below the population mean.

If a researcher is comparing a sample mean to a population mean and gets Cohen’s d = -2.0, this means that...

the results are unlikely to occur by chance if the null hypothesis is true.

If a researcher is using alpha = .05 and gets a p-value for the z-test of p = .02, then...

None of the other choices is correct.

If a research conducts a z-test and does not reject the null hypothesis, then...

know the population standard deviation.

A researcher who wants to use a z-test to compare a sample mean to a population mean must first...

the proportion of the distribution in the regions of rejection

If you draw a picture of the null distribution with the critical values and regions of rejection marked, then the alpha level is represented by...

Increasing n

If a researcher believes that the null hypothesis is false and wants to have the greatest chance of rejecting it with their study, then which of the following would make it more likely that the null hypothesis would be rejected?

whether their means are different.

If a researcher used a one-sample z-test to determine whether an experimental group was different from a general population, what she would actually be testing is...

it is most common to use Cohen's d.

When calculating an effect size for the z-test...

a false positive

A Type I error is also called...

.01

Which level of alpha for a hypothesis test has the lowest risk of a Type I error?

retain (i.e., fail to reject) the null hypothesis.

If a researcher is using an critical  value of 1.96 for a z-test and gets an observed z (i.e., test value) of +0.55 for a sample of n = 40, then the researcher should...

Sample A

Imagine two studies that are identical in every respect except the size of their samples. Sample A has an effect size of d = .40 and p-value of .001. Sample B also has an effect size of d = .40 but a p-value of .10. Which sample likely had the larger sample size?

a Type I error has occurred.

If a person's blood sample tests positive for a disease when, in fact, the person does nothave the disease, then...

the researcher should conclude that the results are unlikely to occur by chance if the null hypothesis is true.

If a researcher is using alpha = .01 and gets a p-value for the z-test of p = .005, then...

know the population standard deviation.

In order to compute a one-sample z-test you must...

Getting as large a sample as possible

If a sample's mean really is different from the comparison population's mean, then what is the easiest way to make sure that the null hypothesis would be rejected?