STATISTICS CHAPTER 8

A group of 200 students takes the Kaplan course in hopes that it will improve their SAT scores above the national mean of 500 on the math section. The population standard deviation of the SAT is known to be 100. Use an alpha level of .05 when answering the following questions. What should be the critical value?

+1.645

The probability, given a true null hypothesis, of not making a Type I error--that is, of failing to reject a false null hypothesis--is defined by:

. 1 - á

As part of the process of hypothesis testing, the task of a researcher is to choose between _____.

. H0 and H1

Type II errors have a probability of occurring equal to _____.

. â

As a rough guide, investigators generally attempt to achieve statistical power (the probability of correctly rejecting the null hypothesis when it is false. in the range of _____ to _____.

.80-.95

Traditionally, _____ is the probability associated with alpha.

0.05

Which of the following symbols represents the power of a statistical test?

1-b

A researcher in sports psychology is interested in the resting pulse rate of long-distance college runners. She does some research and finds data from the U.S. Olympics team showing their long-distance runners have a resting pulse rate of 60 beats per minute. She wants to know if the pulse rate for college runners is different from the Olympic team's m of 60. She randomly samples 20 long-distance runners, and finds What is the estimated standard error of the mean?

1.28

A probability value that defines a region associated with unexpected results is known as _____.

alpha

In hypothesis-testing, the size of the portion of the tails of the sampling distribution that fall outside your critical values (i.e., your "rejection regions") is determined by your _____.

alpha level

The _____ is a probability value determined by the experimenter to define the _____, which is the set of all scores more extreme than the critical values.

alpha level; rejection region

Rejection regions are determined with reference to a probability value known as a(n):

alpha levles

Which of the following statements is NOT true?

as b increases, power increases

The values that define the boundaries of the _____ are called the _____.

confidence interval, confidence limits

The alpha level directly affects the power of the statistical test, with more _____ alpha levels yielding _____ tests, everything else being equal.

conservative, less powerful

To avoid making a Type I error, we should use _____ level.

conservative, á

A 95% confidence interval for the mean:

defines the range of scores in which there is a .95 probability the population mean will fall . is computed using the standard error of the mean

In a one-sample z test, when you have evidence or reasoning to suggest that your sample mean will most likely differ from the hypothesized population value in one direction (for example, "it will be higher than the hypothesized value"), you would use a

directional ( one tailed ) test

An alternative hypothesis that specifies that a population mean is different from a given value and also indicates the direction of that difference is called a:

directional alternative hypothesis

The one-sample z test is used to determine whether the difference between your sample mean and the hypothesized population value is _____.

due to samling error

A t value is analogous to a z score except that it represents the number of _____ a sample mean is from ì.

estimated standard errors

When the observed value of z falls within the range defined by the critical values, we _____ the null hypothesis.

fail to reject

Type II errors are made when you _____ H0 and H0 is _____.

fail to reject; false

Which of the following accurately defines a Type II error?

failing to reject a H0 when it is false

When a researcher obtains a result that is consistent with the null hypothesis, he or she _____ the null hypothesis.

fails to reject

The statement "to fail to reject the null hypothesis" would be made when the observed value of z ______.

falls withiin the region bounded by the critical values

In general, a directional test will be _____ than a corresponding nondirectional test if the actual population mean and the hypothesized population mean differ in the specified direction.

more powerful

In principle, we can _____ accept the null hypothesis as being _____ via our statistical methods.

never, true

In hypothesis testing, which of the following is assumed to be true?

null hypothesis

Informally, the _____ hypothesis can be thought of as the hypothesis of _____

null, no difference

If the observed result of an investigation is so discrepant from the expected result that the difference cannot be attributed to chance, then the _____ hypothesis is _____.

null; rejected

Directional tests are often referred to as :

one tailed tests

The terms "statistically significant" and "statistically nonsignificant" are meant to apply:

only to the statistical outcome

The probability that an investigator will correctly reject the null hypothesis when it is false is called the _____ of the statistical test.

power

A researcher in sports psychology is interested in the resting pulse rate of long-distance college runners. She does some research and finds data from the U.S. Olympics team showing their long-distance runners have a resting pulse rate of 60 beats per minute. She wants to know if the pulse rate for college runners is different from the Olympic team's m of 60. She randomly samples 20 long-distance runners, and finds Based on the above calculations, what is your decision regarding the null hypothesis?

reject H0

Type I errors occur when we ______.

reject a hypothesis that is true

if you conducted an experiment and observed results that indicated a very large discrepancy between the observed and expected results, then you probably would ______.

reject the null hypothesis

If the observed and expected results of some experiment are not identical, then the null hypothesis (no differences) should be ______.

rejected only if the discrepancy cannot be attributed to chance

Which of the following accurately defines a Type I error?

rejecting a H0 when it is true

he set of all standard scores that are more extreme than the critical values (that is, less than the negative critical value or greater than the positive critical value. is called a(n) _____ region and constitutes a(n) _____ result.

rejection, unexpected

When we say that a test is _____ to violations of a distributional assumption, we mean that the frequency of Type I and Type II errors, and, thus, the accuracy of our conclusions, are relatively unaffected as compared to when the assumption is met.

robust

Which characteristics of the t distribution influences its shape?

sample size

The t-distribution should be used when _____, while the z-distribution should be used when _____.

sample sizes are small; m and s are known or sample sizes are large

The one-sample t-test is robust to violations against which of the following assumptions?

scores on the variables are normally distributed in the population

The _____ the sample size, the _____ the statistical test will be, everything else being equal.

smaller/larger, more/less powerful

The fourth step in the one sample z test is the conversion of the observed sample mean into a z value to determine how many _____ it is away from _____, assuming the null hypothesis is true.

standard errors, ì

Based on the Method of Presentation section of Chapter 8, suppose you obtained a statistically significant t value of 2.5 with 15 subjects using an alpha level of .05. How would this be reported in a psychological journal?

t (14) = 2.5, p < .05

Which of the following "t statements" is the proper way to present data in an manuscript using APA format?

t(29) = 3.93, p<.05.

A researcher performs a hypothesis test and rejects the null hypothesis. If, in reality, the null hypothesis should not have been rejected, then the researcher has made a

type 1 error

If a researcher rejects a null hypothesis that is true, then a _____ has been made.

type 1 error

Rejection of the null hypothesis when it is true is called a:

type 1 error

The probability of making a _____ error is traditionally called beta.

type 2

Failure to reject the null hypothesis when it is false is called a:

type 2 error

In a one-sample z-test, the term "statistically significant difference" tells you _____.

your sample mean differes form the hypothesized value by more than would be expected from sampling error alone

A group of 200 students takes the Kaplan course in hopes that it will improve their SAT scores above the national mean of 500 on the math section. The population standard deviation of the SAT is known to be 100. Use an alpha level of .05 when answering the following questions. The students who took the Kaplan course obtain a mean of 520 on the math SAT. Compute the one-sample z test statistic.

z = 2.83

The formula that we use to test the hypothesis that a simple mean was drawn from a population with µ=100 and ó=9 is _____.

z=(- ì)/ ó

The probability for Type I error is equal to _____.

á

The formula for determining the standard error of the population mean is _____.

ó/

For an alpha level of .05, an unexpected result in the one sample z test includes any sample mean occurring more than _____ standard errors below or more than _____ standard errors above the value of ì represented in the null hypothesis.

1.96

A researcher in sports psychology is interested in the resting pulse rate of long-distance college runners. She does some research and finds data from the U.S. Olympics team showing their long-distance runners have a resting pulse rate of 60 beats per minute. She wants to know if the pulse rate for college runners is different from the Olympic team's m of 60. She randomly samples 20 long-distance runners, and finds Using a nondirectional test with a = .05, what are your critical values?

2.093

A sampling distribution of means based on all possible random samples of N=25, drawn from a population having a µ of 25 and a ó of 4, will have a mean of _____ and standard deviation of _____.

25,8

A researcher in sports psychology is interested in the resting pulse rate of long-distance college runners. She does some research and finds data from the U.S. Olympics team showing their long-distance runners have a resting pulse rate of 60 beats per minute. She wants to know if the pulse rate for college runners is different from the Olympic team's m of 60. She randomly samples 20 long-distance runners, and finds What value is obtained when calculating the test statistic?

3.93

When _____, and the raw scores in the population are normally distributed, then the normal and t distributions are quite _____ one another.

N > 40; similar to

. A group of 200 students takes the Kaplan course in hopes that it will improve their SAT scores above the national mean of 500 on the math section. The population standard deviation of the SAT is known to be 100. Use an alpha level of .05 when answering the following questions. What conclusions can be made, based on this test statistic?

The Kaplan course helped the students score statistically significantly higher than the national mean.

In a computer printout of a one-sample t test, what does a p value of 0.000 indicate?

The actual p value is .0005 or less.

If you fail to reject the H0 when H0 is false then you made a _____ with a probability equal to ______.

Type II error; â

When there is exclusive concern that the population mean differs from a value in a specified direction, we should use _____.

a directional test

A researcher in sports psychology is interested in the resting pulse rate of long-distance college runners. She does some research and finds data from the U.S. Olympics team showing their long-distance runners have a resting pulse rate of 60 beats per minute. She wants to know if the pulse rate for college runners is different from the Olympic team's m of 60. She randomly samples 20 long-distance runners, and finds What is the 95% confidence interval for the above statistical test?

60-70.06

If N = 30, the sample mean is 12, and the estimated standard error of the mean is 2, what are the 95% confidence intervals?

7.91 to 16.09

A researcher takes a very large, nationwide random sample of 7th grade students and computes a mean verbal ability score of 85.50 with a standard deviation of 8.35. From this information, she computes a standard error of the mean of 2.64. What are the upper and lower limits of the 95% confidence interval for the mean?

80.33 to 90.67

In the process of hypothesis testing, the investigator begins by stating a proposal, or hypothesis, that is assumed to be:

A. true

Which of the following describes a typical null hypothesis?

A. µ=150

If a researcher sets a critical z value equal to 1.96, then test statistics falling beyond that range _____.

D. suggest that the alternative hypothesis is true

A group of 200 students takes the Kaplan course in hopes that it will improve their SAT scores above the national mean of 500 on the math section. The population standard deviation of the SAT is known to be 100. Use an alpha level of .05 when answering the following questions. What is the null hypothesis?

H0: ì = 500

Which of the following alternative hypotheses would require using a one-tailed test?

H1: ì < 100 or . H1: ì > 100

A group of 200 students takes the Kaplan course in hopes that it will improve their SAT scores above the national mean of 500 on the math section. The population standard deviation of the SAT is known to be 100. Use an alpha level of .05 when answering the following questions. What is the alternative hypothesis?

H1: ì > 500

Which of the following statements is an example of a two-tailed alternative hypothesis?

H1:µ1µ2

A sampling distribution of means based on all possible random samples of size 25, drawn from a population with a mean of 100, will have a standard error of _____.

cant determine

As your sample size gets smaller (especially as it gets below about 30-40), the t-distribution and the z-distribution

become more and more differnt

The power of a statistical test can be increased by ____

increasing á level B. increasing sample size

The critical t value needed to reject the null will always be _____ than a Z value for the same set of scores

larger

When the alpha level is .05, a result is defined as being "unexpected" if the probability of obtaining that result, assuming the null hypothesis is true, is:

less than .05

a confidence claim reflects a _____ of an extended number of confidence intervals across all possible random samples of a given size.

long term performance

When we use inferential statistics to address a research question, we _____.

make generalizations from a sample to the population it was sampled from

The probability of making a Type I error is equal to:

the alpha level, .05 in most cases, á

The p value reported in APA manuscripts is commonly referred to as _____.

the beta level

Why would a researcher want high statistical power rather than low statistical power?

the chances of making a type 2 error would be less

What happens when the experimental results are statistically significant?

the null hypotheiss is rejected

researcher in sports psychology is interested in the resting pulse rate of long-distance college runners. She does some research and finds data from the U.S. Olympics team showing their long-distance runners have a resting pulse rate of 60 beats per minute. She wants to know if the pulse rate for college runners is different from the Olympic team's m of 60. She randomly samples 20 long-distance runners, and finds What is the appropriate test statistic for this data?

the one sample t test

The most likely conclusion to make if your observed z exceeds the critical value is the _____.

the population mean is differnt from the value specified in the null hypothesis

A one-sample t test is used in situations where

the s is known.

The one-sample t test is based on the assumption that:

the sample is independently and randomly selected from the population of interest and the scores on the variable are normally distributed

Which of the following is NOT one of the conditions for using the one-sample t test?

the variable under investigation is qualitative and measured on an ordinal level

Which of the following is NOT one of the conditions for using the one-sample z test?

the variable under investivgation is qualitative and measured on a ordianl level

In the Applications to the Analysis of Social Problems section of Chapter 8, the confidence intervals for the mean age at which mothers think parents should talk with children about sex and the confidence intervals for the mean age at which mothers think parents should talk with children about birth control were relatively narrow. What does this mean?

there are small amounts of sampling error