Deck 8: Introduction to Inferential Statistics

Question 1

What is the standard error of the mean for a distribution of scores where $\sigma$ = 15 and n = 100?

A).15
B)1.5
C)15
D)unable to determine

Answer 1

1.5

Question 2

What is the standard error of the mean for a distribution of scores where $\sigma$ = 24 and n = 144?

A)20
B).167
C)2.0
D)unable to determine

Answer 2

2.0

Question 3

A researcher in interested in whether high school students who play sports have a higher or lower body mass index (BMI)than students in the general population.The researcher is unsure whether playing sports will decrease body mass (due to more calories burned)or increase body mass (due to more muscle mass).He compares their average BMI to that of students in the general population and finds that z_obt = +1.92.This is a _____ test and the researcher should conclude _____.

A)one-tailed; that students who are athletes have significantly higher BMIs.
B)two-tailed; that students who are athletes have significantly higher BMIs.
C)one-tailed: that students who are athletes do not have significantly higher BMIs.
D)two-tailed: that students who are athletes do not have significantly higher BMIs.

Answer 3

D

Question 4

The standard deviation of the sampling distribution is called the

A)standard deviation.
B)deviation of the sample.
C)standard error of the mean.
D)standard error of the population.

Question 5

Which of the following is not an assumption of the z-test?

A)The population mean ( $\mu$ )and standard deviation ( $\sigma$ )are known.
B)The data are interval or ratio.
C)The distribution of random samples is normal.
D)The sample size is less than 30.

Question 6

A distribution of sample means based on random samples of a fixed size from a population is the _____.

A)standard error of the mean
B)z test
C)population distribution
D)sampling distribution

Question 7

A researcher in interested in whether students who play sports have a higher or lower body mass index (BMI)than students in the general population.The researcher is unsure whether playing sports will decrease body mass (due to more calories burned)or increase body mass (due to more muscle mass).This is a _____ tailed test and the z_cv is _____.

A)two; ±1.96
B)one; ±1.65
C)two; ±1.65
D)one; ±1.96

Question 8

A researcher in interested in whether students who are musicians have higher intelligence test scores than students in the general population.The researcher predicts that playing a musical instrument is associated with higher intelligence test scores.This is a _____-tailed test and the z_cv is _____.

A)two; ±1.96
B)one; ±1.65
C)two; ±1.65
D)one; ±1.96

Question 9

_____ statistics are used in the process of hypothesis testing.

A)Descriptive
B)Null
C)Alternative
D)Inferential

Question 10

A researcher in interested in whether students who are musicians have higher intelligence test scores than students in the general population.The researcher predicts that playing a musical instrument is associated with higher intelligence test scores.The researcher selects a sample of 75 musicians from local high schools and gives them an intelligence test.She compares their average intelligence to that of students in the general population and finds that z_obt = +1.92.This is a _____ test and the researcher should conclude _____.

A)one-tailed; that students who are musicians score significantly higher on intelligence tests
B)two-tailed; that students who are musicians score significantly higher on intelligence tests
C)one-tailed; that students who are musicians do not score significantly higher on intelligence tests
D)two-tailed; that students who are musicians do not score significantly higher on intelligence tests

Question 11

The standard error of the mean is calculated by dividing _____ by _____.

A) $\sigma$ ; n²
B) $\sigma$ ; the square root of n
C)n²; $\sigma$
D)the square root of n; $\sigma$

Question 12

The formula to determine the _____ is based on the _____.

A)central limit theorem; standard deviation
B)standard deviation; central limit theorem
C)standard error of the mean; central limit theorem
D)central limit theorem; z test

Question 13

A researcher in interested in whether students who are musicians have higher intelligence test scores than students in the general population.The researcher predicts that playing a musical instrument is associated with higher intelligence test scores.The researcher selects a sample of 75 musicians from local high schools and gives them an intelligence test.The mean for the sample is 105.The mean for the general population (µ)is 100 with a standard deviation ( $\sigma$ )of 15.What is z_obt for this sample?

A).33
B)1.89
C)2.89
D)3.25

Question 14

The standard error of the mean will always be ____ the standard deviation for a distribution of individual scores.

A)smaller than
B)larger than
C)the same as
D)the same as or larger than

Question 15

Inferential statistics allow us to

A)infer something about the sample based on the population.
B)infer something about the population based on the sample.
C)infer that the sample is representative.
D)do all of the above

Question 16

The sampling distribution is a distribution of ____ means based on random _____ of a fixed size from a _____.

A)population; samples; population
B)sample; samples; population
C)population; populations; sample
D)sample; populations; sample

Question 17

What is the standard error of the mean for a distribution of scores where $\sigma$ = 50 and n = 75?

A)5.77
B).066
C)1.5
D)unable to determine

Question 18

Z_cv for a one-tailed test is _____ whereas Z_cv for a two-tailed test is _____.

A) $\pm$ 1.645; $\pm$ 1.96
B) $\pm$ 1.96; $\pm$ 1.645
C).01; .05
D).05; .01

Question 19

A researcher in interested in whether high school students who play sports have a higher or lower body mass index (BMI)than students in the general population.The researcher is unsure whether playing sports will decrease body mass (due to more calories burned)or increase body mass (due to more muscle mass).The researcher selects a sample of 60 athletes and finds that their average BMI is 22.The average (µ)in the general population of students is 22.5 with a standard deviation ( $\sigma$ )of 3.What is z_obt for this sample?

A).98
B)1.29
C)1.96
D)2.25

Question 20

A parametric inferential statistical test of the null hypothesis for a single sample where the population variance is known is the

A)t test.
B)standard deviation.
C)z test.
D)standard error test.

Question 21

If a researcher reported for a one-tailed single-sample t-test that t(14)= 2.25,then

A)p < .025.
B)p < .05.
C)p < .01.
D)p < .001.

Question 22

The set of distributions that although symmetrical and bell-shaped,are not normally distributed is known as

A)Student's t distribution.
B)Gosset's t distribution.
C)the z distribution.
D)none of the options is correct

Question 23

To estimate the standard deviation of the sampling distribution when using a single-sample t test,we use the

A)estimated standard deviation.
B)estimated population standard deviation.
C)estimated standard error of the mean.
D)true standard error of the mean.

Question 24

In a study with 16 participants and s = 10,the estimated standard error of the mean would be

A)1.0.
B)1.5.
C)2.0.
D)2.5.

Question 25

Imagine that you conducted a single-sample t-test with 15 participants.For a one-tailed test,the t_cv at $\alpha$ = .05 would be

A) $\pm$ 1.761.
B) $\pm$ 1.753.
C) $\pm$ 2.179.
D) $\pm$ 2.201.

Question 26

If a researcher reported for a single-sample t-test that t(17)= 2.90,p< .02,how many participants were there in the study?

A)18
B)20
C)10
D)9

Question 27

Imagine that you conducted a single-sample t-test with 8 participants.For a two-tailed test,the t_cv at $\alpha$ = .05 would be

A) $\pm$ 1.796.
B) $\pm$ 2.365.
C) $\pm$ 2.179.
D) $\pm$ 2.201.

Question 28

The number of scores in a sample that are free to vary represents the

A)sample size.
B)N. c the degrees of freedom.
D)none of the other options is correct

Question 29

In order to increase the power of z test,one might

A)increase sample size.
B)use a two-tailed test.
C)decrease sample size.
D)none of the options is correct

Question 30

The _____ distribution is a set of distributions that,although symmetrical and bell-shaped,are not normally distributed.

A)standard normal
B)normal
C)Student's t-
D)alternative

Question 31

If a researcher reported for a single-sample t-test that t(10)= 2.50,p< .05,how many participants were there in the study?

A)10
B)9
C)11
D)12

Question 32

A _____-tailed test and a _____ sample size will both increase the power of the test.

A)two; larger
B)one; larger
C)two; smaller
D)one; smaller

Question 33

For a single-sample t test with 18 participants,the degrees of freedom are

A)17.
B)18.
C)16.
D)unable to be determined.

Question 34

Sometimes researchers use estimation of population means,rather than hypothesis tests.These estimations are based on

A)the standard error of the mean.
B)the standard deviation.
C)the z test.
D)confidence intervals.

Question 35

The estimated standard error of the mean is calculated by dividing _____ by _____.

A)s; the square root of n
B)s; n²
C)n²; s
D)the square root of n; s

Question 36

When comparing a sample to a population,if you know $\mu$ and $\sigma$ and have a sample size larger than 30,you should conduct a _____ test.

A)t
B)z
C) $\chi$ ²
D)phi

Question 37

For a single-sample t test with 10 participants,the degrees of freedom are

A)10.
B)9.
C)8.
D)unable to be determined.

Question 38

Imagine that you conducted a single-sample t-test with 12 participants.For a two-tailed test,the t_cv at $\alpha$ = .05 would be

A) $\pm$ 1.796.
B) $\pm$ 2.074.
C) $\pm$ 2.179.
D) $\pm$ 2.201.

Question 39

For a single-sample t test with 12 participants,the degrees of freedom are

A)10.
B)11.
C)12.
D)unable to be determined.

Question 40

In a study with 25 participants and s = 15,the estimated standard error of the mean would be

A)0.6.
B)3.0.
C)2.0.
D)2.6.

Question 41

Assume that the average person in America weighs 150 pounds ( $\mu$ ).You want to determine whether college students weigh less than the average American.Following are the weights collected on a sample of college students: 120,105,166,170,145,149,135,115,168,138.

Question 42

Which of the following is not an assumption of the t-test?

A)The data should be ordinal or nominal.
B)The population distribution of scores should be symmetrical.
C)The population mean ( $\mu$ )is known,but the population standard deviation ( $\sigma$ )is not known.
D)The sample size is typically less than 30.

Question 43

If a researcher reported for a two-tailed single-sample t-test that t(13)= 1.46,then

A)p < .02.
B)p < .05.
C)p < .01.
D)the results is not significant.

Question 44

A researcher in interested in whether students who attend private elementary schools do any better on a standard test of intelligence than the general population of elementary school children.A random sample of 75 students at a private elementary school is tested and has a mean intelligence test score of 103.5.The average for the general population of elementary school children is 100 ( $\sigma$ = 15).

Question 45

Chi-square is calculated by summing the[(_____ -_____)² divided by _____].

A)observed; expected; observed
B)expected; observed; observed
C)observed; expected; expected
D)observed; observed; expected

Question 46

What is a t test,when is it used,and what does it tell us?

Question 47

Nonparametric is to parametric as _____ is to _____.

A)t-test; z-test
B)z-test; t-test
C) $\chi$ ²-test; t-test
D)t-test; $\chi$ ²-test

Question 48

How does sample size affect the t_cv?

Question 49

What is a z test,when is it used,and what does it tell us?

Question 50

Rich performed a two-tailed test for an experiment in which n=15.He could not find his t critical values table but he remembered the t_cv at df = 20.He decided to compare his t_obt to this t_cv.Is he more likely to make a Type I or a Type II error in this situation?

Question 51

What is the sampling distribution and how is it related to the standard error of the mean?

Question 52

Given: For one section of the SAT: $\mu$ = 500 and $\sigma$ = 100.The SAT was given to a sample of n=35 and the mean SAT for this sample was 536.Calculate the z-test for this sample mean.Does this sample differ significantly from the population for a two-tailed test?

Question 53

What are the assumptions of the z test?

Question 54

Explain why decreases as the size of the samples in the sampling distribution increase.Your answer should include an explanation based on the formula for and an explanation of why this formula makes sense (in other words,why would increasing the size of each sample in the sampling distribution cause to decrease?

Question 55

Rich performed a two-tailed test for an experiment in which n=20.He could not find his t critical values table but he remembered the t_cv at df = 15.He decided to compare his t_obt to this t_cv.Is he more likely to make a Type I or a Type II error in this situation?

Question 56

Which of the following is not an assumption of the $\chi$ ²-test?

A)It is a nonparametric test.
B)It is appropriate only for ordinal data.
C)The frequency in each cell should be at least 5.
D)The sample should be randomly selected.

Question 57

If a researcher reported for a one-tailed single-sample t-test that t(10)= 1.96,then

A)p < .02.
B)p < .05.
C)p < .01.
D)p < .001.

Question 58

If a researcher reported for a two-tailed single-sample t-test that t(10)= 2.25,then

A)p < .02.
B)p < .05.
C)p < .01.
D)p < .001.

Question 59

How does a t test differ from a z test in terms of when it is used,how it is calculated,and how we determine significance?

Question 60

When comparing a sample to a population,if you know $\mu$ but not $\sigma$ and have a sample size smaller than 30,you should conduct a _____ test.

A)t
B)z
C) $\chi$ ²
D)phi

Question 61

According to the U.S.Bureau of the Census,75% of adults regularly drank alcohol in 1985.An investigator predicts that fewer adults drink now than drank then.A sample of 100 adults is asked about their current drinking habits and 67 report drinking and 33 report not drinking.

Question 62

What are the assumptions of the t test?

Question 63

What are the assumptions of the $\chi$ ²-test?