Deck 8: Testing Hypotheses

Question 1

Which of the following illustrates an important difference between the Z and t statistics?

A)The denominator of the Z statistic is subject to sampling error.
B)The denominator of the t statistic is subject to sampling error.
C)The sampling distribution of the Z statistic is not normal.
D)The numerator of the t statistic is the standard error based on the population standard deviation.

Answer 1

The denominator of the t statistic is subject to sampling error.

Question 2

According to the Central Limit Theorem,if the sample size is larger than 50,the sampling distribution of the mean is

A)positively skewed.
B)negatively skewed.
C)bimodally distributed.
D)approximately normal.

Answer 2

approximately normal.

Question 3

A left-tailed test is one where the sample outcome is hypothesized to be

A)at the right tail of the sampling distribution.
B)at the left tail of the sampling distribution.
C)approximately normal within ± 1 Z scores.
D)curvilinear over the distribution.

Answer 3

at the left tail of the sampling distribution.

Question 4

A measure of how unusual or rare an obtained statistic is,is referred to as

A)alpha.
B)beta.
C)Z score.
D)p value.

Question 5

A ______ test is conducted when we have no theoretical reason for specifying a direction in the research hypothesis.

A)right-tailed
B)left-tailed
C)two-tailed
D)tailed

Question 6

A statement of "no difference" that contradicts the research hypothesis and is always expressed in terms of population parameters is called the

A)null hypothesis.
B)right-tailed test.
C)t statistic.
D)specified value.

Question 7

When a one-tailed test specifies that the population mean is greater than some specified value,we call it a ______ test.

A)right-tailed
B)left-tailed
C)binominal
D)distributive

Question 8

The probability associated with rejecting the null hypothesis when it is true is called

A)Type I error.
B)Type II error.
C)alpha.
D)lambda.

Question 9

In calculating the standard error,the population standard deviation is estimated by

A) ,the population variance.
B) ,the sample standard deviation.
C) ,the population variance.
D) ,the sample standard deviation.

Question 10

The probability at which the null hypothesis is rejected is referred to as

A)alpha.
B)beta.
C)Z score.
D)p value.

Question 11

Two sample hypothesis testing assumes that the samples are

A)independent of each other.
B)not randomly selected.
C)disproportionately large.
D)too small.

Question 12

Which is the symbol for the standard error?

A)
B)
C)
D)

Question 13

The probability associated with failing to reject the null hypothesis when it is false is called

A)Type I error.
B)Type II error.
C)alpha.
D)lambda.

Question 14

The probability associated with obtaining a particular value of Z is referred to as its

A)alpha.
B)beta.
C)Z score.
D)p value.

Question 15

Which of the following is the null hypothesis for a two sample t test?

A)µ₁ ≠ µ₂
B)µ₁ < µ₂
C)µ₁ > µ₂
D)µ₁ = µ₂

Question 16

The research hypothesis is symbolized as

A)H₀.
B)H₁.
C)H.
D)h.

Question 17

Making assumptions and selecting the sampling distribution are steps involved in

A)statistical hypothesis testing.
B)calculating the test statistic.
C)interpreting the results.
D)determining the mean.

Question 18

Which of the following is the symbol for the sample variance?

A)
B)
C)
D)

Question 19

When conducting a statistical hypothesis test,what is it that we are actually doing?

A)Determining whether the research hypothesis is true
B)Evaluating the direction of the research hypothesis
C)Falsifying the null hypothesis
D)Specifying a probability that H₁ is equal to zero

Question 20

The null hypothesis is symbolized as

A)H₀.
B)H₁.
C)H.
D)X.

Question 21

Suppose you are interested in testing whether the mean earning of men in the General Social Survey is representative of the earning of the entire U.S.male population.If there are 372 men in the General Social Survey sample and approximately 128 million men in the population,calculate the degrees of freedom for this single-sample t test.

Question 22

Alpha is the level of probability at which the null hypothesis is accepted.

Question 23

Imagine you wish to determine whether the mean number of hours worked per week by men in a sample differs from the 40-hour standard.Use the information below to calculate the value of the single-sample t statistic.

Question 24

SELECT ALL THAT APPLY.To calculate the t statistic,we need to know the values of

A)sample mean.
B)population mean.
C)sample standard deviation.
D)sample size.

Question 25

If the sample variances of two sets of people are 2.15 and 2.04 with sample sizes 50 each,then the t statistic for a difference between means 43.10 AND 40.26 is .29.

Question 26

The degrees of freedom will increase as the sample size increases.

Question 27

Suppose you are interested in testing whether the mean earning of men in California differs significantly from the mean earning of men in New York.If the number of men from California in the sample is 123 and the number of men from New York in the sample is 88,how many degrees of freedom are there?

Question 28

SELECT ALL THAT APPLY.A p value

A)is the probability associated with the obtained value of Z.
B)determines whether the null hypothesis should be rejected or not.
C)is statistically significant if it is less than or equal to the alpha level.
D)can be greater than 1.

Question 29

SELECT ALL THAT APPLY.A research hypothesis (H₁)is said to be a

A)one-tailed test if the research hypothesis is non-directional.
B)right-tailed test if the research hypothesis is directed at the right tail of the sampling distribution.
C)left-tailed test if the research hypothesis is directed at the left tail of the sampling distribution.
D)two-tailed test if the research hypothesis is directional.

Question 30

Calculate the degrees of freedom for a one-sample t test with 2,822 U.S.adults between the ages of 15 and 64 in the sample.

Question 31

SELECT ALL THAT APPLY.Some of the assumptions in statistical hypothesis testing include that

A)all statistical tests assume random sampling.
B)sample size is smaller than 50.
C)the population under consideration is normally distributed.
D)variables assume interval-ratio level of measurement.

Question 32

The 40-hour work week is considered the standard in American society today.Imagine you wish to use data from the 2010 General Social Survey to determine whether the mean number of hours worked per week by men in the sample differs from the 40-hour standard.What test statistic should you compute and why?

Question 33

The t distribution is also bell-shaped like the standard normal distribution.

Question 34

The 40-hour work week is generally considered as a standard in American society today.Using data from the 2010 General Social Survey,you wish to determine whether the mean number of hours worked per week by men in the sample differs from the 40-hour standard.State the null and research hypotheses for this single-sample t test.

Question 35

If the sample variances of two sets of people are 2.15 and 2.04 with sample sizes 50 each,then the estimated standard error is .29.

Question 36

In a two-sample case,the samples are assumed to be dependent on each other.

Question 37

List the four quantities needed to conduct a single-sample t test.

Question 38

SELECT ALL THAT APPLY.A research hypothesis

A)is a statement of no difference.
B)is denoted by H₀.
C)is a statement reflecting the substantive hypothesis.
D)is always expressed in terms of population parameters.

Question 39

Suppose you are interested in testing whether the mean earning of men in the General Social Survey is representative of the earning of the entire U.S.male population.The average male in the General Social Survey earned $31,607 in 2005 and the average male in the population earned $33,405 in 2005.State the null and research hypotheses.

Question 40

If variables are measured at the nominal or ordinal levels,then they are described in terms of proportions or percentages.

Question 41

What three quantities do you need in order to calculate the independent samples t statistic?

Question 42

Which statistic would you use if you are interested in comparing the mean number of hours worked by sex.

Question 43

Define Type I and Type II error.

Question 44

In a simple random sample of 120 women and 150 men from a population of 150,000,25% of the women and 37% of the men are smokers.Suppose you are interested in comparing the proportion of smokers by sex,compute the estimated standard error.

Question 45

Imagine you wish to determine whether the mean number of hours worked per week by men in a sample differs from the 40-hour standard.Use the information below to calculate the number of degrees of freedom associated with a single-sample t test.

Question 46

Suppose you are interested in comparing the mean number of hours worked by sex.Use the information below to calculate the value of the independent samples t statistic.

Question 47

In a simple random sample of 120 women and 150 men from a population of 150,000,25% of the women and 37% of the men are smokers.Suppose you are interested in comparing the proportion of smokers by sex,state the null and the research hypothesis.

Question 48

In a simple random sample of 120 women and 150 men from a population of 150,000,25% of the women and 37% of the men are smokers.Suppose you are interested in comparing the proportion of smokers by sex,compute the Z statistic.

Question 49

Suppose you are interested in comparing the mean number of hours worked by sex.State the null and the research hypotheses.

Question 50

In a simple random sample of 120 women and 150 men from a population of 150,000,25% of the women and 37% of the men are smokers.Suppose you are interested in comparing the proportion of smokers by sex,do we accept or reject the null hypothesis of assuming the smoking proportions of women and men are the same with alpha .05?