Final Study Questions

Question 1

A financial analyst working for a financial consulting company wishes to find evidence that the average price-to-earnings ratio in the consumer industry is higher than the average price-to-earnings ratio in the banking industry. The alternative hypothesis is

Answer 1

μconsumer>μbanking.

Question 2

A sample size of 500 is sufficiently large to conclude that the sampling distribution of pˆp^ is a normal distribution, when the estimate of the population proportion is .995.

Answer 2

FALSE

Question 3

A Type I error is rejecting a true null hypothesis.

Answer 3

TRUE

Question 4

A Type II error is failing to reject a false null hypothesis.

Answer 4

TRUE

Question 5

A uniform distributionf(x) is a continuous probability distribution, which says the probability thatxis in any 2 intervals of equal length is the same.

Answer 5

TRUE

Question 6

All continuous random variables are normally distributed.

Answer 6

FALSE

Question 7

All of the following are assumptions of the error terms in the simple linear regression model except

Answer 7

error terms are dependent on each other.

Question 8

An independent samples experiment is an experiment in which there is no relationship between the measurements in the different samples.

Answer 8

TRUE

Question 9

As standard deviation increases, sample size _____________ to achieve a specified level of confidence.

Answer 9

increases

Question 10

As the sample size ______________, the variation of the sampling distribution of x¯x¯ ___________.

Answer 10

increases, decreases

Question 11

As the Type II error,β,of a statistical test increases, the power of the test _____________.

Answer 11

decreases

Question 12

Assuming that the null hypothesis is true, the ______________ is the probability of observing a value of the test statistic that is at least as extreme as the value actually computed from the sample data.

Answer 12

p-value

Question 13

Assuming the same level of significanceα, as the sample size increases, the value oftα/2approaches the value ofzα/2.

Answer 13

TRUE

Question 14

Consider two population distributions labeled A and B. Distribution A is highly skewed and nonnormal, while distribution B is slightly skewed and near normal. In order for the sampling distributions of A and B to achieve the same degree of normality,

Answer 14

population A will require a larger sample size.

Question 15

First, a 90 percent confidence interval is constructed from a sample size of 100. Then, for the same identical data, a 92 percent confidence interval is constructed. The width of the 90 percent interval is wider than the 92 percent confidence interval.

Answer 15

FALSE

Question 16

For a continuous distribution, the exact probability of a particular value is zero.

Answer 16

TRUE

Question 17

For a fixed sample size, the lower we setα, the higher is the ___________.

Answer 17

Type II error

Question 18

For any sampled population, the population of all sample means is approximately normally distributed.

Answer 18

FALSE

Question 19

For the same set of observations on a specified dependent variable, two different independent variables were used to develop two separate simple linear regression models. A portion of the results is presented below. Model 1 r2=.92 s=1.65 Model 2 r2=.85 s=-1.91

Answer 19

a prediction based on Model 1 is better than a prediction based on Model 2.

Question 20

Given the following information about a hypothesis test of the difference between two means based on independent random samples, which one of the following is the correct rejection region at a significance level of .05? HA:μA>μB, X¯¯¯1X¯1= 12, X¯¯¯2X¯2= 9,s1= 4,s2= 2,n1= 13,n2= 10.

Answer 20

RejectH0ift> 1.721.

Question 21

If the random variableXhas a mean ofµand a standard deviationσ, then the mean and standard deviation, respectively, of (X−µ)/σare

Answer 21

0 and 1.

Question 22

If the random variablexis normally distributed, ______ percent of all possible observed values ofxwill be within three standard deviations of the mean.

Answer 22

99.73

Question 23

If the sampled population has a mean of 48 and standard deviation of 16, then the mean and the standard deviation for the sampling distribution of x¯x¯ forn= 16 are

Answer 23

48 and 4.

Question 24

If we are testing the difference between the means of two normally distributed independent populations with samples ofn1= 10,n2= 10, the degrees of freedom for thetstatistic is ______.

Answer 24

18

Question 25

If we are testing the hypothesis about the mean of a population of paired differences with samples of n1 = 10, n2 = 10, the degrees of freedom for the t statistic is ____.

Answer 25

9

Question 26

If we have a sample size of 100 and the estimate of the population proportion is .10, we can estimate the sampling distribution of  pˆp^  with a normal distribution.

Answer 26

TRUE

Question 27

If r = −1, then we can conclude that there is a perfect relationship between X and Y.

Answer 27

TRUE

Question 28

In a simple linear regression analysis, the correlation coefficient (r) and the slope (b) ___________ have the same sign.

Answer 28

always

Question 29

In an experiment involving matched pairs, a sample of 12 pairs of observations is collected. The degrees of freedom for the t statistic is 10.

Answer 29

FALSE

Question 30

In order to test the effectiveness of a drug called XZR designed to reduce cholesterol levels, the cholesterol levels of 9 heart patients are measured before they are given the drug. The same 9 patients use XZR for two continuous months. After two months of continuous use, the cholesterol levels are measured again. The comparison of cholesterol levels before versus after administering the drug is an example of testing the difference between

Answer 30

matched pairs from two dependent populations.

Question 31

In simple regression analysis, r2 is a percentage measure and measures the proportion of the variation explained by the simple linear regression model.

Answer 31

TRUE

Question 32

In testing for the equality of means from two independent populations, if the hypothesis of equal population means is rejected at α = .01, it will __________ be rejected at α = .05.

Answer 32

always

Question 33

In testing the difference between the means of two normally distributed populations using independent random samples, the alternative hypothesis always indicates no differences between the two specified means.

Answer 33

FALSE

Question 34

In testing the difference between two means from two independent populations, the sample sizes do not have to be equal.

Answer 34

TRUE

Question 35

In testing the difference between two means from two normally distributed independent populations, the distribution of the difference in sample means will be

Answer 35

normally distributed.

Question 36

The ___________ is a graphic that is used to check visually whether data come from a normal population.

Answer 36

normal probability plot

Question 37

The actual weight of hamburger patties is an example of a continuous random variable.

Answer 37

TRUE

Question 38

The area under the normal curve between z = 0 and z = 1 is ________________ the area under the normal curve between z = 1 and z = 2.

Answer 38

greater than

Question 39

The Central Limit Theorem states that as sample size increases, the population distribution more closely approximates a normal distribution.

Answer 39

TRUE

Question 40

The Central Limit Theorem states that as the sample size increases, the distribution of the sample ____________ approaches the normal distribution.

Answer 40

means

Question 41

The exact spread of the t distribution depends on the _________.

Answer 41

number of degrees of freedom

Question 42

The first step to constructing a normal probability plot is to

Answer 42

order the values in the data.

Question 43

The larger the p-value, the more we doubt the null hypothesis.

Answer 43

FALSE

Question 44

The least squares regression line minimizes the sum of the

Answer 44

squared differences between actual and predicted Y values.

Question 45

The manager of the quality department for a tire manufacturing company wants to know the average tensile strength of rubber used in making a certain brand of radial tire. The population is normally distributed, and the population standard deviation is known. She uses a z test to test the null hypothesis that the mean tensile strength is less than or equal to 800 pounds per square inch. The calculated z test statistic is a positive value that leads to a p-value of .067 for the test. If the significance level is .10, the null hypothesis would be rejected.

Answer 45

TRUE

Question 46

The number of defective pencils in a lot of 1000 is an example of a continuous random variable.

Answer 46

FALSE

Question 47

The population of all sample proportions has a normal distribution if the sample size (n) is sufficiently large. The rule of thumb for ensuring that n is sufficiently large is

Answer 47

np ≥ 5 and n(1 − p) ≥ 5.

Question 48

The random variable x has a uniform distribution when x lies between the values of 4 and 10. When x = 10, what is the value of f(x)?

Answer 48

0

Question 49

The residual is the difference between the observed value of the dependent variable and the predicted value of the dependent variable.

Answer 49

TRUE

Question 50

The sampling distribution of  x¯x¯  must be a normal distribution with mean = 0 and standard deviation = 1.

Answer 50

FALSE

Question 51

The slope of the simple linear regression equation represents the average change in the value of the dependent variable per unit change in the independent variable (X).

Answer 51

TRUE

Question 52

The standard deviation of all possible sample proportions increases as the sample size increases.

Answer 52

FALSE

Question 53

The standard error of the sample mean is s/√n.

Answer 53

TRUE

Question 54

The width of a confidence interval will be

Answer 54

narrower for 90 percent confidence than for 95 percent confidence.

Question 55

The t distribution always has n degrees of freedom.

Answer 55

FALSE

Question 56

The t distribution approaches the _______________ distribution as the sample size ___________.

Answer 56

z, increases

Question 57

There are two types of machines, called type A and type B. Both type A and type B can be used to produce a certain product. The production manager wants to compare efficiency of the two machines. He assigns each of the 15 workers to both types of machines to compare their hourly production rate. In other words, each worker operates machine A and machine B for one hour each. These two samples are independent.

Answer 57

FALSE

Question 58

Using the p-value rule for a population proportion or mean, if the level of significance is less than the p-value, the null hypothesis is rejected.

Answer 58

FALSE

Question 59

When comparing two independent population means, if n1 = 13 and n2 = 10, degrees of freedom for the t statistic is 22.

Answer 59

FALSE

Question 60

When constructing a confidence interval for a population mean, if a population is normally distributed and a small sample is taken, then the distribution of  X¯¯¯X¯  is based on the ____________ distribution.

Answer 60

t

Question 61

When determining the sample size, if the value found is not an integer initially, you should ____________ choose the next highest integer value.

Answer 61

always

Question 62

When testing a hypothesis about a single mean, if the sample size is 20, the population standard deviation is unknown, and the population is assumed to be a normal distribution, the correct test statistic to use is ___________.

Answer 62

t

Question 63

When testing a hypothesis about a single mean, if the sample size is 51 and the population standard deviation is known, the correct test statistic to use is ___________.

Answer 63

z

Question 64

When testing the difference between two population proportions using large independent random samples, the __________ test statistic is used.

Answer 64

z

Question 65

When the margin of error is added to and subtracted from the sample mean, an interval is formed that will contain μ with a probability of (1 − α).

Answer 65

TRUE

Question 66

When the population is normally distributed and the population standard deviation σ is unknown, then for any sample size n, the sampling distribution of  x¯x¯  is based on the z distribution.

Answer 66

FALSE

Question 67

Whenever the population has a normal distribution, the sampling distribution of  x¯x¯  is a normal or near normal distribution

Answer 67

for any sample size.

Question 68

A continuous probability distribution having a rectangular shape, where the probability is evenly distributed over an interval of numbers, is called a uniform probability distribution.

Answer 68

TRUE