UCF QMB 3200 Final Exam

Doubling the size of the sample will

reduce the standard error of the mean

The sample mean is the point estimator of

U

A simple random sample of size n from an infinite population of size N is to be selected. Each possible sample should have

the same probability of being selected

Which of the following statements regarding the sampling distribution of sample means is incorrect?

The standard deviation of the sampling distribution is the standard deviation of the population.

A simple random sample of size n from an infinite population is a sample selected such that

each element is selected independently and is selected from the same population

The fact that the sampling distribution of sample means can be approximated by a normal probability distribution whenever the sample size becomes large is based on the

central limit theorem.

Cluster sampling is

a probability sampling method.

The central limit theorem states that

if the sample size n is large, then the sampling distribution of the sample mean can be approximated by a normal distribution.

The value of the _____ is used to estimate the value of the population parameter

sample statistic

The sampling distribution of is the

probability distribution of all possible values of the sample proportion.

Which of the following is not a symbol for a parameter?

S.

The sample statistic characteristic s is the point estimator of

σ..

The distribution of values taken by a statistic in all possible samples of the same size from the same population is called a

sampling distribution.

Which of the following is a point estimator?

S.

As a rule of thumb, the sampling distribution of the sample proportion can be approximated by a normal probability distribution when

n(1 - p) ≥ 5 and np ≥ 5.

A sample of 92 observations is taken from an infinite population. The sampling distribution of is approximately

normal because of the central limit theorem.

The central limit theorem is important in Statistics because it enables reasonably accurate probabilities to be determined for events involving the sample average

when the sample size is large regardless of the distribution of the variable.

The distribution of values taken by a statistic in all possible samples of the same size from the same population is the sampling distribution of

The sample

Which of these best describes a sampling distribution of a statistic?

It is the distribution of all of the statistics calculated from all possible samples of the same sample size.

The probability distribution of all possible values of the sample proportion is the

sampling distribution of p.

For a fixed confidence level and population standard deviation, if we would like to cut our margin of error in half, we should take a sample size that is

four times as large as the original sample size.

We can reduce the margin of error in an interval estimate of p by doing any of the following except

increasing the planning value p* to .5.

When computing the sample size needed to estimate a proportion within a given margin of error for a specific confidence level, what planning value of p should be used when no estimate of p is available?

0.50

A statistics teacher started class one day by drawing the names of 10 students out of a hat and asked them to do as many pushups as they could. The 10 randomly selected students averaged 15 pushups per person with a standard deviation of 9 pushups. Suppose the distribution of the population of number of pushups that can be done is approximately normal. Which of the following statements is true?

A t distribution should be used because σ is unknown.

The z value for a 99% confidence interval estimation is

2.58

In an interval estimation for a proportion of a population, the critical value of z at 99% confidence is

2.576.

In interval estimation, as the sample size becomes larger, the interval estimate

becomes narrower.In general, higher confidence levels provide larger confidence intervals.

One way to have high confidence and a small margin of error is to

increase the sample size.

From a population that is normally distributed, a sample of 30 elements is selected and the standard deviation of the sample is computed. For the interval estimation of μ, the proper distribution to use is the

t distribution with 29 degrees of freedom.

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution

becomes smaller.

The value added and subtracted from a point estimate in order to develop an interval estimate of the population parameter is known as the

margin of error.

What is the symbol for the population mean? If the population follows a normal distribution, the confidence interval is _____ and can be used for any sample size. If the population does not follow a normal distribution, the confidence interval will be _____. Which of the following choices correctly complete this statement?

exact; approximate.

The t value for a 99% confidence interval estimation based upon a sample of size 10 is

3.250.

To compute the necessary sample size for an interval estimate of a population proportion, all of the following procedures are recommended when p is unknown except

using .95 as an estimate.

Using an α = .04, a confidence interval for a population proportion is determined to be .65 to .75. If the level of significance is decreased, the interval for the population proportion

becomes wider.

For a fixed confidence level and population standard deviation, if we would like to cut our margin of error to 1/3 of the original size, we should take a sample size that is

nine times as large as the original sample size.

The sampling distribution of can be approximated by a normal distribution as long as

np> 5 and n(1-p)>5 greater or equals.

When "s" is used to estimate "σ," the margin of error is computed by using the

t distribution.

The margin of error in an interval estimate of the population mean is a function of all of the following except the

sample mean.

For a fixed sample size, n, in order to have a higher degree of confidence, the margin of error and the width of the interval

must be larger.

The probability that the interval estimation procedure will generate an interval that does not contain µ is known as the

level of significance.

As the sample size increases, the margin of error

decreases.

When the level of confidence decreases, the margin of error

becomes smaller.

An approximate value of a population parameter that provides limits and believed to contain the value of the parameter is known as

the interval estimate.

To compute the necessary sample size for an interval estimate of a population mean, all of the following procedures are recommended when σ is unknown except

using σ = 1.

For the interval estimation of μ when σ is known and the sample is large, the proper distribution to use is

the normal distribution.

What is the symbol for the sample mean?

X bar

A student wants to determine if pennies are really fair, meaning equally likely to land heads up or tails up. He flips a random sample of 50 pennies and finds that 28 of them land heads up. What are the appropriate null and alternative hypotheses?

H0: p=.5, Ha:p not =.5.

For a lower tail test, the p-value is the probability of obtaining a value for the test statistic

at least as small as that provided by the sample.

The average hourly wage of computer programmers with 2 years of experience has been $21.80. Because of high demand for computer programmers, it is believed there has been a significant increase in the average wage of computer programmers. To test whether there has been an increase, the correct hypotheses to be tested are

H0:u<21.80, Ha: u>21.80.

In hypothesis testing, the tentative assumption about the population parameter is called

the null hypothesis.

For a two-tailed test, the p-value is the probability of obtaining a value for the test statistic as

unlikely as that provided by the sample.

The average number of hours for a random sample of mail order pharmacists from company A was 50.1 hours last year. It is believed that changes to medical insurance have led to a reduction in the average work week. To test the validity of this belief, the hypotheses are

H0:u>50.1, Ha:u<50.1.

Whenever the probability of making a Type II error has not been determined and controlled, only two conclusions are possible. We either reject H0 or

Do not reject H0.

Applications of hypothesis testing that only control for the Type I error are called

significance tests.

The p-value is a probability that measures the support (or lack of support) for the

null hypothesis.

As the test statistic becomes larger, the p-value

becomes smaller.

A news reporter states that the average number of temperature in January has never dropped below 10 degrees Fahrenheit. You go online to research this claim. The appropriate hypotheses are

H0: u>10, Ha: u<10.

The probability of making a Type I error when the null hypothesis is true as an equality is called the

level of significance.

Which of the following null hypotheses cannot be correct?

H0: u not=10.

It has been stated that at least 75 out of every 100 people who go to the movies on Saturday night buy popcorn. Identify the null and alternative hypotheses.

H0: p>.75, Ha: p<.75.

A fast food restaurant has automatic drink dispensers to help fill orders more quickly. When the 12 ounce button is pressed, they would like for exactly 12 ounces of beverage to be dispensed. There is, however, undoubtedly some variation in this amount. The company does not want the machine to systematically over fill or under fill the cups. Which of the following gives the correct set of hypotheses?

H0: u=12, Ha: u not=12

Which of the following describes a Type II Error?

Accept H0 when H0 is false.

Which of the following does not need to be known in order to compute the p-value?

The level of significance.

What is the probability of making a Type I error?

𝛼 alpha.

The p-value

must be a number between 0 and 1.

The normal probability distribution can be used to approximate the sampling distribution of as long as

np>5 and n(1-p)>5.

For the case where σ is unknown, which statistic is used to estimate σ?

S

For the case where σ is unknown, the test statistic has a t distribution. How many degrees of freedom does it have? n-1Which of the following describes a Type I Error?

Reject H0 when H0 is true.

The matched sample design often leads to a smaller sampling error than the independent sample design. The primary reason is that in a matched sample design

variation between subjects is eliminated because the same subjects are used for both treatments.

Suppose we are constructing an interval estimate for the difference between the means of two populations when the standard deviations of the two populations are unknown. Suppose it can be assumed that the two populations have equal variances. If n1 is the size of sample 1 and n2 is the size of sample 2, we must use a t distribution with

degrees of freedom.

A researcher recruits 25 people to participate in a study on alcohol consumption and its interactions with Tylenol. The 25 participants had to come to a check-in center every day at 7:00 a.m. for one week. They were given various amounts of alcohol. Each day, each participant would flip a coin to determine if they also took Tylenol with their alcohol. They found that their BAC was 25% higher on days when they were given Tylenol with their alcohol than when they drank alcohol alone. This is an example of a(n)

matched sample design.

The standard error of is given by

The one that has a root square covering the entire thing

Which of the following scenarios follows a matched sample design?

A teacher uses a pretest and then a post test with her students to see how much they have improved.

A company wants to identify which of the two production methods has the smaller completion time. One sample of workers is selected and each worker first uses one method and then uses the other method. The sampling procedure being used to collect completion time data is based on

Matched samples.

Regarding inferences about the difference between two population means, the alternative to the matched sample design, as covered in the textbook, is

independent samples.

When developing an interval estimate for the difference between two sample means, with sample sizes of n1 and n2

n1 and n2 can be of different sizes

A doctor would like to know if men and women got the same amount of sleep per night or if women tended to get less sleep than men. He took a random sample of 100 of his male and 100 of his female patients and asked them how many hours of sleep they got, per night, on average. The women slept an average of 6.75 hours and the men slept an average of 7.5 hours. Suppose we also knew the population standard deviations to be 1.25 hours and 1.5 hours for men and women, respectively. Formulate the null and alternative hypotheses to test whether women sleep less than men do, on average

H0:: Um-Um=0, Ha: Um-UW<0

In most applications of the interval estimation and hypothesis testing procedures, random samples withn1 ≥ 30 and n2 ≥ 30 are adequate. In cases where either or both sample sizes are less than 30

the distribution of the populations becomes an important consideration.

The sampling distribution of is approximated by a

Normal distribution.

A local entrepreneur would like to know if those who live in a rural community are more likely to buy a real Christmas tree than those who live in an urban community. He takes a random sample of 100 people who reside in the city and a separate random sample of 100 people who live in the country and asks them if they buy a real tree at Christmas time. Of the urban participants, 22 buy a real tree. Of the rural participants, 28 buy a real tree. Let P1= the proportion of all people who live in rural communities and buy a real Christmas tree, and let P2 = the proportion of all people who live in urban communities and buy a real Christmas tree. State the null and alternative hypotheses.

H0: p1-p2<0, Ha:p1-p2>0

The sampling distribution of P1-P2 is approximated by a normal distribution when

N1P1,N1(1-P1), N2P2, and N2(1-P2) are all greater than or equal to 5.

When completing a two-tailed hypothesis test about the difference between two population means,

the p-value must be doubled.

If two large independent random samples are taken from two populations, the sampling distribution of the difference between the two sample means

can be approximated by a normal distribution.

Regarding hypothesis tests about , the pooled estimate of P is a

weighted average of P1 and P2.

When x is unknown, which of the following is used to estimate x? s Suppose we have a t distribution based upon two sample means with unknown population standard deviations, which we are unwilling to assume are equal. When we calculate the appropriate degrees of freedom, we should

round the calculated degrees of freedom down to the nearest integer.

If we are interested in testing whether the proportion of items in population 1 is larger than the proportion of items in population 2, then the

alternative hypothesis should state.

In regression analysis, the equation in the form y = 𝛽0 + 𝛽1x + ε is called the

Regression model.

The model developed from sample data that has the form y^hat=bo+b1x is known as the

regression equation.

The tests of significance in regression analysis are based on several assumptions about the error term ɛ. Additionally, we make an assumption about the form of the relationship between x and y. We assume that the relationship between x and y is

Linear.

If a residual plot of x versus the residuals, y - ŷ, shows a non-linear pattern, then we should conclude that

the regression model is not an adequate representation of the relationship between the variables.

When working with regression analysis, an outlier is

any observation that does not fit the trend shown by the remaining data.

Observations with extreme values for the independent variables are called

high leverage points.

The difference between the observed value of the dependent variable and the value predicted using the estimated regression equation is called a(n)

residual.

If the coefficient of determination is a positive value, then the coefficient of correlation

Can be either negative or positive

The tests of significance in regression analysis are based on assumptions about the error term ɛ. One such assumption is that the error term ɛ is a random variable with a mean or expected value of

0.

When studying the relationship between two quantitative variables, whenever we want to predict an individual value of y for a new observation corresponding to a given value of x, we should use a(n)

Prediction interval.

Graphical representation of the residuals that can be used to determine whether the assumptions made about the regression model appear to be valid is called a

Residual plot.

The coefficient of determination

cannot be negative.

If a significant relationship exists between x and y and the coefficient of determination shows that the fit is good, the estimated regression equation should be useful for

Estimation and prediction.