Stats

Which of the following would be information in a question asking you to find the area of a region under the standard normal curve as a​ solution?

A distance on the horizontal axis is given

A​ magazine, which does not accept free products or advertising from​ anyone, prints a review of new cars. Are there sources of bias in this​ situation?

There do not appear to be any sources of bias.

Washington University obtained word counts from the most popular novels of the past five years.

There does not appear to be a potential to create a bias. The organization would not gain from putting a spin on the results.

The measure of center that is the value that occurs with the greatest frequency is the​ _______.

mode.

A histogram aids in analyzing the​ _______ of the data.

shape of the distribution

The Ericsson method is one of several methods claimed to increase the likelihood of a baby girl. In a clinical​ trial, results could be analyzed with a formal hypothesis test with the alternative hypothesis of p>​0.5, which corresponds to the claim that the method increases the likelihood of having a​ girl, so that the proportion of girls is greater than 0.5. If you have an interest in establishing the success of the​ method, which of the following​ P-values would you​ prefer: 0.999,​ 0.5, 0.95,​ 0.05, 0.01,​ 0.001? Why?

0.001, alternative, is

Which of the following is NOT true when investigating two population​ proportions?

A conclusion based on a confidence interval estimate will be the same as a conclusion based on a hypothesis test.

Which of the following is NOT true when testing a claim about a​ proportion?

A conclusion based on a confidence interval estimate will be the same as a conclusion based on a hypothesis test.

Which of the following is NOT true of confidence interval estimates of the difference between two population​ proportions?

A confidence interval is used to test a claim about two population proportions.

What is a scatterplot and how does it help​ us?

A scatterplot is a graph of paired​ (x, y) quantitative data. It provides a visual image of the data plotted as​ points, which helps show any patterns in the data.

Which of the following is NOT a true statement about error in hypothesis​ testing?

A type I error is making the mistake of rejecting the null hypothesis when it is actually false.

In a certain​ survey, 522 people chose to respond to this​ question: "Should passwords be replaced with biometric security​ (fingerprints, etc)?" Among the​ respondents, 53​% said​ "yes." We want to test the claim that more than half of the population believes that passwords should be replaced with biometric security. Complete parts​ (a) through​ (d) below.

A. The sample observations are not a random​ sample, so a test about a population proportion using the normal approximating method cannot be used. B. This statement means that if the​ P-value is very​ low, the null hypothesis should be rejected. C. This statement seems to suggest that with a high​ P-value, the null hypothesis has been proven or is​ supported, but this conclusion cannot be made. D. Choosing this specific of a significance level could give the impression that the significance level was chosen specifically to reach a desired conclusion.

Which of the following would NOT cast doubt of the usefulness of sample​ data?

An effective sampling method

A bottle contains a label stating that it contains pills with 500 mg of vitamin​ C, and another bottle contains a label stating that it contains pills with 325 mg of aspirin. When testing claims about the mean contents of the​ pills, which would have more serious​ implications: rejection of the vitamin C claim or rejection of the aspirin​ claim? Considering only a type I error and using the same sample​ size, is it wise to use the same significance level for hypothesis tests about the mean amount of vitamin C and the mean amount of​ aspirin?

Aspirin, Aspirin, Vitamin C, Larger

Which of the following is not​ true?

A​ z-score is an area under the normal curve.

Heights of adult males are normally distributed. If a large sample of heights of adult males is randomly selected and the heights are illustrated in a​ histogram, what is the shape of that​ histogram?

Bell-shaped

Which of the following is NOT one of the three common errors involving​ correlation?

Correlation does not imply causality

Which of the following is not equivalent to the other​ three?

Dependent variable

Which of the following is typically the least important factor to consider when conducting a statistical analysis of​ data?

Formula calculation

Which of the following is NOT true for a hypothesis test for​ correlation?

If ​|r|>critical ​value, we should fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim of a linear correlation.

Which of the following is NOT a requirement in determining whether there is a linear correlation between two​ variables?

If r>​1, then there is a positive linear correlation.

An ad for a device used to discourage car thefts stated that "This device reduces your odds of car theft by 350 percent." What is wrong with this​statement?

If the device eliminated all car thefts, it would reduce the odds of car theft by 100%,

An ad for a device used to discourage laptop thefts stated that "This device reduces your odds of laptop theft by 400 percent." What is wrong with this​ statement?

If the device eliminated all laptop thefts, it would reduce the odds of laptop theft by 100%,

Which of the following is not a commonly used​ practice?

If the distribution of the sample means is normally​ distributed, and n>​30, then the population distribution is normally distributed.

Which of the following is NOT a requirement for testing a claim about a mean with σ ​known?

If the sample results​ (or more extreme​ results) cannot easily occur when the null hypothesis is​ true, we explain the discrepancy between the assumption and the sample results by concluding that the assumption is​ true, so we do not reject the assumption.

Which of the following is NOT a criterion for making a decision in a hypothesis​ test?

If the​ P-value is less than​ 0.05, the decision is to reject the null hypothesis.​ Otherwise, we fail to reject the null hypothesis.

In a survey of 696 human resource​ professionals, each was asked about the importance of the experience of a job applicant. The survey subjects were randomly selected by pollsters from a reputable market research firm.

It appears to be sound because the data are not biased in any way

The confidence level is 95​%, σ is not​ known, and the normal quantile plot of the 17 salaries​ (in thousands of​ dollars) of basketball players on a team is as shown.

Neither the normal distribution nor the t distribution applies.

If we have a large voluntary response sample consisting of weights of subjects who chose to respond to a survey posted on the​ Internet, can a graph help to overcome the deficiency of having a voluntary response​ sample?

No, a graph cannot help to overcome the deficiency. If the sample is a bad​ sample, there are no graphs or other techniques that can be used to salvage the data.

The IQ score and brain volume are listed for each of five different subjects. Refer to the table of measurements below. Given that the data are matched and considering the units of the​ data, does it make sense to use the difference between each IQ score and brain volume that is in the same​ column? Why or why​ not?

No, it does not make sense to use the difference between each IQ score and brain volume in the same​ column, because IQ scores and brain volumes use different units of measurement.

If we find that there is a linear correlation between the concentration of carbon dioxide in our atmosphere and the global​ temperature, does that indicate that changes in the concentration of carbon dioxide cause changes in the global​ temperature?

No. The presence of a linear correlation between two variables does not imply that one of the variables is the cause of the other variable.

A study is conducted to measure​ children's growth rates without any treatment applied to the children. What best classifies this​ study?

Observational study

Which of the following is NOT true of using the binomial probability distribution to test claims about a​ proportion?

One requirement of this method is that np>5 and nq>5.

Which measure of variation is most sensitive to extreme​ values?

Range

The​ _______ states that​ if, under a given​ assumption, the probability of a particular observed event is exceptionally small​ (such as less than​ 0.05), we conclude that the assumption is probably not correct.

Rare Event Rule for Inferential Statistics

​If, under a given​ assumption, the probability of a particular observed event is extremely​ small, we conclude that the assumption is probably not correct. This represents the​ _______.

Rare Event Rule.

Use software or a calculator to find the​ range, variance, and standard deviation of the​ F-scale measurements from the tornadoes listed the data set available below. Be careful to account for missing data.

Since the data are missing at ​random, the tornadoes with missing values can be deleted from the data set.

​"Because the digits​ 0, 1,​ 2, . . .​ , 9 are the normal results from lottery​ drawings, such randomly selected numbers have a normal​ distribution."

Since the probability of each digit being selected is​ equal, lottery digits have a uniform​ distribution, not a normal distribution.

Why is it important to learn about bad​ graphs?

So that we can critically analyze a graph to determine whether it is misleading

Which of the following is NOT needed to determine the minimum sample size required to estimate a population​ proportion?

Standard Deviation

Which of the following is not a characteristic of the t​ test?

The Student t distribution has a mean of t=0 and a standard deviation of s=1

Which of the following is NOT a requirement for constructing a confidence interval for estimating a population mean with σ ​known?

The confidence level is​ 95%

Which of the following is NOT a reason why the procedures to estimate differences of two proportions or testing a claim about two proportions​ work?

The form of the confidence interval utilizes the same variance as when testing claims using hypothesis tests.

Which of the following is NOT true about the tails in a​ distribution?

The inequality symbol in the alternative hypothesis points away from the critical region.

Which of the following is NOT a property of the linear correlation coefficient​ r?

The linear correlation coefficient r is robust. That​ is, a single outlier will not affect the value of r.

Which of the following is NOT a requirement of testing a claim about a population proportion using a formal method of hypothesis​ testing?

The lowercase​ symbol, p, represents the probability of getting a test statistic at least as extreme as the one representing sample data and is needed to test the claim.

Which of the following is not a requirement for regression​ analysis?

The method for regression analysis line is not robust. It is seriously affected by a small departure from a normal distribution.

Which of the following is not a requirement for testing a claim about a population with σ not​ known?

The population​ mean, μ​, is equal to 1.

In the largest clinical trial ever​ conducted, 401,974 children were randomly assigned to two groups. The treatment group consisted of​ 201,229 children given the Salk vaccine for​ polio, and the other​ 200,745 children were given a placebo. Among those in the treatment​ group, 33 developed​ polio, and among those in the placebo​ group, 115 developed polio. If we want to use the methods for testing a claim about two population proportions to test the claim that the rate of polio is less for children given the Salk​ vaccine, are the requirements for a hypothesis test​ satisfied? Explain.

The requirements are​ satisfied; the samples are simple random samples that are​ independent, and for each of the two​ groups, the number of successes is at least 5 and the number of failures is at least 5.

Which of the following is NOT a requirement of testing a claim or constructing a confidence interval estimate for two population​ portions?

The sample is at least​ 5% of the population.

Twelve different video games showing violence were observed. The duration times of violence were​ recorded, with the times​ (seconds) listed below. What requirements must be satisfied to test the claim that the sample is from a population with a mean greater than 85 ​sec? Are the requirements all​ satisfied?

The sample observations must be a simple random sample. Either the population is normally​ distributed, or n>​30, or both. No. The sample size is not greater than​ 30, the sample does not appear to be from a normally distributed​ population, and there is not enough information given to determine whether the sample is a simple random sample.

Which of the following is NOT a requirement for testing a claim about a population mean with σ ​known?

The sample​ mean, x is greater than 30.

Which of the following is NOT required to determine minimum sample size to estimate a population​ mean?

The size of the​ population, N

Which of the following is NOT a property of the Student t​ distribution?

The standard deviation of the Student t distribution is s=1.

In this section we use r to denote the value of the linear correlation coefficient. Why do we refer to this correlation coefficient as being​ linear?

The term linear refers to a straight​ line, and r measures how well a scatterplot fits a​ straight-line pattern.

Which of the following is NOT a requirement of testing a claim about two population means when σ1 and σ2 are unknown and not assumed to be​ equal?

The two samples are dependent.

What is the relationship between the linear correlation coefficient r and the slope b1 of a regression​ line?

The value of r will always have the same sign as the value of b1.

Which of the following is NOT true when dealing with independent​ samples?

The variance of the differences between two independent random variables equals the variance of the first random variable minus the variance of the second random variable.

If your score on your next statistics test is converted to a z​ score, which of these z scores would you​ prefer: −​2.00, −​1.00, ​0, 1.00,​ 2.00? Why?

The z score of 2.00 is most preferable because it is 2.00 standard deviations above the mean and would correspond to the highest of the five different possible test scores.

Which of the following is not true when using the confidence interval method for testing a claim about μ when σ is​ unknown?

The​ P-value method and the classical method are not equivalent to the confidence interval method in that they may yield different results.

Which of the following is NOT true about​ P-values in hypothesis​ testing?

The​ P-value separates the critical region from the values that do not lead to rejection of the null hypothesis.

When making predictions based on regression​ lines, which of the following is not listed as a​ consideration?

Use the regression line for predictions only if the data go far beyond the scope of the available sample data.

Which of the following is not a strategy for finding​ P-values with the Student t​ distribution?

Use the table in the book to find the​ P-value rounded to at least 4 decimal places.

What design principle is stressed for experiments or observational​ studies?

Using dependent samples with paired data is generally better than using two independent samples

For conducting a​ two-tailed hypothesis test with a certain data​ set, using the smaller of n1−1 and n2−1 for the degrees of freedom results in df=​11, and the corresponding critical values are t=±2.201. Using the formula for the exact degrees of freedom results in df=​19.063, and the corresponding critical values are t=±2.093. How is using the critical values of t=±2.201 more​ "conservative" than using the critical values of ±​2.093?

Using the critical values of t=±2.201 is less likely to lead to rejection of the null hypothesis than using the critical values of ±2.093.

Which of the following is NOT a misuse of​ statistics?

Utilizing valid statistical methods and correct sampling techniques

Which of the following would be a correct interpretation of a​ 99% confidence interval such as 4.1<μ<​5.6?

We are​ 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of μ.

Which of the following is NOT an advantage of pooling sample​ variances?

We often know that σ1=σ2.

Which of the following statements about correlation is​ true?

We say that there is a positive correlation between x and y if the​ x-values increase as the corresponding​ y-values increase.

Which of the following is NOT a property of the standard​ deviation?

When comparing variation in samples with very different​ means, it is good practice to compare the two sample standard deviations. Your answer is correct.

If you are asked to find the 85th​ percentile, you are being asked to find​ _____.

a data value associated with an area of 0.85 to its left

In a​ graph, if one or both axes begin at some value other than​ zero, the differences are exaggerated. This bad graphing method is known as​ _______.

a nonzero axis.

Twenty different statistics students are randomly selected. For each of​ them, their body temperature ​(°​C) is measured and their head circumference​ (cm) is measured. a. For this sample of paired​ data, what does r​ represent, and what does ρ ​represent? b. Without doing any research or​ calculations, estimate the value of r. c. Does r change if body temperatures are converted to Fahrenheit​ degrees?

a. r is a statistic that represents the value of the linear correlation coefficient computed from the paired sample​ data, and ρ is a parameter that represents the value of the linear correlation coefficient that would be computed by using all of the paired data in the population of all statistics students. B. The value of r is estimated to be 00​, because it is likely that there is no correlation between body temperature and head circumference. C. The value of r does not​ change, because r is not affected by converting all values of a variable to a different scale.

In a probability​ histogram, there is a correspondence between​ _______.

area and probability.

What conditions would produce a negative​ z-score?

a​ z-score corresponding to an area located entirely in the left side of the curve

Which of the following is NOT a measure of​ center?

census

A​ _______ random variable has infinitely many values associated with measurements.

continuous

A​ __________ exists between two variables when the values of one variable are somehow associated with the values of the other variable.

correlation

The number of​ _______ for a collection of sample data is the number of sample values that can vary after certain restrictions have been imposed on all data values.

degrees of freedom

Two samples are​ ________________ if the sample values are paired.

dependent

Methods used that summarize or describe characteristics of data are called​ _______ statistics.

descriptive

A​ _______ random variable has either a finite or a countable number of values.

discrete

A​ _______ is a graph of each data value plotted as a point.

dotplot

The​ _______ of a discrete random variable represents the mean value of the outcomes.

expected value

The heights of the bars of a histogram correspond to​ _______ values.

frequency

A​ _____________ is a procedure for testing a claim about a property of a population.

hypothesis test

Two samples are​ ____________ if the sample values from one population are not related to or somehow naturally paired or matched with the sample values from the other population.

independent

Paired sample data may include one or more​ ___________, which are points that strongly affect the graph of the regression line.

influential points

A straight line satisfies the​ __________________ if the sum of the squares of the residuals is the smallest sum possible.

least-squares property

The​ ______________ measures the strength of the linear correlation between the paired quantitative​ x- and​ y-values in a sample.

linear correlation coefficient r

In working with two variables related by a regression​ equation, the​ _________________ in a variable is the amount that it changes when the other variable changes by exactly one unit.

marginal change

The​ _________ hypothesis is a statement that the value of a population parameter is equal to some claimed value.

null

In a​ scatterplot, a(n)​ ______________ is a point lying far away from the other data points.

outlier

When drawings of objects are used to depict​ data, false impressions can be made. These drawings are called​ _______.

pictographs.

A​ _______ variable is a variable that has a single numerical​ value, determined by​ chance, for each outcome of a procedure.

random

Given a collection of paired sample​ data, the​ ____________________ y=b0+b1x algebraically describes the relationship between the two​ variables, x and y.

regression equation

For a pair of sample​ x- and​ y-values, the​ ______________ is the difference between the observed sample value of y and the​ y-value that is predicted by using the regression equation.

residual

A​ ______________ is a scatterplot of the​ (x,y) values after each of the​ y-coordinate values has been replaced by the residual value y−y.

residual plot

The​ _______ is the best point estimate of the population mean.

sample mean

When determining whether there is a correlation between two​ variables, one should use a​ ____________ to explore the data visually.

scatterplot

The​ ___________ is a value used in making a decision about the null hypothesis and is found by converting the sample statistic to a score with the assumption that the null hypothesis is true.

test statistic

For data sets having a distribution that is approximately​ bell-shaped, _______ states that about​ 68% of all data values fall within one standard deviation from the mean.

the Empirical Rule

Twenty-one different video games showing drug use were observed. The duration times of drug use ​(in seconds) were recorded. When using this sample for a t test of the claim that the population mean is greater than 89 ​sec, what does df​ denote, and what is its​ value?

the number of degrees

What does the notation zα indicate?

to its right.

The bars in a histogram​ _______.

touch.

The square of the standard deviation is called the​ _______.

variance.

Twenty different statistics students are randomly selected. For each of​ them, their body temperature ​(°​C) is measured and their head circumference​ (cm) is measured. If it is found that r=​0, does that indicate that there is no association between these two​ variables?

​No, because while there is no linear​ correlation, there may be a relationship that is not linear.

Which of the following is NOT an equivalent expression for the confidence interval given by 161.7<μ<​189.5?

161.7±27.8

Computers are commonly used to randomly generate digits of telephone numbers to be called when conducting a survey. Can a nonstandard normal distribution be used to find the probability that when one digit is randomly​ generated, it is less than 3​? Why or why​ not? What is the probability of getting a digit less than 3​?

A nonstandard normal distribution cannot be used because randomly generated digits have a uniform distribution meaning that each number is equally likely to be chosen. The probability of getting a digit less than 3 is .3000.

A researcher was once criticized for falsifying data. Among his data were figures obtained from 8 groups of subjects​, with 25 individual subjects in each group. These values were given for the percentage of successes in each​ group: 53%,​ 58%, 63%, 46%, 48%, 67%, 54%, 42%. What's wrong with those​ values?

All percentages of success should be multiples of 4. (could be 20) The given percentages cannot be correct.

The​ _______ tells us that for a population with any​ distribution, the distribution of the sample means approaches a normal distribution as the sample size increases.

Central Limit Theorem

Which of the following is always​ true?

In a symmetric and​ bell-shaped distribution, the​ mean, median, and mode are the same.

Survey questions may be misleading if they are​ "loaded." To what does​ "loaded" refer?

Intentionally worded to elicit a desired response

In the data table​ below, the​ x-values are the weights​ (in pounds) of cars and the​ y-values are the corresponding highway fuel consumption amounts​ (in mi/gal).

Is there a relationship or an association between the weight of a car and its fuel consumption​ amount?

In a survey of 662 ​subjects, each was asked how often he or she drank milk. The survey subjects were internet users who responded to a question that was posted on a news website.

It is flawed because it is a voluntary response sample.

Several studies showed that after eating a low-fat cereal for two meals a day​, subjects had lost some weight. A cereal company financed this research. Identify what is wrong.

It is questionable that the sponsor is a cereal company because this sponsor can be greatly affected by the conclusion.

A magazine published a list consisting of the state tax on each gallon of gas. If we add the 50 state tax amounts and then divide by​ 50, we get 27.3 cents. Is the value of 27.3 cents the mean amount of state sales tax paid by all U.S.​ drivers? Why or why​ not?

No, the value of 27.3 cents is not the mean because the 50 amounts are all weighted equally in the​ calculation, but some states consume more gas than​ others, so the mean amount of state sales tax should be calculated using a weighted mean.

Weights of golden retriever dogs are normally distributed. Samples of weights of golden retriever​ dogs, each of size n=​15, are randomly collected and the sample means are found. Is it correct to conclude that the sample means cannot be treated as being from a normal distribution because the sample size is too​ small? Explain.

No; the original population is normally​ distributed, so the sample means will be normally distributed for any sample size.

What does it mean to say that the confidence interval methods for the mean are robust against departures from​ normality?

The confidence interval methods for the mean are robust against departures from​ normality, meaning they work well with distributions that​ aren't normal, provided that departures from normality are not too extreme.

Refer to the sample of body temperatures​ (degrees Fahrenheit) in the table below. Given these​ temperatures, what issue can be addressed by conducting a statistical analysis of the​ data?

The data can be used to address the issue of whether there is a correlation between body temperatures at 8 AM and at 12 AM.

Listed below are body temperatures (°​F) of healthy adults. Why is it that a graph of these data would not be very effective in helping us understand the​ data?

The data set is too small for a graph to reveal important characteristics of the data.

Which of the following is NOT a conclusion of the Central Limit​ Theorem?

The distribution of the sample data will approach a normal distribution as the sample size increases.

Which of the following is NOT a descriptor of a normal distribution of a random​ variable?

The graph is centered around 0.

Which of the following is NOT a requirement for a density​ curve?

The graph is centered around 0.

Which of the following does NOT describe the standard normal​ distribution?

The graph is uniform.

What requirements are necessary for a normal probability distribution to be a standard normal probability​ distribution?

The mean and standard deviation have the values of μ=0 and o=1

Which of the following is NOT a characteristic of the​ mean?

The mean is called the average by statisticians.

If we collect a large sample of blood platelet counts and if our sample includes a single​ outlier, how will that outlier appear in a​ histogram?

The outlier will appear as a bar far from all of the other bars with a height that corresponds to a frequency of 1.

Which of the following calculations is NOT derived from the confidence​ interval?

The population​ mean, μ= (upper confidence limit)+ (lower confidence limit)

The table to the right lists probabilities for the corresponding numbers of girls in three births. What is the random​ variable, what are its possible​ values, and are its values​ numerical?

The random variable is​ x, which is the number of girls in three births. The possible values of x are​ 0, 1,​ 2, and 3. The values of the random value x are numerical.

A movie with a​ 4-star rating is twice as good as one with a​ 2-star rating.

The ratio level of measurement does not apply

An article noted that chocolate is rich in flavonoids. The article reports that​ "regular consumption of foods rich in flavonoids may reduce the risk of coronary heart​ disease." The study received funding from a candy company and a chocolate manufacturers association. Identify and explain at least one source of bias in the study described. Then suggest how the bias might have been avoided.

The researchers may have been more inclined to provide favorable results because funding was provided by a party with a definite interest. The bias could have been avoided if the researchers were not paid by the candy company and the chocolate manufacturers.

A newspaper posted this question on its​ website: "How often do you seek medical information​ online?" Of 1072 Internet users who chose to​ respond, 38% of them responded with​ "frequently." What term is used to describe this type of survey in which the people surveyed consist of those who decided to​ respond? What is wrong with this type of sampling​ method?

The respondents are a​ self-selected sample. Your answer is correct. The respondents are a voluntary response sample. Your answer is correct. Responses may not reflect the opinions of the general population. Many people may choose not to respond to the survey.

A researcher collects a simple random sample of​ grade-point averages of statistics​ students, and she calculates the mean of this sample. Under what conditions can that sample mean be treated as a value from a population having a normal​ distribution?

The sample has more than 30​ grade-point averages. If the population of​ grade-point averages has a normal distribution.

A magazine ran a survey about a web site for downloading music. Readers could register their responses on the​ magazine's web site. Identify what is wrong.

The sample is a voluntary response​ sample, so there is a good chance that the results do not reflect the population.

What is the difference between a standard normal distribution and a nonstandard normal​ distribution?

The standard normal distribution has a mean of 0 and a standard deviation of​ 1, while a nonstandard normal distribution has a different value for one or both of those parameters.

A defunct website listed the​ "average" annual income for Florida as​ $35,031. What is the role of the term average in​ statistics? Should another term be used in place of​ average?

The term average is not used in statistics. The term mean should be used for the result obtained by adding all of the sample values and dividing by the total number of sample values.

A certain medical organization tends to oppose the use of meat and dairy products in our​ diets, and that organization has received hundreds of thousands of dollars in funding from an animal rights foundation.

There does appear to be a potential to create a bias. There is an incentive to produce results that are in line with the​ organization's creed and that of its funders.

Which of the following is NOT true about statistical​ graphs?

They utilize areas or volumes for data that are​ one-dimensional in nature.

What is the goal of learning​ statistics?

To learn to distinguish between statistical conclusions that are likely to be valid and those that are seriously flawed

Which of the following is a common distortion that occurs in​ graphs?

Using a​ two-dimensional object to represent data that are​ one-dimensional in nature

Refer to the accompanying data display that results from a sample of airport data speeds in Mbps. The results in the screen display are based on a​ 95% confidence level. Write a statement that correctly interprets the confidence interval.

We have​ 95% confidence that the limits of 13.05 Mbps and 22.15 Mbps contain the true value of the mean of the population of all data speeds at the airports.

The population of ages at inauguration of all U.S. Presidents who had professions in the military is​ 62, 46,​ 68, 64, 57. Why does it not make sense to construct a histogram for this data​ set?

With a data set that is so​ small, the true nature of the distribution cannot be seen with a histogram.

Refer to the table of body temperatures​ (degrees Fahrenheit). Is there some meaningful way in which each body temperature recorded at 8 AM is matched with the 12 AM​ temperature?

Yes. Each column of 8 AM and 12 AM temperatures is recorded from the same​ subject, so each pair is matched.

Finding probabilities associated with distributions that are standard normal distributions is equivalent to​ _______.

finding the area of the shaded region representing that probability.

We utilize statistical​ _______ to look for features that reveal some useful or interesting characteristics of the data set.

graphs

A value at the center or middle of a data set is​ a(n) _______.

measure of center.

​A(n) _______ distribution has a​ "bell" shape.

normal

A​ _______ histogram has the same shape and horizontal scale as a​ histogram, but the vertical scale is marked with relative frequencies instead of actual frequencies.

relative frequency

In a​ _______ distribution, the frequency of a class is replaced with a proportion or percent

relative frequency

If we are collecting sample data for a​ study, the _____________ that we choose can greatly influence the validity of our conclusions. For​ example, we can use sound statistical methods to analyze data in voluntary response​ samples, but the results are not necessarily valid.

sampling method

A​ _______ is a plot of paired data​ (x,y) and is helpful in determining whether there is a relationship between the two variables.

scatterplot

The standard deviation of the distribution of sample means is​ _______.

sigma/ (square root) n

A data value is considered​ _______ if its​ z-score is less than −2 or greater than 2.

significantly low or significantly high

Whenever a data value is less than the​ mean, _______.

the corresponding z-score is negative.

The notation ​P(z<​a) denotes​ _______.

the probability that the z-score is less than a.

Where would a value separating the top​ 15% from the other values on the graph of a normal distribution be​ found?

the right side of the horizontal scale of the graph

When a data value is converted to a standardized scale representing the number of standard deviations the data value lies from the​ mean, we call the new value a​ _______.

z-score.

Annual incomes are known to have a distribution that is skewed to the right instead of being normally distributed. Assume that we collect a large ​(n>​30) random sample of annual incomes. Can the distribution of incomes in that sample be approximated by a normal distribution because the sample is​ large? Why or why​ not?

​No; the sample means will be normally​ distributed, but the sample of incomes will be skewed to the right.

In the data table​ below, the​ x-values are the weights​ (in pounds) of cars and the​ y-values are the corresponding highway fuel consumption amounts​ (in mi/gal).

​Yes, because​ consumers, in​ general, would prefer to buy a car with a higher level of fuel efficiency. In this​ case, the source of the data would be suspect with a potential for bias.

Which of the following groups of terms can be used interchangeably when working with normal​ distributions?

​areas, probability, and relative frequencies

A​ _______ helps us understand the nature of the distribution of a data set.

frequency distribution