Stats Final

The value of a parameter may change as the sample value changes.

A type of research inference involves using a statistic to estimate a parameter

The value of a statistic is fixed

In theory, the value of a continuous variable may take any value in some interval of numbers

A random sample guarantees a representative sample

For an experiment, a researcher manipulates conditions under which observations are made

A random sample maximizes the probability of obtaining a representative sample

The science of statistics can be used to prove anything a researcher would like to prove

For an observational study, a researcher merely records values of the dependent variable. That is, the researcher does not manipulate conditions under which observations are made.

The value of a statistic may change as the sample changes

Boxplots are a graphical display of the 5-number summary

If two events A and B are disjoint, then A ∩ B = {0}

For the data set consisting of the four numbers -3, -2, -2, -5, a valid measure of spread for all the data will be <0

The sample mean x̄, is always the balance point of the relative frequency histogram for the data

The sample median x̃, is always the balance point of the relative frequency histogram of the data

A positive correlation between two quantitative variables X and Y implies that as one increases the other tends to decrease

A positive correlation between two quantitative variables X and Y implies that as one increases, the other tends to increase

If two events are disjoint, then A U B = ϕ

The probability of the sample space is less than 1 when the probability of all the events contained in the sample space is less than 1.

The Standard Normal Curve is always symmetric around 0

When two events A and B are independent, the P (A and B) = P (A) X P (B)

When Z~ N (0, 1), then P (Z ≤ -1.34) = P (Z > 1.34)

When X~ N ( μ, σ), then x̄~ N ( μ, σ/√n)

When two events A and B are independent, then P (A ∩ B) = P (A) + P (B)

The Rule of Thumb for independence when drawing without replacement from a population states when the sample size is ≤ 5% of the population size, we can assume the draws are independent

H0: μ = 0 is only rejected when the p-value is > 0.05

H1: μ ≠ 0 is only accepted when the p-value > 0.05.

Suppose a 95% confidence interval for a population mean μ is given by (-17.32, 13.1). Then there is a 5% chance that μ will fall outside this interval.

Suppose a 95% confidence interval for a population mean μ is given by (-17.32, 13.1). Then there is a 95% chance that μ will fall in this interval.

If the sampled population is normal, then the sampling distribution of x̄ is normal when based on a random sample.

The number of new projects started each month at a cancer research center for the last nine months are: 0, 6, 10, 10, 12, 12, 16, 30 The sample median x̃ for the data is given by:

The number of new projects started each month at a cancer research center for the last nine months are: 0, 6, 10, 10, 12, 12, 16, 30 The IQR for the above data is:

The number of new projects started each month at a cancer research center for the last nine months are: 0, 6, 10, 10, 12, 12, 16, 30 Based on our Rule of Thumb for outliers, the following holds:

Which of the following sets of numbers has the smallest possible variance?

The variance of 11 measurements of newborn height's (measured in inches) is computed to be 4 with a sample mean height of 20. The units for the sample mean are:

The variance of 11 measurements of newborn height's (measured in inches) is computed to be 4 with a sample mean height of 20. The standard deviation of these measurements is:

The units for the variance are

Volunteers for a research study were divided into three groups. Group 1 listened to Western religious music, Group 2 listened to Western rock music, and Group 3 listened to Chinese religious music. The blood pressure of each volunteer was measured before and after listening to the music, and the change in blood pressure was recorded. The scatterplot is given below What does the scatterplot suggest about the correlation between change in blood pressure and type of music?

Volunteers for a research study were divided into three groups. Group 1 listened to Western religious music, Group 2 listened to Western rock music, and Group 3 listened to Chinese religious music. The blood pressure of each volunteer was measured before and after listening to the music, and the change in blood pressure was recorded. The scatterplot is given below What could we do to explore the relationship between type of music and change in blood pressure?

Events A, B, and C represent all possible outcomes of an experiment. That is, the sample space is given by S= {A, B, C}. Which of the following does not have to be true?

A fair coin is tossed two times in succession and the following events are defined: A: {Observes at least one head} B: {Observe exactly two heads} C: {Observe exactly one head} The sample space for this experiment is given by:

A fair coin is tossed two times in succession and the following events are defined: A: {Observes at least one head} B: {Observe exactly two heads} C: {Observe exactly one head} Using classical assignment of probability, the P(C) is:

Three experimental groups representing fitness levels for a random sample of U.S. men aged 35-45 were determined. The following chart represents the boxplots for the variable resting heart rate: Which experimental group has the largest IQR?

Which of the following recorded variables is continuous?

Which of the following recorded variables is categorical?

Which of these variables is categorical?

Does ginkgo biloba enhance memory? In a study to find out, 100 adult subjects who take ginkgo biloba once a day were randomly selected and 100 adults who do not take ginkgo biloba were randomly selected. Each group was given a memory test. The average score for the ginkgo biloba group was 82.78 and for the no-ginkgo group the average score was 73.46 The population(s) of interest are:

Does ginkgo biloba enhance memory? In a study to find out, 100 adult subjects who take ginkgo biloba once a day were randomly selected and 100 adults who do not take ginkgo biloba were randomly selected. Each group was given a memory test. The average score for the ginkgo biloba group was 82.78 and for the no-ginkgo group the average score was 73.46 The parameters of interest for this study are:

Does ginkgo biloba enhance memory? In a study to find out, 100 adult subjects who take ginkgo biloba once a day were randomly selected and 100 adults who do not take ginkgo biloba were randomly selected. Each group was given a memory test. The average score for the ginkgo biloba group was 82.78 and for the no-ginkgo group the average score was 73.46 The dependent variable for this study is given by:

Does ginkgo biloba enhance memory? In a study to find out, 100 adult subjects who take ginkgo biloba once a day were randomly selected and 100 adults who do not take ginkgo biloba were randomly selected. Each group was given a memory test. The average score for the ginkgo biloba group was 82.78 and for the no-ginkgo group the average score was 73.46 The statistics calculated for this study are:

Does ginkgo biloba enhance memory? In a study to find out, 100 adult subjects who take ginkgo biloba once a day were randomly selected and 100 adults who do not take ginkgo biloba were randomly selected. Each group was given a memory test. The average score for the ginkgo biloba group was 82.78 and for the no-ginkgo group the average score was 73.46 Is the claim "ginkgo biloba causes memory improvement" supported by this study?

The Gallup survey organization obtained a random sample of 2,527 U.S. citizens. The proportion in the sample who favored a constitutional amendment that would define marriage as being between a man and a woman was 1289/2527 = 51% The population of interest consists of:

The Gallup survey organization obtained a random sample of 2,527 U.S. citizens. The proportion in the sample who favored a constitutional amendment that would define marriage as being between a man and a woman was 1289/2527 = 51% The percentage of the 2527 citizens who favor the amendment is an example of:

The Gallup survey organization obtained a random sample of 2,527 U.S. citizens. The proportion in the sample who favored a constitutional amendment that would define marriage as being between a man and a woman was 1289/2527 = 51% The dependent variable is:

A study was conducted to determine the effect of a new low-density lipoprotein (LDL) cholesterol lowering drug compared to the currently prescribed drug. 5000 U.S. adults aged 45-65 with "high" LDL cholesterol (> 130 milligrams per deciliter (mg/dL)) were randomly selected. 2500 of the adults were randomly assigned to the new drug group and 2500 of the adults were randomly assigned to the control (currently prescribed) drug group. At the end of the 1-year study period, the average LDL cholesterol level for the 2500 patients in the new drug group was 112 mg/dL and the average LDL cholesterol level for the control drug group was 125 mg/dL. What are the population(s) of interest for this study?

A study was conducted to determine the effect of a new low-density lipoprotein (LDL) cholesterol lowering drug compared to the currently prescribed drug. 5000 U.S. adults aged 45-65 with "high" LDL cholesterol (> 130 milligrams per deciliter (mg/dL)) were randomly selected. 2500 of the adults were randomly assigned to the new drug group and 2500 of the adults were randomly assigned to the control (currently prescribed) drug group. At the end of the 1-year study period, the average LDL cholesterol level for the 2500 patients in the new drug group was 112 mg/dL and the average LDL cholesterol level for the control drug group was 125 mg/dL. What is the dependent variable?

A study was conducted to determine the effect of a new low-density lipoprotein (LDL) cholesterol lowering drug compared to the currently prescribed drug. 5000 U.S. adults aged 45-65 with "high" LDL cholesterol (> 130 milligrams per deciliter (mg/dL)) were randomly selected. 2500 of the adults were randomly assigned to the new drug group and 2500 of the adults were randomly assigned to the control (currently prescribed) drug group. At the end of the 1-year study period, the average LDL cholesterol level for the 2500 patients in the new drug group was 112 mg/dL and the average LDL cholesterol level for the control drug group was 125 mg/dL. What type of variable is the dependent variable?

A study was conducted to determine the effect of a new low-density lipoprotein (LDL) cholesterol lowering drug compared to the currently prescribed drug. 5000 U.S. adults aged 45-65 with "high" LDL cholesterol (> 130 milligrams per deciliter (mg/dL)) were randomly selected. 2500 of the adults were randomly assigned to the new drug group and 2500 of the adults were randomly assigned to the control (currently prescribed) drug group. At the end of the 1-year study period, the average LDL cholesterol level for the 2500 patients in the new drug group was 112 mg/dL and the average LDL cholesterol level for the control drug group was 125 mg/dL. What type of variable is the independent variable drug?

A study was conducted to determine the effect of a new low-density lipoprotein (LDL) cholesterol lowering drug compared to the currently prescribed drug. 5000 U.S. adults aged 45-65 with "high" LDL cholesterol (> 130 milligrams per deciliter (mg/dL)) were randomly selected. 2500 of the adults were randomly assigned to the new drug group and 2500 of the adults were randomly assigned to the control (currently prescribed) drug group. At the end of the 1-year study period, the average LDL cholesterol level for the 2500 patients in the new drug group was 112 mg/dL and the average LDL cholesterol level for the control drug group was 125 mg/dL. The statistics calculated for this study are:

A study was conducted to determine the effect of a new low-density lipoprotein (LDL) cholesterol lowering drug compared to the currently prescribed drug. 5000 U.S. adults aged 45-65 with "high" LDL cholesterol (> 130 milligrams per deciliter (mg/dL)) were randomly selected. 2500 of the adults were randomly assigned to the new drug group and 2500 of the adults were randomly assigned to the control (currently prescribed) drug group. At the end of the 1-year study period, the average LDL cholesterol level for the 2500 patients in the new drug group was 112 mg/dL and the average LDL cholesterol level for the control drug group was 125 mg/dL. The parameters of interest in this study are:

A study was conducted to determine the effect of a new low-density lipoprotein (LDL) cholesterol lowering drug compared to the currently prescribed drug. 5000 U.S. adults aged 45-65 with "high" LDL cholesterol (> 130 milligrams per deciliter (mg/dL)) were randomly selected. 2500 of the adults were randomly assigned to the new drug group and 2500 of the adults were randomly assigned to the control (currently prescribed) drug group. At the end of the 1-year study period, the average LDL cholesterol level for the 2500 patients in the new drug group was 112 mg/dL and the average LDL cholesterol level for the control drug group was 125 mg/dL. The research inference of interest is given by:

A study was conducted to determine the effect of a new low-density lipoprotein (LDL) cholesterol lowering drug compared to the currently prescribed drug. 5000 U.S. adults aged 45-65 with "high" LDL cholesterol (> 130 milligrams per deciliter (mg/dL)) were randomly selected. 2500 of the adults were randomly assigned to the new drug group and 2500 of the adults were randomly assigned to the control (currently prescribed) drug group. At the end of the 1-year study period, the average LDL cholesterol level for the 2500 patients in the new drug group was 112 mg/dL and the average LDL cholesterol level for the control drug group was 125 mg/dL. The design of this study is given by:

The legal profession conducted a study to determine the percentage of cardiologists who had been sued for malpractice in the last five years. The sample was randomly chosen from a national directory of doctors. What is the dependent variable of interest in this study?

Ignoring twins and other multiple births, assume babies born at a hospital are independent events with the probability that a baby is a boy and the probability that a baby is a girl both equal to 0.5 What is the probability that the next two babies are of the same sex?

Ignoring twins and other multiple births, assume babies born at a hospital are independent events with the probability that a baby is a boy and the probability that a baby is a girl both equal to 0.5 Define the events A = { the next two babies are boys}, and B = { the next two babies are girls}. What do we know about events A and B?

Draws made with replacement are:

Draws made without replacement are:

In the last mayoral election in a large city, 47% of the adults over the age of 65 voted Republican. A researcher wishes to determine if the proportion of adults over the age of 65 in the city who plan to voted Republican in the next mayoral election has changed. Let p represent the proportion of the population of all adults over the age of 65 in the city who plan to vote Republican in the next mayoral election. In terms of p, the researcher should test which of the following null and alternative hypotheses?

The resting pulse rate for all runners in the New York City marathon for 2013 has a mean of μ = 70 and standard deviation of σ = 3. Suppose 49 runners are randomly selected from this population. The distribution of x̄, the sample average resting pulse rate, is given by:

The resting pulse rate for all runners in the New York City marathon for 2013 has a mean of μ = 70 and standard deviation of σ = 3. Suppose 49 runners are randomly selected from this population. Find the probability that the sample average pulse rate of the 49 runners exceeds 70.86.

The power of a test of hypotheses is defined as:

You have measured the systolic blood pressure of a random sample of 80 employees of a large company located near you. You use the default confidence interval formula of a statistical software package to calculate a 95% confidence interval for the mean systolic blood pressure for all employees of this company ( denoted by μ). The calculated confidence interval is (122, 138) What requirements are necessary for this confidence interval to be valid?

You have measured the systolic blood pressure of a random sample of 80 employees of a large company located near you. You use the default confidence interval formula of a statistical software package to calculate a 95% confidence interval for the mean systolic blood pressure for all employees of this company ( denoted by μ). The calculated confidence interval is (122, 138) Which of the following statements gives a valid interpretation of the phrase "95% confident μ is in the interval (122, 138)?

Suppose the resting pulse rate for all runners in the 2015 New York City marathon a week after the event has a mean of μ = 70 and a standard deviation of σ = 3. Supposed 64 runners will be randomly selected from this population The distribution of x̄, the sample average resting pulse rate, is given by:

Suppose the resting pulse rate for all runners in the 2015 New York City marathon a week after the event has a mean of μ = 70 and a standard deviation of σ = 3. Supposed 64 runners will be randomly selected from this population Find the probability that the sample average resting pulse rate of the 64 runners is less than 70.9375

Suppose that A and B are two independent events. The probability that event A occurs in 0.4 (i.e. P(A) = 0.4), and that B occurs is P(B) = 0.2. What is the probability that both A and B occur?

A random sample of size n = 36 is to be drawn from a population with μ = 500 and σ = 200. What is the probability that the sample mean exceeds 400?

The scores of individual students interested in majoring in a Health Science program on the American College Testing (ACT) Program Composite College Entrance Examination are normally distributed with a mean of 18.6 and standard deviation of 6.0. Find the proportion of scores that are greater than 33.6

The scores of individual students interested in majoring in a Health Science program on the American College Testing (ACT) Program Composite College Entrance Examination are normally distributed with a mean of 18.6 and standard deviation of 6.0. Find the proportion of scores falling in the interval [12.42, 31.2]

The scores of individual students interested in majoring in a Health Science program on the American College Testing (ACT) Program Composite College Entrance Examination are normally distributed with a mean of 18.6 and standard deviation of 6.0. Find the proportion of scores that are less than 4.02

The attached table provides data from "A Case-Control Study of the Effectiveness of Bicycle Safety Helmets in Preventing Facial Injury" For the group that did not wear helmets, find the risk for facial injury

The attached table provides data from "A Case-Control Study of the Effectiveness of Bicycle Safety Helmets in Preventing Facial Injury" For those who did not wear helmets, find the odds of facial injuries to non-facial injuries

The attached table provides data from "A Case-Control Study of the Effectiveness of Bicycle Safety Helmets in Preventing Facial Injury" Find the odds ratio for facial injuries in the group that did not wear helmets to the group that did wear helmets