Question 1

The bigger the margin of error,the smaller the confidence interval.

Accepted Answer

The bigger the margin of error, the larger the confidence interval, as the margin of error reflects the range within which the true population parameter is expected to lie with a certain level of confidence.

Question 2

A student draws a playing card from a standard pack of 52.What is the probability that the student draws a king or a heart?
A)1/4
B)4/13
C)7/52
D)13/52

Accepted Answer

The probability of drawing a king is 4/52 (since there are 4 kings in a deck of 52 cards), and the probability of drawing a heart is 13/52 (since there are 13 hearts in a deck). However, one of the hearts is also a king, so we must subtract the probability of drawing the king of hearts so it's not counted twice. This gives us (4/52 + 13/52) - 1/52 = 16/52 - 1/52 = 15/52, which simplifies to 4/13.

Question 3

The standard error is a measure of variability.

Accepted Answer

The standard error measures the variability or dispersion of the sampling distribution of a statistic, typically the mean, indicating how much the sample mean is expected to vary from the true population mean.

Question 4

A sample consists of four observations,scored as 1,3,5,7.What is the standard deviation?
A)2.55
B)2.58
C)3.02
D)3.99

Accepted Answer

The answer of A sample consists of four observations,scored as...

Question 5

A sample survey is an example of an observational study.

Accepted Answer

In a sample survey, researchers collect data by observing or questioning participants without manipulating any variables, which is characteristic of an observational study.

Question 6

The centre of a confidence interval is a sample statistic.

Accepted Answer

The center of a confidence interval is typically the point estimate of the parameter being estimated, which is a sample statistic (e.g., sample mean, sample proportion).

Question 7

The standard error is a measure of central tendency.

Accepted Answer

The standard error is a measure of the variability or precision of a sample statistic (such as the mean) estimate of a population parameter, not a measure of central tendency.

Question 8

A sample mean is an example of a point estimate.

Accepted Answer

A sample mean is used to estimate the population mean, making it a point estimate which represents a single value estimate of a population parameter.

Question 9

A population mean is an example of a point estimate.

Accepted Answer

The answer of A population mean is an example of...

Question 10

The average height of a randomly selected group of adult males could be a discrete random variable.

Accepted Answer

The average height of a group is a continuous random variable because height can take on any value within an interval, making it possible to have fractions of a unit (e.g., centimeters or inches), which is characteristic of continuous data.

Question 11

900 secondary school students are selected randomly from across the country because they have achieved 10 GCSEs at grade A -C.There is a standard deviation of 0.4.Assuming a 95% confidence rate,what is the margin of error?
A)0.011
B)0.025
C)0.178
D)0.555

Accepted Answer

The margin of error is calculated using the formula: Margin of Error = Z * (σ/√n). For a 95% confidence level, the Z-score is approximately 1.96. Given σ = 0.4 and n = 900, the margin of error is 1.96 * (0.4/√900) = 0.025.

Question 12

The confidence interval is a type of point estimate.

Accepted Answer

A confidence interval is a type of interval estimate that is used to indicate the reliability of an estimate. It is not a point estimate, which refers to a single value that serves as the best guess or prediction of a parameter.

Question 13

The standard error is calculated only from sample attributes.

Accepted Answer

The standard error measures the dispersion or variability of a sampling distribution, and it is calculated using attributes (such as the mean or proportion) from a sample, not the entire population.

Question 14

The annual number of UK lottery winners could be a discrete random variable.

Accepted Answer

The annual number of UK lottery winners is countable and each outcome is distinct and separate, fitting the definition of a discrete random variable.

Question 15

The best method for investigating casual relationships is an observational study.

Accepted Answer

The best method for investigating causal relationships is an experimental study, where the researcher manipulates one variable to observe the effect on another variable, allowing for control over confounding variables.

Question 16

An observational study requires fewer resources than an experiment.

Accepted Answer

The answer of An observational study requires fewer resources than...

Question 17

The standard deviation requires knowledge of at least one population parameter.

Accepted Answer

The standard deviation is a measure of the spread of a population, and it requires knowledge of the population mean.

Question 18

A sample survey is an example of an experimental study.

Accepted Answer

A sample survey is an example of an observational study, not an experimental study, because it involves observing and recording information without manipulating any variables.

Question 19

The standard deviation is calculated only from sample attributes.

Accepted Answer

The standard deviation can be calculated from both sample and population data, not just sample attributes.

Question 20

The number of twentieth-century US presidential elections is not a discrete random variable.Why not?
A)There is no integer.
B)The integer does not vary and is not random.
C)It results from random process.
D)Another reason.

Accepted Answer

The number of twentieth-century US presidential elections is a fixed count (not varying or random), making it a constant rather than a discrete random variable.

Quiz 12: Comparing Several Means