Question 1

An "error" in statistics refers to a quality of the data that arises due to poor scientific skills.

Accepted Answer

An "error" in statistics refers to a random variation or deviation from the true value, which can occur due to a variety of reasons such as sampling error, measurement error, or natural variation. While poor scientific skills could potentially contribute to these errors, they are not the only cause.

Question 2

Descriptive statistics enable scientists to make predictions and estimate a phenomenon.

Accepted Answer

Descriptive statistics summarize and describe the features of a dataset, but they do not enable predictions or estimations about a phenomenon; that's the role of inferential statistics.

Question 3

Kinnebrook's error was that his recorded observations differed from someone else's observations.

Accepted Answer

Kinnebrook's error was that his recorded observations disagreed with another observer's recorded observations.

Question 4

The Central Limit Theorem is not an assumption of inferential statistics as long as the sample size is large enough.

Accepted Answer

The answer of The Central Limit Theorem is not an...

Question 5

The Central Limit Theorem allows scientists to make inferences about the population parameters based on an empirical set of observations.

Accepted Answer

The Central Limit Theorem states that sampling distribution of the means of any independent, random variable will be normal or nearly normal, if the sample size is large enough. This allows scientists to make inferences about population parameters based on the sample mean and its distribution, assuming certain conditions are met.

Question 6

When researchers use parametric inferential statistics to make decisions, they are assuming that the Central Limit Theorem is true.

Accepted Answer

The Central Limit Theorem is a fundamental concept in parametric inferential statistics, which assumes that if the sample size is large enough, the distribution of the sample means will be approximately normal regardless of the underlying distribution of the population. Therefore, researchers using parametric inferential statistics assume that the Central Limit Theorem is true.

Question 7

Inferential statistics are used mainly for formality. If the sample mean of one group is larger than the other group, you can safely conclude that there was a statistically significant different based on the existence of a difference alone, without computing any statistics.

Accepted Answer

Inferential statistics are used to draw conclusions about a population based on sample data. Simply observing a difference between two groups does not necessarily mean that the difference is statistically significant. Statistical tests must be conducted to determine the likelihood of the observed difference occurring by chance.

Question 8

The Central Limit Theorem makes claims about individual scores.

Accepted Answer

The Central Limit Theorem does not make claims about individual scores, but rather about the distribution of sample means from a population.

Question 9

The sampling distribution of means is a distribution of experimental effects.

Accepted Answer

The sampling distribution of means is a theoretical distribution that represents the distribution of sample means over repeated sampling from the same population, not a distribution of experimental effects.

Question 10

In a sampling distribution of means, the observations that make up a sample must be randomly selected.

Accepted Answer

In order for a sampling distribution of means to accurately represent the population mean, the samples must be randomly selected. When samples are not randomly selected, the results may be biased and not representative of the population.

Question 11

Under the Central Limit Theorem, the mean of your observed sample in an experiment will always be equal to the population mean.

Accepted Answer

The Central Limit Theorem states that as sample size increases, the distribution of sample means approaches a normal distribution with a mean equal to the population mean. However, the mean of a specific observed sample may not necessarily be equal to the population mean.

Question 12

The further away from the distribution mean a sample mean is, the less likely it is to occur.

Accepted Answer

This is true according to the properties of normal distributions, which are symmetric and centered around their mean. Therefore, extreme values on either side of the mean have lower probabilities of occurring compared to values closer to the mean.

Question 13

The mean of a sampling distribution is the same value as the population mean.

Accepted Answer

The mean of a sampling distribution is an unbiased estimator of the population mean, hence it should be the same value as the population mean.

Question 14

A sampling distribution that is made up of a sample size of 5 will have smaller variability than a sampling distribution that is made up of a sample size of 10.

Accepted Answer

A larger sample size typically leads to a smaller variability in the sampling distribution, so a sampling distribution with a sample size of 10 would likely have smaller variability than a sampling distribution with a sample size of 5.

Question 15

The standard deviation of a sampling distribution of n = 20 will be larger than the standard deviation of a sampling distribution of n = 50.

Accepted Answer

The standard deviation of a sampling distribution decreases as sample size increases. Therefore, a larger sample size (n = 50) will have a smaller standard deviation than a smaller sample size (n = 20).

Question 16

A sample mean that falls within one standard deviation of the population mean is considered an outlier.

Accepted Answer

A sample mean that falls within one standard deviation of the population mean is not considered an outlier. In fact, a sample mean within one standard deviation of the population mean is quite common and expected. An outlier is typically defined as a data point that is unusually far from the rest of the data, often falling more than three standard deviations away from the mean.

Question 17

In hypothesis testing, the null hypothesis is a hypothesis of an effect.

Accepted Answer

The null hypothesis is actually a hypothesis that there is no effect or relationship between variables.

Question 18

If we know the actual means of our null and alternative populations, we do not need to conduct hypothesis testing.

Accepted Answer

If we already know the actual means of our null and alternative populations, then we don't need to conduct hypothesis testing since we would already know whether they are significantly different or not.

Question 19

In hypothesis testing, you first have to select the alpha level before calculating the test statistic.

Accepted Answer

This is true. The alpha level is often set at 0.05, meaning there is a 5% chance of rejecting the null hypothesis when it is actually true. It is important to select an appropriate alpha level based on the context and potential consequences of a Type I error.

Question 20

Which of the following describes an "error" in statistics?
A) A careless mistake made by scientists during measurement of an observation.
B) A range of values obtained by measuring an observation.
C) The amount by which an observation differs from its expected value.
D) None of the above

Accepted Answer

An "error" in statistics is the amount by which an observation differs from its expected value. A careless mistake made by scientists during measurement would be considered a "mistake" rather than an error, and a range of values obtained by measuring an observation would be considered a "margin of error" or "uncertainty" rather than an error.

Quiz 8: The Central Limit Theorem and Hypothesis Testing