Question 1

A random sample of females was observed to exhibit a lower average level of self-esteem than a random sample of males. To assess the likelihood that this observed difference reflects a real difference in the average self-esteem of the total population of males and females, it is necessary to

Accepted Answer

To assess the likelihood that the observed difference reflects a real difference in the average self-esteem of the total population of males and females, we need to conduct a statistical significance test where we can compare the means of the two groups and determine if the difference is statistically significant. Other options such as constructing a scatterplot or calculating a correlation coefficient are not relevant in this scenario as they refer to assessing the association between two variables, while we are interested in assessing the difference in means between two groups. Plotting the distribution of self-esteem levels among all males and females could be informative, but it does not directly address the question of whether the observed difference is statistically significant or not.

Question 2

To compare verbal intelligence at different age levels, researchers tested and retested a group of children from the time they were 2 until they reached the age of 20. The researcher were clearly using a

Accepted Answer

The researchers were studying the same group of children over a long period of time, which indicates the use of a longitudinal study. A cross-sectional study involves testing different age groups at the same time, and a correlation coefficient and regression toward the mean are statistical methods, not study designs.

Question 3

The ________ can be a particularly misleading indication of what is average for a ________ distribution of scores.

Accepted Answer

The answer of The ________ can be a particularly misleading...

Question 4

Research in which the same group is tested and retested over a period of years is a

Accepted Answer

A longitudinal study involves testing the same group of individuals over a period of time to observe changes or stability in behavior or characteristics. Cross-sectional studies involve testing different groups of individuals at the same time, while scatterplots and regression toward the mean are statistical concepts, not research designs.

Question 5

Ahmed has five sisters who are 3, 3, 5, 9, and 10 years of age. The number "5" represents the ________ of the sisters' ages.

Accepted Answer

The answer of Ahmed has five sisters who are 3,...

Question 6

To test for age differences in intelligence, at the beginning of the school year a researcher gave the same mathematics test to groups of children who were 8, 10, 12, and 14 years of age. This procedure best illustrates a

Accepted Answer

This is because a cross-sectional study involves comparing groups of people at different ages at a single point in time. In this case, the researcher is comparing children of different ages (8, 10, 12, and 14) by giving them the same mathematics test at the beginning of the school year. A scatterplot is a graphical representation of a correlation between two variables, which is not relevant to this scenario. A longitudinal study involves following the same group of individuals over a long period of time to study changes or patterns, which is not the case here. Standard deviation is a measure of the variability or spread of a set of data, which is not relevant to the design of the study.

Question 7

The maximum height of a normal curve corresponds to the ________ of a normal distribution.

Accepted Answer

The maximum height of a normal curve corresponds to the mean of a normal distribution.

Question 8

Statistical significance refers to whether research

Accepted Answer

Statistical significance refers to the probability that research findings are not due to chance variations. It does not indicate whether variables are causally related or if participants were randomly assigned to conditions. While significant results may add support to previous findings, this is not the primary definition of statistical significance.

Question 9

When people's symptoms of emotional distress are at their worst, whatever they do to try to alleviate the condition is likely to be followed by improvement rather than further deterioration. This is best explained in terms of

Accepted Answer

This phenomenon is known as regression toward the mean, which means that extreme scores on any measure tend to be followed by less extreme scores on subsequent measurements due to chance factors. In this case, it means that when people's symptoms are at their worst, they are likely to improve simply due to the fact that it is unlikely for symptoms to remain at such an extreme level over time.

Question 10

When interpreting the results of cross-sectional studies, it is especially important to consider the effects of ________ between generations.

Accepted Answer

Cross-sectional studies compare different groups of people at one point in time, typically looking at a single outcome or characteristic. Social and cultural differences between generations can significantly impact the results of these studies, particularly if the study is attempting to make comparisons between different age groups. It is important to consider how societal changes have occurred over time, and how these might influence the findings of cross-sectional research.

Question 11

After his property was vandalized by a small group of teenagers, Mr. Majka concluded that most teenagers are irresponsible and delinquent. Mr. Majka ought to be reminded that accurate generalizations depend on

Accepted Answer

To make accurate generalizations, it is important to observe representative samples, meaning a sample that reflects the characteristics of the population being studied. Mr. Majka's conclusion is based on a small group of teenagers who vandalized his property, which may not be representative of all teenagers. Therefore, his conclusion is not accurate and he needs to observe a representative sample to draw correct conclusions about teenagers.

Question 12

Faustin, a member of his college's golf team, has an opportunity to play against a nationally acclaimed professional golfer. How many holes of golf should Faustin choose to play with the professional in order to maximize his own slim chances of winning?

Accepted Answer

Playing fewer holes, such as 9, increases the likelihood of variability and chance playing a larger role, which could help Faustin against a more skilled opponent.

Question 13

Although Shien once scored 37 points during a single high school basketball game, he was subsequently unable to beat or match this record no matter how hard he tried. His experience may be at least partially explained in terms of

Accepted Answer

Regression toward the mean suggests that extreme events or scores are unlikely to be repeated and will tend to move toward the average or mean over time. In this case, Shien's initial high score may have been an outlier and thus, unlikely to be replicated.

Question 14

Unusual ESP subjects who defy chance when first tested nearly always lose their "psychic powers" when retested. This best illustrates

Accepted Answer

This phenomenon is known as regression toward the mean, meaning that extreme scores on a measure tend to be followed by scores closer to the mean on subsequent measurements. This is likely due to chance factors that may have influenced the initial measurement. Therefore, when the subjects are retested, they are likely to score closer to the mean, and their abilities are no longer considered unusual or paranormal. This is a well-documented statistical phenomenon and has been observed in various domains, including sports performance, academic achievement, and health outcomes.

Question 15

An observed difference between two sample groups is more likely to be statistically significant if

Accepted Answer

The standard deviation of the sample groups indicates the amount of dispersion in the data. A smaller standard deviation means the data points are closer to the mean, which can increase the likelihood of a statistically significant difference between the two groups.

Question 16

If half the students at Quincy College have blue eyes, which of the following events is most probable?

Accepted Answer

Since half of the students have blue eyes, the probability of each student having blue eyes is 0.5. Using the binomial distribution, the probability that 80% or more of a class of 15 students will have blue eyes is approximately 0.023, which is the highest amongst the given options. The probability decreases as the class size increases, making options B and C even less probable. Therefore, option A is the most probable event.

Question 17

As the size of a sample ________, the size of the standard deviation is most likely to ________.

Accepted Answer

As the size of a sample increases, the standard deviation is most likely to decrease due to the fact that there is more data and therefore more accuracy.

Question 18

One can most accurately estimate a population mean if a sample is

Accepted Answer

A larger sample size allows for a more representative sample of the population, and low variability means that the data points are closer to the population mean. Both of these factors contribute to a more accurate estimate of the population mean.

Question 19

The average scores of two samples taken from the same population are most likely to differ if

Accepted Answer

The answer of The average scores of two samples taken...

Question 20

The ________ is a measure of ________.

Accepted Answer

The standard deviation is a measure of variation, representing how spread out the data is from the mean. The median (A) is a measure of central tendency, specifically the middle value in a distribution. The range (B) also measures variation, but only considers the difference between the highest and lowest values, rather than the spread of all the data. The correlation coefficient (D) measures the strength and direction of a relationship between two variables, not central tendency or variation.

Quiz 16: Statistical Reasoning in Everyday Life