True or False 1.The goal of descriptive statistics is to simplify, summarize, and organize data. 2.A summary value, usually numerical, that describes

1. The goal of descriptive statistics is to simplify, summarize, and organize data. $[\text{True}]$
2. A summary value, usually numerical, that describes a sample is called a parameter. $[\text{False}]$
3. A researcher records the average age for a group of 25 preschool children selected to participate in a research study. The average age is an example of a statistic. $[\text{True}]$
4. The median is the most commonly used measure of central tendency. $[\text{False}]$
5. The mode is the best way to measure central tendency for data from a nominal scale of measurement. $[\text{True}]$
6. A distribution of scores and a mean of 55 and a standard deviation of 4. The variance for this distribution is 16. $[\text{True}]$
7. In a distribution with a mean of $M=36$ and a standard deviation of $SD=8$, a score of 40 would be considered an extreme value. $[\text{False}]$
8. In a distribution with a mean of $M=76$ and a standard deviation of $SD=7$, a score of 91 would be considered an extreme value. $[\text{True}]$
9. A negative correlation means that as the X values decrease, the Y values also tend to decrease. $[\text{True}]$
10. The goal of a hypothesis test is to demonstrate that the patterns observed in the sample data represent real patterns in the population and are not simply due to chance or sampling error. $[\text{True}]$

Step 1. The goal of descriptive statistics is to simplify, summarize, and organize data.
True. Descriptive statistics aims to provide a clear and concise summary of the data by using various measures, such as measures of central tendency (mean, median, mode) and measures of dispersion (variance, standard deviation). It helps in understanding the main characteristics of the data set.
Step 2. A summary value, usually numerical, that describes a sample is called a parameter.
False. A summary value that describes a sample is called a statistic, not a parameter. Parameters are summary values that describe a population, while statistics describe a sample.
Step 3. A researcher records the average age for a group of 25 preschool children selected to participate in a research study. The average age is an example of a statistic.
True. The average age recorded by the researcher for the group of 25 preschool children is an example of a statistic. It is a summary value calculated from the sample data.
Step 4. The median is the most commonly used measure of central tendency.
False. The median is one of the measures of central tendency, but it is not necessarily the most commonly used. The choice of measure depends on the nature of the data and the specific research question.
Step 5. The mode is the best way to measure central tendency for data from a nominal scale of measurement.
True. For data from a nominal scale of measurement, where the values are categories or labels without any inherent numerical value, the mode is the most appropriate measure of central tendency. It represents the category that occurs most frequently in the data set.
Step 6. A distribution of scores has a mean of $M=55$ and a standard deviation of $SD=4$. The variance for this distribution is 16.
True. The variance is equal to the square of the standard deviation. In this case, the standard deviation is $SD=4$, so the variance can be calculated as $S{D}^2=4^2=16$.
Step 7. In a distribution with a mean of $M=36$ and a standard deviation of $SD=8$, a score of 40 would be considered an extreme value.
False. To determine if a score is considered an extreme value, we need to consider how far the score deviates from the mean in terms of standard deviations. In this case, the score of 40 is within one standard deviation from the mean, so it would not be considered an extreme value.
Step 8. In a distribution with a mean of $M=76$ and a standard deviation of $SD=7$, a score of 91 would be considered an extreme value.
True. To determine if a score is considered an extreme value, we need to consider how far the score deviates from the mean in terms of standard deviations. In this case, the score of 91 is more than two standard deviations above the mean, so it would be considered an extreme value.
Step 9. A negative correlation means that as the X values decrease, the Y values also tend to decrease.
False. A negative correlation means that as the X values increase, the Y values tend to decrease. It indicates an inverse relationship between the variables, where one variable tends to decrease as the other variable increases.
Step 10. The goal of a hypothesis test is to demonstrate that the patterns observed in the sample data represent real patterns in the population and are not simply due to chance or sampling error.
True. The goal of a hypothesis test is to assess whether the observed patterns or differences in the sample data are statistically significant and can be generalized to the population. It helps in determining whether the patterns are likely to be real and not just due to random chance or sampling error.