stat 201 exam 1 homework questions
Which of the following is a continuous variable?
daily high temperature in New York City
Your statistics teacher has gathered information on each of the students in your class in order to illustrate the difference between discrete and continuous variables. For each student, she has recorded their height, number of credit hours completed and the time it took for them to complete their last exam. The variable "number of credit hours completed" is
discrete.
A social worker records the marital status of each of her patients and whether or not they suffer from depression. Indicate whether each variable is categorical or quantitative.
marital status: categorical; depression: categorical
Would you expect the following pair of variables measured for 200 individuals aged 18-32 to have a positive association, negative association, or no association: age of vehicle and mileage for vehicle?
positive association
The regression equation predicting the average weight of a male aged 18-24 (y) based on his height (x) is given by ModifyingAbove y with caretyequals=minus−172.63plus+4.842x. Describe the correlation between height and weight based on the slope of the regression line
positive correlation since the slope is positiv
A distribution that has the right tail longer than the left tail is considered
skewed to the right
For the following variable, indicate whether you would expect its histogram to be symmetric, skewed to the right, or skewed to the left. The scores of students (out of 100 points) on a very difficult exam in which most score poorly, but a few score very well
skewed to the right
median
the midpoint of the observations when they are ordered from the smallest to the largest (or from the largest to the smallest) When the number of observations n is odd, the median is the middle observation in the ordered sample. When the number of observations n is even, two observations from the ordered sample fall in the middle, and the median is their average the number of observations is even, the median is the average of the two middle values
mean
the sum of the observations divided by the number of observations
mode
the value that occurs most frequently
The characteristics observed to address the questions posed in a study are called
variables.
Give an example of a quantitative variable. Select all that apply.
weight number of siblings
A survey of American adults asks "Would you like to see more or less government spending on natural disasters?" Of the 1496 respondents, 723 responded "more" or "much more". What does the population of interest consist of?
All American adults
Give an example of a categorcal variable. Select all that apply.
Dating status Religious affiliation
The statement "A meteorologist constructs a graph showing the total precipitation in Phoenix, Arizona in each of the months of a given year" refers to which aspect of a statistical study?
Description
The statement "The average age of the students in a statistics class is 25 years" refers to which aspect of a statistical study?
Description
According to a study, the median household income was $ 51 comma 341$51,341 for one group, and $ 30 comma 799$30,799 for another. The mean for each group was $ 72 comma 154$72,154 and $ 45 comma 010$45,010, respectively. Does this suggest that the distribution of houshold income for each group is symmetric, skewed to the right, or skewed to the left? Explain.
The fact that the mean is larger than the median for each group indicates that there are extremely large incomes that are affecting the mean, suggesting that the shape is skewed to the right
A survey of American adults asks "Would you like to see more or less government spending on natural disasters?" Of the 1496 respondents, 723 responded "more" or "much more". The proportion of respondents who responded "more" or "much more" is an example of what?
A statistic
What is the difference between categorical and quantitative variables?
A variable is called categorical if each observation belongs to one of a set of categories. A variable is called quantitative if observations on it take numerical values that represent different magnitudes of the variable.
Determine whether the summary measure is better described as a parameter or a statistic. The average weekly amount spent on groceries by a family of four based on a random sample of 100 families
Statistic
A survey of American adults asks "Would you like to see more or less government spending on natural disasters?" Of the 1496 respondents, 723 responded "more" or "much more". What does the sample consist of?
The 1496 respondents
The regression equation predicting the average weight of a male aged 18−24 (y) based on his height (x) is given by (y=−172.63+4.842x ) Interpret the slope of the regression line.
For every unit increase in height, the predicted weight increases by 4.842 pounds.
The statement "Based on previous clients, a marriage counselor concludes that the majority of marriages that begin with cohabitation before marriage will result in divorce" refers to which aspect of a statistical study?
Inference
From past figures, it is predicted that 39% of the registered voters in California will vote in the June primary. Which type of statistics does this statement reflect, inferential statistics or descriptive statistics?
Inferential statistics
The distribution of salaries of professional basketball players is skewed to the right. Which measure of central tendency would be the best measure to determine the location of the center of the distribution?
Median
Determine whether the summary measure is better described as a parameter or a statistic. The average height of horse jockeys
Parameter
Your statistics teacher has gathered information on each of the students in your class in order to illustrate the difference between categorical and quantitative variables. For each student, she has recorded their major, gender, age and height. The variable "age" is an example of what type of variable?
Quantitative
Suppose you were to collect data for the pair of given variables in order to make a scatterplot. For the variables time spent on homework and exam grade, which is more naturally the response variable and which is the explanatory variable?
Time spent on homework: explanatory variable Exam grade: response variable
Empirical Rule
To find the interval for approximately 68% of the observations, calculate (x-s) and (x+s) To find the interval for approximately 95% of the observations, calculate (x-2s) and (x+2s) To find the interval that contains all or nearly all of the observations, calculate (x-3s) and (x-3s)
A lobbyist for a major airspace firm assigns a number to each legislator and then uses a computer to randomly generate ten numbers. The lobbyist contacts the legislators corresponding to these numbers. This technique produces a random sample.
True
The information we gather with experiments and with surveys is collectively called data
True
Almost all of the acidity of soda pop comes from the phosphoric acid which is added to give them a sharper flavor. Is there an association between the pH of the soda and the amount of phosphoric acid (in grams)? The correlation between pH and phosphoric acid is minus−0.991. Describe the association.
Very strong linear association in a negative direction
Describe a situation in which it is inappropriate to use the correlation to measure the association between two quantitative variables.
When the association is not linear
A survey of automobiles parked in the student and staff lots at a large college recorded the make and model of the automobiles. The variable "make" is
categorical.
Your statistics teacher has gathered information on each of the students in your class in order to illustrate the difference between discrete and continuous variables. For each student, she has recorded their height, number of credit hours completed and the time it took for them to complete their last exam. The variable "height" is
continuous.
