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Terms in this set (18)
Suppose a student earns a 75 on his statistics exam, and his grade has a z-score of 1.5. Since the class did not perform well on the exam, the professor announces that she will adjust the grades by adding 10 points to each score. How will this adjustment change the student's z-score?
Your z-score will not change since the adjustment shifts the entire distribution of scores but does not change the relative position of your score in the class.
How can you tell from a boxplot if the distribution is symmetric?
The median is in the center of the box, and the left and right whiskers are approximately the same length.
Suppose every student in a class is surveyed and it is found that 75% of the class plans to take another math class. It is reported that 75% of all students at the school plan to take another math class. Is this an example of descriptive or inferential statistics? Explain.
Inferential statistics; the results of the class sample are extended to make a generalization about the population of all students at the school.
What is the symbol used to represent the population mean?
μ
A community college faculty is negotiating a new contract with the school board. The distribution of faculty salaries is skewed right by several faculty members who make over $100,000 per year. If the faculty want to give the community the impression that they deserve higher salaries, should they advertise the mean or median of their current salaries?
The faculty should use the median to make their argument. The median will be lower than the mean since the mean is influenced by the few extremely high salaries.
When an odd number of data values are arranged in order, the median is the middle value.
...
If someone's gross annual income has a z-score of positive 2, what can be concluded?
Their income is 2 standard deviations above the mean income.
Suppose the list below shows how many text messages Elyse sent each day for the last 10 days. If Elyse wants to know how many text messages she typically sends each day, which measure of central tendency better describes the typical number of text messages per day?
Median; The median of 27.5 is a better representative of the center since it is resistant to the one extreme value. The mean of 33.3 is not representative of the typical number of texts since only one number is larger than the mean.
Which measure of center (mean or median) is resistant? Explain what it means for that measure to be resistant.
The median is resistant because it is not sensitive to extreme values in the data set. If the largest observation was doubled, for example, the median would not change since that largest value does not factor into its computation.
In a typical boxplot, the length of the box indicates which measure of spread?
IQR
If each monthly cell phone bill in the country were doubled, how would the mean of the cell phone bills be affected?
The mean of the cell phone bills would double.
A company advertises a mean lifespan of 1000 hours for a particular type of light bulb. If you were in charge of quality control at the factory, would you prefer that the standard deviation of the lifespans for the light bulbs be 5 hours or 50 hours? Why?
5 hours would be preferable since a smaller standard deviation indicates more consistency.
A company was conducting a survey to investigate people's spending habits and how they may have changed in recent years. One question on the survey was, "Did you spend more/less/the same amount of money this year as you did in 2007, the year the recession began in earnest in this country?" Is this question biased? If so, what answer does it favor?
This question is biased toward "spend less," since it mentions the recent recession. Many people would feel that they should answer that they spent less, since the country is in a recession.
The mean is found by adding all the data values and dividing by the total number of values.
...
Suppose every student in a class is surveyed and it is reported that 75% of the class plans to take another math class. Is this an example of descriptive or inferential statistics? Explain.
Descriptive statistics; The results of the class sample are described without making any generalizations about the population of all students at the school.
What must be true for a sample to be considered a simple random sample?
Every possible sample of that size must have the same chance of being selected.
Which of the following is NOT needed to construct a boxplot?
Mean
In a television advertisement, a company called "Waist Away" claimed the workout program on their set of DVDs would help people lose weight more than any other DVD workout program. To test this claim, an independent company, called "Slim Down," selected one other DVD program. They then randomly assigned half the volunteers to the Waist Away program and the other half to the Slim Down program. Each participant was weighed before they started the program and then regularly participated in their assigned program for one month. After one month, each participant was weighed again. The percent of weight lost was recorded for each person, where negative values indicated a weight gain. What type of study was performed?
experiment
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