AP Statistics : AP Statistics
Study concepts, example questions & explanations for AP Statistics
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Example Questions
Example Question #2 : How To Identify Characteristics Of A Normal Distribution
Which is the following is NOT a property of the normal distribution?
The total area under the curve is equal to 1
The probability that a random data point is within one standard deviation of the mean is approximately 78%
The normal curve is symmetrical about the mean μ
The mean is at the middle and divides the area into halves
The probability that a random data point is within one standard deviation of the mean is approximately 78%
The empirical rule tells us that the probability that a random data point is within one standard deviation of the mean is approximately 68%, not 78%.
Example Question #1 : How To Identify Characteristics Of A Normal Distribution
Which is the following is true about the standard normal distribution?
It has a mean of 1 and a standard deviation of 0
It has a mean of 1 and a standard deviation of 1
It has a mean of 0 and a standard deviation of 0
It has a mean of 0 and a standard deviation of 1
It has a mean of 0 and a standard deviation of 1
The standard normal distribution is just like any other normal distribution that you might have looked at except that it has a standard deviation of 1 and a mean of 0.
Example Question #11 : Normal Distribution
Cheyenne is worried about food thieves in the break room at work, and she believes that, as the week progresses, and people get lazy and ready for the weekend, more food theft occurs. She gathered the following data on number of thefts per day, and fell very behind in her work for a week.
Which of the following statements about the data are true?
i: the data is normally distributed
ii: the data is skewed left
iii: the data supports Cheyenne's theory
iv: the data is a representative sample
i, iii & iv
ii & iii only
i, ii, and iii
ii, iii & iv
iii only
ii & iii only
The data is not normal by virtue of being skewed left, which also supports Cheyenne's theory... there is no way of knowing wether this data was a representative sample, but also no option with ii, iii and iv was provided to avoid frustration/confusion
Example Question #12 : Normal Distribution
In order to be considered a normal distribution, a data set (when graphed) must follow a bell-shaped symmetrical curve centered around the mean.
It must also adhere to the empirical rule that indicates the percentage of the data set that falls within (plus or minus) 1, 2 and 3 standard deviations of the mean.
In order to be a normal distribution, what percentage of the data set must fall within:
1)
2)
3)
1) 68
2) 95
3) 99.7
1) 65
2) 98
3) 99.7
1) 68
2) 95
3) 98
1) 68
2) 95
3) 98.7
1) 65
2) 98
3) 99.9
1) 68
2) 95
3) 99.7
1) Percentile for Z=1 is .8413 - or - .1587 in one tail - or - .3174 in both tails -
1 - .3174=.6826
2) Percentile for Z=2 is .9772 - or - .0228 in one tail - or - .0456 in both tails -
1 - .0456=.9544
3) Percentile for Z=3 is .9987 - or - .0013 in one tail - or - .0026 in both tails -
1 - .0026=.9974
Example Question #1 : Sampling Distributions
A researcher wants to determine whether there is a significant linear relationship between time spent meditating and time spent studying. What is the appropriate null hypothesis for this study?
This question is about a linear regression between time spent meditating and time spent studying. Therefore, the hypothesis is regarding Beta1, the slope of the line. We are testing a non-directional or bi-directional claim that the relationship is significant. Therefore, the null hypothesis is that the relationship is not significant, meaning the slope of the line is equal to zero.
Example Question #102 : Statistical Patterns And Random Phenomena
Example Question #1 : Sampling Distributions
Example Question #2 : Sampling Distributions
The president of a country is trying to estimate the average income of his citizens. He randomly samples residents and collects information about their salaries. A 
There is a 
There is a 
If he was to take another sample of the same size and compute a 
There is a 
There is a
A confidence interval is a statement about the mean of the population the sample is drawn from so there is a 
Example Question #101 : Statistical Patterns And Random Phenomena
Assume you have taken 100 samples of size 64 each from a population. The population variance is 49.
What is the standard deviation of each (and every) sample mean?
.7
.35
.9
.65
.875
.875
The population standard deviation =
The sample mean standard deviation =
Example Question #2 : How To Find Sampling Distribution Of A Sample Mean
Reaction times in a population of people have a standard deviation of 
Use the fact that 
Alternately, you can use the fact that the variance of the sample mean varies inversely by the square root of the sample size, so to reduce the variance by a factor of 10, the sample size needs to be 100.
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