Exam 2 Flashcards
You randomly sample 100 students on campus and find that 57 of them prefer pepsi products to coke products. You want to test is this significantly different from the US average preference of pepsi products of 50%
Test?
1 or 2 tailed?
1 pop test for percent
2 tailed
You sample Lake Jones and find an average of 40 Corbicula per sq. meter in the sediments. Somehow, you know the population standard deviation of # of Corbicula is 0.4. Is the number of Corbicula in Lake Jones significantly less than the US avg. of 50 per square meter?
Test?
1 or 2 tailed?
1 pop z-test for mu
1 tailed
has the percent of people that exercise daily increased? you compare the percent found for 100 randomly chosen people to the known percent for 2012.
test?
1 or 2 tailed?
1 pop z-test for percent
1 tailed
For a binomial data set, if p=0.1 and n=4, then the distribution of all possible outcomes will always be_______
skewed right
Showing the possible outcomes using a graph is called a probability __________-.
histogram
what are the 4 aspects of a good sample?
- random
- independent
- no bias
- covers entire population
T/F for a binomial distribution, the distribution of all possible outcomes and their probabilities will appear normally distributed if n is large enough.
False
Which hypothesis is tested directly? Null or alternative?
Null hypothesis
what type of correct decision do you want to make and why?
Type B
What type of wrong decision do you least want to make and why?
Type II
Explain three ways you could reduce the length of a confidence interval (make the interval contain fewer values)?
- increase sample size (n)
- decrease level of confidence
- decrease population mean
If you DON’T want to reject the null hypothesis, what will you need to do to support your claim that the null hypothesis is really true in the population?
increase sample size
T/F if the population is normally distributed, then the sample distribution of sample means will also always be normally distributed.
true
T/F the standard deviation of the sampling distribution of sample means is a measure of the variability in possible sample means that could be sampled from a population.
True
Numerical random variables are divided into what two groups?
Discrete random variables and continuous random variables
what is probability?
all possible outcomes and their population probabilities
what do probability distributions represent?
theoretical populations and population parameters
what must the sum of all the probabilities equal?
1 or 100%
what is a binomial variable?
a subgroup with 2 possible outcomes which are classified as success or failure
what is classified as a rare event?
any outcome with a probability that is less than 0.05
what is the shape of the binomial probability distribution at with a mean of 50%?
unimodal and symmetric
what is the shape of the binomial probability distribution with a mean of 25%
unimodal and skewed right
what is the shape of the binomial probability distribution with a mean of 75%
unimodal and skewed left
what can impact binomial histogram shape?
sample size and probability
will a normal probability distribution always look unimodal, symmetric, and bell shaped
not always, but often
what does p represent?
the probability of a desired outcome
what is q representative of?
the probability of a nondesired outcome
normal distribution provides a reasonable approximation to a binomial probability when what?
np > 5 and nq > 5
what are the 4 key concepts of statistics?
- good sample
- sampling error
- sampling distribution of sample means (SDSM)
- central limit theorem
T/F in the statistical sense, sampling error is not a mistake
T
What is sampling error?
a measure of variability in possible samples
what does xbar represent?
sample mean
what is the sampling distribution of sample means?
the distribution of all possible sample means that could be sampled in some population
will n decreasing or increasing give more information about the population?
increasing
as n increases, will the sample mean grow closer to the population mean?
yes it will
if a population is normal, the SDSM will _____ be normal
always
what is the central limit theorem
the SDSM from a population that is not normal will still look normal if n is large enough
how big must n be for us to assume it will be normally distributed
n > 30
what is standard error and what does it represent
a measure of variability in possible sample means from the same population
as sample size increases what happens to standard error and why?
it decreases because we have more information about the population
what is inference
when you take sample information and draw conclusions about the population
sample value is a ______ for _________
point estimate
population parameter
what is a point estimate a best guess of?
the population parameter
sample mean symbol
x bar
population mean symbol
mu
sample standard deviation
s
population standard deviation
sigma
how do you back up point estimates?
use interval estimates
what are confidence intervals
range of numbers you think include the true population value
what sentence do you use to explain the confidence interval?
“I am 95% confident that (parameter) is between (lower limit) and (upper limit)
when describing the confidence interval, what must you say?
- the level of confidence (ex: 95%)
- the upper and lower limits
- the specific parameter
what factors are confidence interval size tied to?
level of confidence
sample size
standard deviation
how does confidence interval length react if sample size increases?
length decreases
how does confidence interval length react if standard deviation increases?
length increase
what two types of hypotheses are there?
- null hypothesis (H(o))
- alternative hypothesis (H(a))
which hypothesis is directly tested?
the null hypothesis
if you do not have a statistically different outcome, ______
you cannot reject the null hypothesis
can you prove a null hypothesis is true
no, only that you cannot reject it
what do t-distribution curves depend on for shape?
sample size, as n decreases, t-distribution curve becomes less peaked and more spread out
alpha represents
the probability of a type I error
T/F if your test statistic fall in the ‘critical region,’ you will accept the null hypothesis
false
decreasing the sample size will cause the length of the confidence level to ______
increase
Decreasing the variability in the population will cause the length of the confidence interval to:
decrease
Decreasing the sample mean will cause the confidence interval to _____
not change
F or T For every statistical test we have discussed so far, if we reject the null hypothesis, the probability of a type one error is less than 5%
True
T or F The risk of a Type I error is directly controlled in a hypothesis test by establishing a level for alpha
true
T/F if our decision in a hypothesis test is to fail to reject the null hypothesis, then we know that the null hypothesis must be true
False
explain the difference between point estimates and interval estimates.
Point estimate: one number that is your best guess of a population point parameter
interval estimate: a range of values you think include the true population value
You have failed to reject the null hypothesis when it is false, and therefore you have made a A) Type A correct decision. B) Type B correct decision. C) Type I error. D) Type II error.
D) type II error
T/F if the P value is less than the level of significance, then the decision must not reject the null hypothesis
False
T/F for a 95% confidence interval, you are 95% sure that the interval includes the sample mean.
False
T/F all else equal, a 95% confidence interval will have a larger interval length compared to a 90% confidence interval
true
You est the null hypothesis that ear infections as a child do not affect later hearing ability You end up reject the null hypothesis. You could have made:
a) a Type I Error
b) a Type II Error
c) You know you didn’t make an error since you rejected the null hypothesis
d None of the above are correct answers
A) a type I error
T/F random variables require that they are the outcome of some chance event
True
one possible reason why your data do not follow a binomial distribution could be that the data are or are not randomly distributed.
Are not
For the standard normal distribution, the mean will always equal 0 and the standard deviation will be 1.
true
If you have lots of observations for a continuous variable, you can smooth out the frequency histogram bars into a _______
density curve
T/F the standard normal curve is always symmetric around a value of 0.
true
for the standard normal curve, what number value divides the upper 50% from the rest?
the mean
T/F the histograms of all sampling distributions of sample means will be symmetrical.
False
T/F the standard error is equal to the standard deviation of the sampling distribution of the sample mass.
True
T/F if the population is normally distributed then the sampling distribution of the sample means will always be normally distributed.
True
As sample size increases, a randomly selected sample will have a sample mean that is closer to the true population value. T/F
True
As sample size increases, the sampling distribution of sample means will become more peaked and less spread out. T/F
True
T/F For n < 100, the t-distribution will be more peaked and less spread out than the z-distribution.
False
