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Chapters 8,9
Questions and Formulas
69
Other
Undergraduate 1
10/28/2013

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Term
What are the two branches of statistics?
Definition
descriptive and inferential
Term
One of the most common uses of the inferential branch is to use sample statistics, such as ___, to estimate population parameters, such as ___.
Definition
x bar; mu
Term
X bar is a ____of mu because x should be pretty close to the value of mu.
Definition
point estimate
Term
What do sample statistics estimate?
Definition
population parameters
Term
If x bar is a point estimate of mu than p hat is a point estimate of ___.
Definition
p
Term
We know the value of x bar is porbably pretty close to mu, but we want to get even closer. So rather than just say x bar is close to mu, we are going to build an interval around x bar, and then say that mu probably lies somewhere on this interval. We call this an____.
Definition
interval estimate
Term
Since we can't get the full population mean, we go for the next best thing. WE take a sample and calculate a sample mean and what we add and subtract from the sample mean to get the interval estimate is the _____.
Definition
margin of error
Term
When we construct interval estimates, we call them_____.
Definition
confidence intervals
Term
So a confidence interval of a parameter consists of an interval of numbers, and this interval is our_____.
Definition
point estimate +/-our margin of error
Term
WE call the value we obtain when we take the point estimate MINUS the margin of error the_____or______.
Definition
lower limit or lower bound
Term
We call the value we obtain when we take the point estimate plus the margin of error the_____or_____.
Definition
upper limit or upper bound
Term
As you increase the level of confidence, what happens to the size of the interval?
Definition
they get wider
Term
How do you calculate the wdith of a confidence interval?
Definition
subtract the upper limit from the lower limit
Term
How do you calculate the sample mean if you know the confidence interval?
Definition
add the lower limit and the upper limit and divide by two
Term
The sample mean, x bar will always be in the middle of the confidence interval. The sample mean x bar will always be in the confidence interval but the population mean ___may or may not be on the confidence interval.
Definition
mu
Term
How do you calculate the margin of error if you know the sample mean and the confidence interval?
Definition
subtract the sample mean from the upper limit. or subtact the lower limit from the sample mean
Term
The level of confidence is always written as a ____.
Definition
percent
Term
When dealing with population proportions, the confidence interval is the sample proportion p hat. P hat can be determined by dividing x/n. X is ________and n is _____.
Definition
x is the number of indviduals in the sample with the desired characteristic and n is the sample size
Term
The ____will always be a multiple of the standard error.
Definition
margin of error
Term
The standard error when constructing a confidence interval to estimate a population proportion will be:
Definition
sqrt phat(1- p hat)/n
Term
The margin fo error when constructing a confidence interval to estimate a population proportion will always be _____.
Definition
some number times the formula to calculate standard error for a population proportion. The number you multiply by the standard error to get the margin of error completely depends on the level of confidence
Term
What is the general formual for a confidence interval for a population proportion?
Definition
p hat +/- Z sqrt p hat(1- phat)/n
Term
In 95 percent confidence intervals, the Z value equals ____.
Definition
1.96
Term
For these confidence intervals to be valid, we need to check some requirements as we did back when we were determinng the sampling dsitribution for the sample proportion. The following two things must be true:
Definition
n(p hat) greater than or equal to 15 AND
n(1-p hat) greater than or equal to 15
Term
The drug Lipitor is meant to lower cholesterol levels. In a clinical trial of 884 randomly selected patients who received 10 mg doses of Lipitor daily, 221 reported a headache as a side effect. Obtain a point estimate for the population proportion of users who will experience a headache.
Definition
p hat=221/884=.25
Term
The drug Lipitor is meant to lower cholesterol levels. In a clinical trial of 884 randomly selected patients who received 10 mg doses of Lipitor daily, 221 reported a headache as a side effect. Verify that the requirements for constructing a confidence interval about p are satisfied.
Definition
n(p hat)=221 which is greater than 15
n(1- p hat)=663 which is greater than 15
yes it is a valid interval
Term
How do you find 1.96 for a 95% confidence interval?
Definition
1-.95=.5 .5/2=.025. put it stat crunch calculator with mean=zero and sd=1, hit compute and you get 1.96
Term
How do you find the z score for a 90% confidence interval?
Definition
10/100/2=.05 go to stat, calc, normal, plug in a mean of zero and a sd of 1. look for the second blank and plug .05 in the third blank. the second blank will be the z score
Term
To get the margin of error you multiply the ____by the standard error.
Definition
z score
Term
Can there ever be a 100 percent confidence interval?
Definition
no
Term
What happens to the interval if you increase the sample size?
Definition
it gets narrower
Term
As the level of confidence increases, the margin of error____and the confidence interval gets______.
Definition
increases; wider
Term
AS the level of confidence decreases, the margin of error_____and the confidence interval gets_____.
Definition
decreases; narrower
Term
As the sample size increases, the margin of error_____and the confidence interval gets_____.
Definition
decreases; narrower
Term
As the sample size decreases, the margin of error_____and the confidence interval gets_____.
Definition
increases; wider
Term
When calculating the confidence interval for the population proportion, the symbol for point estimate is what?
Definition
p hat
Term
When calculating the confidence interval for the population proportion, what is the formula for margin of error?
Definition
Z[sqrt p hat(1- p hat)/n]
Term
When calculating the confidence interval for the population proportion, how do you find the standard error?
Definition
sqrt p hat(1-phat)/n
Term
How do you calculate the confidence interval for the population proportion?
Definition
p hat +/- sqrt phat(1-phat)/n
Term
Can you use statcrunch to calculate confidence intervals for population proportions?
Definition
yes
Term
When you are constructing a confidence interval to estimate a population mean, what is the point estimate?
Definition
the sample mean
Term
When constructing a confidence interval to estimate a population mean, how do you find the standard error?
Definition
s/sqrt n
Term
What is s in the standard error formula when constructing a confidence interval to estimate a population mean?
Definition
standard deviation
Term
How do you find degrees of freedom?
Definition
n-1
Term
How do you calculate the confidence interval for a population mean?
Definition
x bar +/- T (s/sqrt n)
Term
When is the confidence interval for a population mean considered valid?
Definition
when you use a random sample AND either use a sample size >30 OR when we are sampling from a normal population
Term
When you are constructing a confidence interval for a population mean, what is the point estimate?
Definition
x bar
Term
When you are constructing a confidence interval for a population mean, how do you find the margin of error?
Definition
T s/sqrt n
Term
HOw do yuo find the standard error when you are constructing a confidence interval for a population mean?
Definition
s/sqrt n
Term
HOw dyou find a confidence interval for a population mean?
Definition
x bar +/- T (x/sqrt n)
Term
When the null hypothesis is rejected, we say that there is or is not enough evidence to reject the null hypothesis and side with the alternative hypothesis?
Definition
there is enough evidence
Term
When the null hypothesis is not rejected, do we say there is or is not enough evidence to reject the null hypothesis?
Definition
is not enough evidence
Term
When performing significance tests about a population proportion, what three assumptions must be true?
Definition
the data is categorical, the data are obtained using randomization, we need the shape of the sampling distribution of the sample proportion to be approximately normal (np >15 and n(1-pnought)>15
Term
What is the p value if it is a right tailed test?
Definition
the area to the right of the z score
Term
What is the p value if you are doing a left tailed test?
Definition
the area to the left of the z score
Term
What is the p value if you are doing a two tailed test?
Definition
the sum of the area to the left of the negatie z score plus the area to the right of the positive z score
Term
What is another word for significance value?
Definition
alpha
Term
What do you do if the p value is less than alpha?
Definition
reject the null hypothesis
Term
What do you do if the p value is greater than alpha(signifance value)?
Definition
we do not reject the null hypothesis
Term
When performing significance tests about a population mean, what three assumptions need to be true?
Definition
the variable is quantitative, the data are obtained using randomization, the population distribution is approximately normal or we are using a sample size greater than 30
Term
What is a type one error?
Definition
we reject H nought when H in fact H nought is true
Term
What is a type two error
Definition
We do not reject H nought when in fact H nought is false and Ha is true
Term
If a type 1 error was made, what three statements would apply?
Definition
the null hypothesis was rejected, the researcher decided there was enough evidence to indicate a change in the mean age, actually the mean age has not changed significantly
Term
If a type two error was amde, which of the following statements would apply?
Definition
the null hypothesis was not rejected, the researcher decided there was not enough evidence to indicate a change in the mean age, actually the mean age has changed significantly
Term
A type one error means we reject the null hypothesis when the null hypothesis is_____.
Definition
actually true
Term
A type two error means we do not reject the null hypothesis when the null hypothesis is _____.
Definition
really false
Term
If the confidence interval contains the value we are testing then do we reject or not reject the null hypothesis?
Definition
we do not reject the null hypothesis
Term
IF the confidence interval does not contain the value we are testing then do we reject or not reject the null hpothesis?
Definition
do not reject
Term
Are you more likely to reject H nought with a large or small p value?
Definition
small
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