chapter 1 Flashcards
(38 cards)
what is probability distribution of a random variable X?
it tells us what values X can take and how to assign probabilities to those values
if we take a simple random sample from a normal population, what is the distribution of the sample?
It is also normal distribution
if we take a simple random sample from a population that is skewed, what kind of distribution does the sample follow?
it will follow the same probability distribution unless the sample is big enough for the central limit theory to kick in
what is the central limit theory?
if the sample size from the population is equal or larger than 30 than you can assume that the probability distribution of the sample is normal
when you find the probability on the Z score, what is the area under the curve?
it the the left area under the curve
review formula for confidence interval?
slide 44 chapter 1
review the formula for the margin of error
slide 44 chapter 1
what is the critical Z value?
the Z value for the percentage of the confident interval
interpret this confidence interval, a 95% confidence interval for the true mean sentence time for all criminals convicted of this crime?
if we took repeated samples of 10 criminals and calculated the interval in a similar manner, then 95% of such intervals would contain the true mean sentence time for all criminals convicted of this crime
an airport manager would like to estimate the true mean number of minutes passengers arrive before their scheduled flight departure. suppose it is known that arrival times follow a normal distribution with standard deviation 15 minutes. a random sample of 9 passengers arrived an average of 70 minutes before their flight. construct a 98% confidence interval?
(58.37, 81.63)
a manager at a grocery store would like to estimate the true mean amount of money spent by customers in the express lane. she selects a simple random sample of 50 receipts and calculates a 97% confidence interval for the true mean to be ($15.50, $20.25). interpret this. confidence interval?
97% of similarly constructed intervals would contain the population mean
as the confidence level of the confidence interval increase, how does that impact the confidence interval?
the confidence interval gets wider
92% (103.7, 132.3)
95% (102.0, 134.0)
as we increase confidence, how does that impact the precision of our estimation?
the estimations get further apart, our precision reduces bur our confidence increases
how can we reduce the length of the confidence interval without sacrificing our precision of estimation?
we can increase the sample size (n)
review how to find the margin of error?
slide 69 chap 1
review how to solve for n?
slide 69 chap 1
suppose it is known that the nicotine that the content of a certain brand of cigarettes follows a normal distribution with a standard deviation 0.1 mg. we would like to take a sample of cigarettes large enough to estimate the true mean nicotine content to within 0.04 mg, with 98% confidence. how many cigarettes do we need to sample in order to achieve this?
n= ((Z x standard deviation)/ margin of error) ^2
n= 33.81 = 34
if the P value is greater > than alpha, do we reject or fail to reject Ho?
we fail to reject it
if the P-value us less < than alpha, do we reject or fail to reject Ho?
we reject it
if Z* is greater than Z when Z is positive, do we reject or fail to reject Ho?
we fail to reject it
if Z* is less than Z when Z is positive, do we reject or fail to reject Ho?
we reject Ho
if Z* is greater than Z when Z is negative, do we reject or fail to reject Ho?
we reject Ho
if Z* is less than Z when Z is negative, do we reject or fail to reject Ho?
we fail to reject H0
what is type 1 error?
when you reject Ho but Ho is true
