Chapter 7 Stat Quiz
normal probability distribution
the distribution is bell shaped and follows the empirical rule
sampling error
the gap between sample statistics ad population parameters
higher the confidence lvel
the lower that risk that the interval is not contained in the parameter
margin of error (E)
the width of that range is determined by this
critical value for 90%
z=1.65
critical value for 95%
z=1.96
critical value for 99%
z=2.58
In the same scenario as Question 7.17, suppose you obtained a mean of $167 spent on transportation and a standard deviation of $40. Calculate a 95% confidence interval for the mean and select the values that come closest to those that would fill the spaces in the following interpretation: we can be 95% confident that the mean amount of money spent on transportation lies between _____ and _____ .
$148 and $186, use t formula
calculating ci for the mean with a samll sample and unknown sd
ci= x bar + t(s/ sq rt n)
pop sd unknow n>30
ci= x bar + z(s/sq rt n)
the higher the confidence level the wider the
confidence interval
A common Gallup poll question asks Americans whether they would like to see handguns banned. A recent poll indicated that 27% of those polled by Gallup said "Yes." Calculate the margin of error for that figure, assuming a 95% confidence level and a sample size of 1,000 respondents. (Only input the number)
2.7517
What is the critical value of z for the 95% confidence level?
1.96
Determine the critical value in the z-distribution for a 98% confidence level; make sure to use two decimal places.
2.33
What is the critical value of z for the 99% confidence level?
2.58
Suppose that in the same sample of residents from the preceding question, you were able to change your sample size. For a 95% confidence level, match the following confidence interval limits with their associated sample sizes.
5-8, n=600 6-10, n=400 4-12, n=200
This question is based upon EOC 8.41. You wish to construct a confidence interval that is narrower than the 95% confidence interval. Which level of confidence should you choose?
90%
three most common levels of confidence
90,95,99
Sort the following intervals in order of width, from narrowest to widest (assuming the SD is constant in all three cases).
95 n=500 95 n=100 99 n=100
The highest level of confidence that is conventionally used with large samples is
99
Suppose that you run a survey research firm and have a reasonably good budget but you want to impress your client with your cost efficiency as well as data quality. You can select from three possible options. Which option would you select?
= 1,500, margin of error = ± 1.1
the larger the sample size the narrower the
confidence interval
confidence interval formula
C.I.= x bar +- E (x= sample mean, E= margin of error)
C.I. for the mean with a known population standard deviation
C.I.= x bar =- zc(standard deviation)
A 95% level of confidence means that 95 of every 100 samples taken would do which of the following? (Select all that apply)
Capture the mean from the population., Capture the proportion from the population.
Pretend that you are a Project Manager for a local survey research firm. Your firm has been hired by your city council to ask residents a short survey about local issues, such as whether they supported a proposed by-law which required cat owners to purchase a license for their pet. Your surveys tend to cost $10 per respondent. Which of the following options would you choose?
Sample size of 250, for a margin of error of ±3.5% at the 95% level
Which of the following would be an example of a point estimate? (Select all that apply)v
The percentage of Gallup poll respondents who said that they intended to vote in the next U.S. presidential election., The mean age of a sample of registered voters from the most recent U.S. presidential election.
Imagine that you were studying the weight of children in the United Kingdom. Which of the following would be an example (or examples) of an interval estimate? (Select all that apply)
The proportion of children who are overweight is estimated to be between 35% to 45%., The average weight of all British 5-year-olds is between 39.5 and 44.5 pounds.
Which one of the following sampling methods is more likely to be appropriate for calculating confidence intervals?
Use the telephone book to gather all of the phone numbers of 300 members of a small town and draw 150 of them out of a large hat.
interval estimate
a range of values within the population parameter is likely to fall
point estimate
a single statistic that is used as our best estimate of an unknown population parameter
Confidence interval
a type of probability statistic that specifies the range of values we use to estimate the location of an unknown population parameter
sampling theory
a well drawn probability sample will usually yield results that very closely resemble those that we would get if we measured the entire pop
confidence level
accompanied by the margin of error and tells us how likely our parameter is to lie within that interval
As our confidence level increases, the width of our confidence interval ______.
also increases
the margin of error
an estimate about the amount of difference that we think is possible between our statistic and its corresponding parameter
larger sample size
associated with a narrower width
The reason that you would select the option that you did above is due to what is known as _____.
diminishing returns
probability sample
every element has a known probability of being selected; normally involving a random mechanism
simple random sampling
every member of the pop of interest has an equal chance of selection
Confidence Intervals can be used for almost any type of distribution.
false
Is the following statement true or false? "A 90% confidence level can be interpreted to mean that 90% of residents of New York City have given between $10-$20 to homeless persons."
false
Is the following statement true or false? "A 95% confidence level can be interpreted to mean that 95% of all households in the UK earned between 30,000 GBP and 45,000 GBP last year."
false
precision
give us a specific figure
smaller sample size
greater width
As the confidence level increases, what happens to the margin of error?
increases
The effect of changing the sample size is rooted in the law of , which tells us that the larger our sample size, the less sampling error there is likely to be.
large numbers
higher level of confidence is included with
larger sample sizes
the higher the level the
lower the risk that our interval estimate does not contain the parameter
Imagine that you are conducting a poll to determine the percentage of adults who gamble at least once a month. As your sample size increases (let us say from 100 to 400 cases), which of the following becomes true?
margin of error becomes smaller
Match the following components of a poll with their corresponding examples.
margin of error- =+- 2.8% level of confidence- 19/20 confidence interval limits- 37.2% to 42.8%
example of point estimate
mean number of fb friends among people under 35 is 220, percentage of the under 35 pop whouse fb is 67
example of confidence interval
mean number of fb friends is bw 200 and 240
lower confidence level
more risk tat their interval estimate does not contain the parameter
accuracy
not mistakes but to freedom from error or the extent to which our estimate from the parameter of interests true value
confidence intervals for proportions
p+-zc(sq rt pq/n)
Confidence intervals are based on the idea that it is relatively rare for us to have a known
parameter
Level of confidence refers to the probability that our interval estimate will contain the _____.
parameter
example of interval estimate
people under 35 have between 200 and 240 fb friends
While the main advantage of a point estimate is its _____, its main disadvantage is its _____.
precision, inaccuracy
Another name for sampling error is _____ error.
random
What is the size of the margin of error due to? (Select all that apply)
the amount of variation in the sample, the size of the sample n
The gap between a statistic and its corresponding parameter is known as
sampling error
Sort the following four steps for calculating a confidence interval into their correct order.
select a sample stat, select desired confidence level, determine the margin of error, specify the upper and lower limits of the confidence interval
Sort these items into the order that you would use them in order to calculate the confidence interval for the mean.
select a sample statistic select a desired confidence level determine the margin of error using the standard error of the mean specify the upper and lower limits of the confidence interval
One of the two key assumptions for confidence intervals is that the researcher has used _____ ____ ____. (Hint: 3 words)
simple random sampling
most populations values are unknown bc
size of populations, time and effort it would involve
confidence interval
specifies a range of values within which we estimate that a population parameter will fall
confidence level
specifies the probability that the population parameter will indeed lie within that specified range of vales
standard error for proportions
sq rt pq/n
The symbol σ_x̅ represents the ___ of the mean
standard error
sq rt pq/n
standard error for proportions
unknown population parameter
such as mean or a proportion
Confidence Intervals assume that you have used simple random sampling.
true
the true amount of sampling error is usually
unkown bc the parameter is usually unknown
law of large numbers
w/a sufficiently large sample size, sample statistics (means) will tend to approximate population parameters very closely
example of confidence level
we are 95% confident that the true pop mean number of fb friends falls within a range of 200 to 400 friends
inferential statistics
what confidence intervals lie within
The higher the level of confidence that is used, the ______ confidence interval will be.
wider
margin of error formula
z* or t* (standard error sd/sq rt n)
