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)