chapter 8: confidence intervals

Question 1

what is a confidence interval for a population mean?

Answer 1

interval constructed around the sample mean so that we are reasonably sure, or confident, that this interval contains the population mean

when we actually select the sample, we will observe one particular sample from the extremely large number of possible samples

Therefore, we will obtain one particular confidence interval from the extremely large number of possible confidence intervals

we call the interval [x- ± .22]

supposedly, we do not know for sure the true value of the population mean

Question 2

95 percent confidence interval for μ

Answer 2

95 percent of all intervals that we might obtain contain μ, and 5 percent of these intervals do not contain σ

Question 3

the confidence coefficient

Answer 3

The probability that a confidence interval for a population parameter will contain the population parameter

(before sampling)

we start by choosing the probability (for example, .95 or .99) that the confidence interval will contain the population mean

Question 4

the margin of error

Answer 4

expresses the farthest that the sample mean x- might be from the population mean μ

for a given level of confidence

an be expressed in the form [x- ± margin of error].

Question 5

what are the advantages of increasing a confidence level

Answer 5

the advantage of making us more confident that μ is contained in the confidence interval

Question 6

what are the disadvantages of increasing a confidence level

Answer 6

has the disadvantage of increasing the margin of error and thus providing a less precise estimate of the true value of μ

Question 7

what are 95 percent confidence intervals used for

Answer 7

to make conclusions

Question 8

why would we use a 99 confidence interval

Answer 8

to make conclusions of stronger evidence

Question 9

how do w denote a confidence interval that will not contain the population mean?

Answer 9

α

This implies that 1 – α is the probability that the confidence interval will contain the population mean

Question 10

what happens to the confidence interval when we increase the level of confidence?

Answer 10

the confidence interval becomes longer (wider)

Question 11

what do we do if we don’t know the population standard deviation?

Answer 11

we us the sample standard deviation

Question 12

what is a t distribution

Answer 12

If the sampled population is normally distributed, then for any sample size n this sampling distribution is what is called a t distribution

curve of the t distribution has a shape similar to that of the standard normal curve

Question 13

what is the mean of any t distribution?

why?

Answer 13

0 bruh

A t curve is symmetrical about zero

Question 14

which is more spread out, the t distribution or the standard normal distribution?

Answer 14

the t distribution

Question 15

what does the spread (standard deviation) of the t distribution depend on?

Answer 15

depends on a parameter that is called the number of degrees of freedom (denoted df)

varies depending on the problem

Question 16

what happens to the spread of the distribution when sample size n increases

Answer 16

it decreases

Question 17

what happens to the t distribution when the number of degrees of freedom approaches infinity?

Answer 17

the t distribution becomes more like a normal curve

Question 18

what is t point that is denoted tα?

Answer 18

the point on the horizontal axis under the curve of the t distribution that gives a right-hand tail area equal to α

Question 19

how do we find the degrees of freedom for a t distribution?

Answer 19

n - 1

Question 20

what might make the t based confidence not valid

Answer 20

if n is small and the distribution is non mount shaped

Question 21

what happens if n is small and distribution is not mound shaped

Answer 21

might make the t based confidence not valid

we can use a nonparametric method

Question 22

nonparametric method

Answer 22

a method that makes no assumption about the shape of the sampled population and is valid for any sample size

Question 23

a tolerance interval

Answer 23

an interval that contains a specified percentage of the individual measurements in a population

Question 24

what is the form of a tolerance interval if the distribution is normally distributed

Answer 24

[μ ± zα/2*σ]