Reading Quiz 12

Question 1

steps for significance tests in general

Answer 1

1. state the parameter and population, null and alternative hypothesis, and significance level
2. state the inference procedure to be used (or state with calculations) and verify its conditions (SRS, normal, independence)
3. complete all necessary calculations: z or t statistic formula, values in, z/t statistic value, and p value
4. state conclusion/interpretation, make sure in context

Question 2

normality for sample means

Answer 2

normal if population distribution normal
approx normal by central limit theorem if n greater than or equal to 30
or observe and sketch histogram

Question 3

normality for sample proportions

Answer 3

npnot and nqnot greater than or equal to 10

Question 4

independence additional evidence

Answer 4

10n less than or equal to N

Question 5

significance tests for mean μ of a normal population

Answer 5

based on sample mean x̅ of an SRS of size n
thanks to central limit theorem, resulting procedures are approx correct for other population distributions when sample is large (greater than or equal to 30)

Question 6

when we know σ

Answer 6

use z statistic and standard normal distribution to perform one-sample z test for means

Question 7

when don’t know σ

Answer 7

use one-sample t statistic, which is used for one-sample t test for means

Question 8

t statistic has

Answer 8

t distribution with n-1 degrees of freedom

Question 9

as degrees of freedom increases, shape of t distribution

Answer 9

more and more closely approximates the standard normal distribution

Question 10

t statistic interpretation

Answer 10

says how far away x̅ is from its mean μ in standard deviation units

Question 11

significance tests for Ho: μ = μo are based on

Answer 11

t statistic

use p values or fixed significance levels from the t (n-1) distribution

Question 12

paired t test

Answer 12

use to analyze paired data by first taking the difference within each pair to produce a single sample
then use one-sample t test procedures
aka one-sample t test on the differences

Question 13

power of a t test

Answer 13

hard to calculate, rely on technology
measures ability to detect deviations from the all hypothesis
higher power important

Question 14

z statistic for tests of Ho: p = pnot

Answer 14

z = (p̂ - pnot) / (sqrt (pnot * qnot)/n) )

Question 15

one-sample z test for proportions

Answer 15

z statistic z = (p̂ - pnot) / (sqrt (pnot * qnot)/n) ) used with p values calculated from the standard Normal distribution

Question 16

important note

Answer 16

use pnot in the denominator for the z test statistic and not p̂. probability calculations assume Ho is true, and since Ho: p = pnot, assuming that p = pnot

Question 17

large sample test

Answer 17

often called one-proportion z test
called large sample because based on Normal approximation to the sampling distribution of p̂ that becomes more accurate as the sample size increases

Question 18

what additional information do confidence intervals provide that significance tests do not

Answer 18

a range of plausible values for the true population parameter p

Question 19

for inference about a population proportion, confidence intervals and two tailed tests

Answer 19

do not have the perfect correspondence that happens with inference about a population mean, but relationship is similar

Question 20

The one sample z-statistic is the z = (xbar - mu not)/(sigma/sqrtn). What is the one sample t-statistic equation?

Answer 20

t = (xbar - mu not)/(s/sqrtn)

Question 21

The one-sample t statistics has the t distribution with ________ degrees of freedom.

Answer 21

n - 1

Question 22

When using the t distribution critical values chart to determine the p-value corresponding to a particular t statistic, if you have degrees of freedom = 58, since there isn’t a df = 58 row should you go down and use the df = 50 values or round up to df = 60?

Answer 22

Always round down if the exact df is not available, in this case you should use the df = 50 values.

Question 23

When two sets of data is paired and you take the difference within each pair to produce a single sample, what are you performing?

Answer 23

a paired t test

Question 24

Suppose someone were to draw many pairs of samples from two populations, and compute the difference between the sample means for each pair. What would the mean of this difference approach as the number of samples drawn approached infinity?

Answer 24

the difference in population means

Question 25

The fact that the mean of the difference in sample means approaches the difference in population means as the number of samples gets larger is a long way of saying that the difference in sample means is an ____ estimator of the difference in population means.

Answer 25

unbiased

Question 26

Something to remember from chapter 10: what is a “robust” procedure? Hint: page 654.

Answer 26

One where the accuracy of a confidence interval or significance test is not very greatly affected by violation of the assumptions.

Question 27

The t procedures are very robust against (non-normality of the population, outliers) but not very robust against (non-normality of the population, outliers).

Answer 27

Non-normality of the population, outliers

Question 28

The main reason why the t procedures are robust against the non-normality of the population is what theorem?

Answer 28

The central limit theorem, i.e. that sample means become more nearly normally distributed as the sample size gets larger, even when the population does not have a normal distribution.

Question 29

The statistic that estimates (in an unbiased way) the population proportion is ____.

Answer 29

the sample proportion

Question 30

What is the equation for a one proportion z statistic?

Answer 30

z = (p̂ - pnot) / (sqrt (pnot * qnot)/n) )

Question 31

If npo and nqo are at least 10, then we can treat the distribution of p-hat as _________________.

Answer 31

approximately Normal. In other words, the Normality condition is then considered met. It is
important to notice that it npo not np-hat.

Question 32

Instead of the method described in the previous problem, can the central limit theorem be used to verify the Normality condition for one-proportion z test?

Answer 32

No, the central limit theorem can only be used with means, this deals with proportions!

Question 33

What additional information do confidence intervals provide that significance tests do not?

Answer 33

Confidence intervals provide a range of plausible values for the true population parameter p.