ISDS 2000 Final Exam Review

estimation and hypothesis testing

What two basic methodologies emerge from the inferential branch of statistics?

Point Estimator

a statistic used to estimate a parameter

Confidence Interval

a range of values that, with a certain level of confidence, contains the population parameter of interest

Interval Estimate

based on a sample statistic and provides a range of plausible values for the population parameter

Margin of Error

a value that accounts for the standard error of the estimator and the desired confidence level of the interval

Point Estimate +/- Margin of Error

The confidence interval for the population mean and the population proportion is constructed as

that μ lies in the given interval

The 95% confidence interval for the population mean μ implies that we can report that with a 95% confidence

"there is a 95% chance that μ lies in the given interval"

It is incorrect to say

The Greek letter a (alpha)

refers to significance level; this is the probability that the estimation procedure will generate an interval that does not contain μ

Confidence Coefficient

(1-a); interpreted as the probability that the estimation procedure will generate an interval that contains μ.

Confidence Level

100(1-a)%

the wider the confidence interval

For a given confidence level 100(1-a)% and a sample size n, the larger the population standard deviation

the wider the confidence level interval

For a given confidence level 100(1-a)% and population standard deviation, the smaller the sample size n

the wider the confidence interval

For a given sample size n and population standard deviation, the greater the confidence level 100(1-a)%

t distribution (aka: Student's t distribution)

a family of distributions that are similar to the z distribution except they have broader tails

Degrees of Freedom (df)

n-1; the number of independent pieces of information that foes into the calculation of a given statistic

tdf characteristics

- bell shaped

- symmetric around 0 with asymptotic tails

- has slightly broader tails than the z distribution

- consists of a family of distributions where the actual shape of each one depends on the degrees of freedom

wider

Uncertainty is increased when we estimate the population standard deviation with the sample standard deviation, making the confidence interval ___________.

np ≥ 5 and n(1-p) ≥ 5

For constructing a confidence interval for the population proportion p, we require

more than E for a given level of confidence

You do not want the sample mean to deviate from the population mean by

Independent Random Samples

two (or more) random samples are considered independent if the process that generates one sample is completely separate from the process that generates the other sample

1. Identify the relevant population parameter

2. determine whether a one- or a two-tailed test is appropriate

3. include some form of the equality sign in the null hypothesis and use the alternative hypothesis to establish a claim

When specifying the competing hypothesis, it is important to

Test for Independence

a goodness-of-fit test analyzing the relationship between two categorical variables

Chi-square test of a contingency table

another name for test for independence

the two categorical variables are dependent

The competing hypotheses for a statistical test for independence are formulated such that rejecting the null hypothesis leads to the conclusion that

e(ij) = (Row i total)x(column j total)/sample size

The expected frequency e(ij) for each cell in a contingency table is calculated as

1.645

What is zα / 2 for a 90% confidence interval of the population mean?

1.96

What is zα / 2 for a 95% confidence interval of the population mean?

2.576

What is zα / 2 for a 99% confidence interval of the population mean?

If the sample size is bigger, the interval is narrower.

For a given confidence level and population standard deviation, which of the following is true in the interval estimation of the population mean?

If the population standard deviation is greater, the interval is wider.

For a given confidence level and sample size, which of the following is true in the interval estimation of the population mean when σ is known?

If the confidence level is greater, the interval is wider.

For a given sample size and population standard deviation, which of the following is true in the interval estimation of the population mean?

FALSE

1st Type is characterized by a measurement

2nd Type is characterized by a pairing of observations

T/F: There is only one type of matched-pairs sampling.

matched-pairs

A common case of dependent sampling is usually referred to as __________ sampling.

margin of error

When constructing a confidence interval for the mean difference μD, we follow the same general format of point estimate ± _________

Data Analysis

To use Excel for solving hypothesis tests for the mean difference you should choose: Data >__________> t-Test: Paired Two Sample for Means options.

A matched-pairs hypothesis test for μD.

A particular personal trainer works primarily with track and field athletes. She believes that her clients run faster after going through her program for six weeks. How might she test that claim?

A t test under dependent sampling

What type of test for population means should be performed when employees are first tested, trained, and then retested?

Dependent random samples with numerical data.

What type of data is required to compare prices of the same textbooks sold by two different vendors?

Which of the following is NOT an example of analyzing the mean difference of two populations based on matched-pairs sampling?

Compare the mean wait time of customers being served at a bank before and after the weekend.

H0: µ1 − µ2 = 0, HA: µ1 − µ2 ≠ 0

A 7,000-seat theater is interested in determining whether there is a difference in attendance between shows on Tuesday evening and those on Wednesday evening. A random sample of 25 weeks is collected for Tuesday; a different sample of 25 weeks is collected for Wednesday. The mean attendance on Tuesday evening is calculated as 5,500, while the mean attendance on Wednesday evening is calculated as 5,850. The known population standard deviation for attendance on Tuesday evening is 550 and the known population standard deviation for attendance on Wednesday evening is 445. Let μ1 be the population mean of Tuesday, μ2 be the population mean of Wednesday, and μD be the mean difference for a matched-pairs sampling. What are the appropriate hypotheses to determine whether there is a difference, on average, in attendance between shows on Tuesday evening and Wednesday evening?

TRUE

TRUE or FALSE :

For a chi-square test of a contingency table, the degrees of freedom are calculated as (r−1)(c−1) where r and c are the number of rows and columns in the contingency table.

TRUE

TRUE OR FALSE:

The chi-square test statistic measures the difference between the observed frequencies and the expected frequencies assuming the null hypothesis is true.

two QUALITATIVE variables

The chi-square test of a contingency table is a test of independence for __________________.

the row total multiplied by the column total divided by the sample size

For the chi-square test of a contingency table, the expected cell frequencies are found as ________________.

Chi-square test for independence

Suppose you want to determine if gender and major are independent. Which of the following tests should you use?