Chapter 13 : Single Sample t-Test

Question 1

When do you use the Z-test?(2)

Answer 1

• When the mean and standard deviation of the null-hypothesis population are KNOWN.
• Usually you will only have the mean.

Question 2

When population standard deviation is UNKOWN what test do you use?

Answer 2

• t-Test

Question 3

What are the three kinds of t-tests?

Answer 3

• Single Sample t-Test
• Correlated samples t-Test
• Independent Samples t-Test

Question 4

What is the t-test formula, what data does it involve??????Difference with z-test?

Answer 4

• Tobt= Xobt- u/ Sx
• *Sx= standard error of sample…
• Z formula uses POPULATION data not sample

Question 5

Probability distribution of t-values:

• variation in t values?
• Probability ?

Answer 5

• different possible t values for samples of a given N

- Probability of getting each value if sampling is random from the null hypothesis population.

Question 6

Characteristics of Sampling distribution of T ?

- shaped similarly to z distribution if: (2)

Answer 6

• Sample size X >/= 30

- If Ho population is normally distributed

Question 7

There is a different curve for each ___(_).

Answer 7

• sample size (N)

Question 8

What are Degrees of freedom? (df)

- When is this the most relevant ?

Answer 8

• number of scores that are free to vary in calculating any statistic.
• Most relevant when dealing with standard deviation.

Question 9

What is the formula for the sum of deviations about the mean?

Answer 9

s = \/E(X-Xbar)^2/N-1

Question 10

What is the formula for Xbar?

Answer 10

Xbar= EX/N

Question 11

T and Z distributions are both ____ at zero. As the df increases, t becomes __ similar to z. As df approaches infinity, t becomes ____ to z. At any value of df ___.

Answer 11

• symmetrical
• more
• identical
• more
• Tcrit>Zcrit

Question 12

Steps to solving single sample t-test problems?

Answer 12

1. solve for tobt
2. find the df
3. find tcrit on table D using Df and alpha
4. If | tobt |>| tcrit |, reject Ho

Question 13

What is the formula for calculating Tobt directly from raw scores? Benefit?

Answer 13

• Tobt= Xbar obt - u/ >/SS/N(N-1)

- no need to calculate S

Question 14

What does the IB has a real effect mean?

Answer 14

• Tobt is greater than Tcrit

- rejected Ho

Question 15

What is the magnitude of the real effect?

Answer 15

• statistical significance vs practical significance.

Question 16

Measures of effect size are calculated using what?

Answer 16

• Cohen’s d

Question 17

Cohen’s d is?(2)

Answer 17

• relationship between mean difference and effect size, Mean diff= Xobt-u
• main interest is magnitude..absolute value!

Question 18

Choen’s d is _____. Divided by the __ standard deviation.

Answer 18

• standardized, sample

Question 19

What is the computational equation for effect size for single sample T-tests?

Answer 19

• d= | xobt- u |/ s

Xobt= sample mean
u= population mean
s= sample standard deviation 
d= estimated d

Question 20

Often the ___ mean is unknown. We use the __ mean to estimate the ___ mean.

Answer 20

• population
• sample
• population

Question 21

Point estimate??

Answer 21

• uses only one value to estimate population mean

Question 22

Interval estimate??

Answer 22

• uses a range of values to estimate population mean

Question 23

What are confidence intervals?

Confidence limits?

Answer 23

• range of values which probably contain the population mean.
• values that bound the confidence interval
  u lower= Xobt- Sxtcrit (Sx = s/ >/N)
  u upper= Xobt + Sxtcrit
• can be CI of 95% or 99%

Question 24

• If the confidence interval is 99% what is the range?

- what of 95%?

Answer 24

• -t 0.025 <= t 0.005

Question 25

List the steps to solving for a confidence interval!

Answer 25

1. find Sx
2. examine alpha, if it’s one or two tail,
3. find df
4. Solve for the lower and upper limits
5. conclude with the interval.

Question 26

How is a proper conclusion for confidence intervals worded?

Answer 26

• The probability is ___ that the interval contains the population mean.