t3

Question 1

What are the simple conditions (and formulas) for various tests: One-sample z-test, one-sample t-test, two-sample t-test?

Answer 1

Z procedures:
- SRS from a NORMALLY distributed population

-SRS from a large population 20x as large as N

-[M] is unknown but [o-] is known

T procedures:
-SRS from a symmetric distributed population

-SRS from a large population 20x as large as N

[M] is unknown and [o-] is unknown. Use S instead (Sample)

Question 2

What are the 3 ways to determine robustness for 1-sample and 2-sample t-tests?

Answer 2

-If N<15 the data needs to be very CLOSE to normally distributed/symmetric

-If N>15 the data can be SOMEWHAT SKEWED but no serious outliers

• If N>_ 40 EVEN skewed samples with outliers is probably fine

Question 3

What is the difference between z* and t* values?

Answer 3

-z* is used for Z tests (normal distributions) and t* is used for t distributions

Question 4

Specifically, how small must p-values be to be significant?

Answer 4

A p-value is considered significant if it is LESS than the significance level (.01, .05)

Question 5

If p-values are significant, what does that mean concerning the null hypothesis (H0)?

Answer 5

We reject the null hypothesis (H0) because there is enough evidence to support the alternative hypothesis (Ha)
​

Question 6

If p-values are not significant, what does that mean concerning the null hypothesis (H0)?

Answer 6

We fail to reject the null hypothesis (H0)
as there is not enough evidence to support (Ha)
​
.

Question 7

What is a confidence level vs. a confidence interval?

Answer 7

Confidence Level: Used to find the confidence interval and is determined beforehand (What level of error we’re willing to accept)

Confidence Interval: The range of values within which the true parameter is likely to fall.

Question 8

What 3 things are needed to write hypotheses for 1-sample z or t-tests?

Answer 8

-The null hypothesis (H0) (must be =) :
​Specifies no effect or no difference.

-The alternative hypothesis (Ha) ( must use inequality) : Specifies the effect or difference.

-The value of the parameter being tested (e.g., population mean).

-uses SAME number for both hypothesis

Question 9

Which of the 3 things is different when writing hypotheses for 2-sample t-tests?

Answer 9

• specifying two distinct groups, rather than comparing a single group mean to a known value

-No numbers are used ( [M1] and [M2] instead)

Question 10

What 3 steps are needed to test the validity of a claim/hypothesis?

Answer 10

-Find P-value
-Compare P-Value to significance levels to see if it’s lower than the levels we chose
-reject or fail to reject

Question 11

What is the formula for standard error in a 1-sample t interval?

Answer 11

SE= s//n

Question 12

What is the formula for the degrees of freedom in a 1-sample t-test?

Answer 12

df= n-1

Question 13

What will a higher degrees of freedom do to a t confidence interval?

Answer 13

It makes the t distribution closer to the normal distribution, resulting in a narrower confidence interval.

Question 14

What 2 ways can a margin of error be reduced in a z confidence interval?

Answer 14

-Increase the sample size (𝑛).

-Lower the confidence level (e.g., from 99% to 95%)