Hypothesis Testing/Confidence Intervals

Question 1

Confidence Interval for p

Answer 1

a range of plausible values for p

takes the form: phat +- Margin of Error

Question 2

ME in a confidence interval depends on…

Answer 2

Sampling Distribution

Question 3

Confidence Interval Statement

Answer 3

We are X% confident than the true proportion of ___ lies between Z and Y.

Question 4

What does the confidence interval tell us?

Answer 4

That we are using a method that will give us t he right answer X% of the time, not that there is a X% Probability that our confidence interval has P in it

Question 5

Sample size calculation ask

Answer 5

How big should n be in a C% confidence interval for p so that the margin of error is a certain size?

Question 6

Hypothesis Testing

Answer 6

A procedure based on sample evidence and probability used to test statements regarding population parameters

Question 7

Null Hypothesis

Answer 7

Hypothesis of no change or status Quo, Presumed True unless overwhelming evidence to the contrary

Question 8

Alternative Hypothesis

Answer 8

Hypothesis the researcher is trying to gather information in favor of. To reject the null hypothesis in favor of the alternative, overwhelming evidence must be demonstrated.

Question 9

Errors in Hypothesis Testing

Answer 9

Rejecting Null H when it is true or not rejecting Null hypothesis when it is false. We have control over these types of errors because we decide what alpha is. Smaller values of a are reserved for situations in which making an error would have a serious consequence

Question 10

Statistically Significant

Answer 10

When observed results are unlikely under the assumption that the null hypothesis is true then we reject the null hypothesis and we say that the result is statistically significant

Question 11

Steps for Hypothesis Testing (general)

Answer 11

1. Define parameter of interest in context
2. State Null
3. State Alternative
4. Calculate Test Statistic
5. Calculate P value
6. Make decision
7. state conclusions in context
8. Check conditions required

Question 12

T-distribution

Answer 12

is bell shaped like normal distribution, more spread out than normal distribution, indexed by degrees of freedom, as the degrees of freedom approach infinity, the t distribution approaches the normal

Question 13

Matched Pairs- Dependent random samples, Case CQ

Answer 13

Suppose we have 2 dependent samples from a matched pairs design, we want to estimate the mean difference so we analyze the differences using the one sample T procudte

Question 14

Independent Random Samples from two populations - Case CQ

Answer 14

Use equations

Question 15

Analysis of Variance

Answer 15

ANOVA

extension of the two sample t-test

Question 16

Are observed differences in sample means are likely to have occcured by chance just because of the random sampling?

Answer 16

Depends on the difference between the sample means and how much variability there is within each sample.

Question 17

Hypothesis Testing- ANOVA, Hnull and Ha

Answer 17

h null- all means are equal

Ha- at least on the above equalities doesn’t hold

Question 18

Case CC- inference for two proportions

Answer 18

two random samples from two populations.. We use sam,bling distribution of estimated proportions to make inferences about the p values.

Question 19

Chi Square Test of Independence Hnull and Ha

Answer 19

Hnull- variables are independent

Halt- two variables are dependent

Question 20

How do you find p value in chi square test?

Answer 20

df, read over to where the value falls in table and read up to bounds of p value on chart

Question 21

Case QQ situation

Answer 21

we have a population of (x, y) pairs from the following populations with unknown means my = a + bx with an unknown standard deviation

Question 22

Least Squares line

Answer 22

mean of case QQ. b is estimate (sigma hat) of population slope B and to make inferences about B we need to know the sampling distribution of b (represented by sigma sub b). This slope is the parameter of interest

Question 23

Confidence Interval for B statement

Answer 23

we are C% confident that the change in mean response (y) per unit increase in x lies between ___ and ___

Question 24

Case QQ Null and Alt

Answer 24

Null = slope is 0, no linear relationship between X and Y
Alt = not 0, greater than (positive linear relationship) or less than 0 (negative linear relationship)