Lecture 7

Question 1

What are the steps in a hypothesis test?

Answer 1

1. identify needed values (n, p-hat, p, s, x-bar, etc)
2. set up null/alt, level of sig, and type of tail
3. choose test statistic
4. calculate test statistic
5. based on tail test/alpha, determine crit. value
6. compare test stat to crit.value and conclude

Question 2

What is a two tailed test?

Answer 2

critical region is split into 2 ends (H1 not equal x)

Question 3

Why are two tail tests preferred?

Answer 3

Because the rejection region is split in 2 (smaller area of rejection) thus are less likely to reject null/make accurate decision about rejecting null (less error)

Question 4

What is a right tailed (upper) test?

Answer 4

critical region to the RIGHT end (H1>x)

Question 5

What is a left tailed (lower) test?

Answer 5

critical region to the LEFT end (H1<x)

Question 6

What is the significance level?

Answer 6

represents how much error is able to be held within the values of X% CI

Question 7

Why are smaller p-values better?

Answer 7

a smaller p-value means there’s less error

Question 8

When something is statistically significant, is the null rejected or accepted?

Answer 8

rejected

Question 9

What two scenarios is the null rejected?

Answer 9

• when crit. value falls in crit.region
• when p-value is LESS than 0.05 (investigator’s findings are true)

Question 10

What are the two types of error in hypothesis testing?

Answer 10

• type I error (null is true even though rejected, false positive)
• • type II error (null is really false even though accepted, false negative)

Question 11

How can type II error be minimized?

Answer 11

with a larger sample size

Question 12

What does the p-value represent?

Answer 12

the probability of making a type I error

Question 13

What is the test statistic for a single sample PROPORTION compared to a population?

Answer 13

z= p-hat - p / root (p*q/n)
- p-hat = x/n (sample proportion)
- p = population proportion in null

Question 14

What two calculations are ran to assume the sample is normally distributed?

Answer 14

np and nq >= 5

Question 15

How does one determine a P-value?

Answer 15

find where the calculated test statistic would hypothetically fit in the crit.values in the row of DF and determine if it would be found > or < of a certain confidence level

Question 16

What is the test statistic for testing a claim about a sample MEAN >=30?

Answer 16

z = X-bar - mew0 / s / root n

Question 17

What is the test statistic for testing a claim about a sample MEAN < 30?

Answer 17

t= X-bar - mew 0 / s / root n

Question 18

In two sided tests, if the test statistic is a negative value, what must be true of the critical value?

Answer 18

it must also be negative

Question 19

What is being compared in multinomial goodness of fit tests?

Answer 19

comparing observed values to expected ones

Question 20

What is the X^2 (test statistic) equation?

Answer 20

X^2 = sum of [(O-E)^2 / E]

Question 21

What are expected values based on?

Answer 21

based on the OPPOSITE of the claim being made

Question 22

If all frequencies are expected to be equal, how are expected values calculated?

Answer 22

E = n (# of trials) / k (# of categories)

Question 23

If all frequencies are NOT expected to be equal, how are expected values calculated?

Answer 23

E = n*p for EACH category
p = each category’s probability

Question 24

Are preferred X^2 values small or large and why?

Answer 24

larger - proves there’s a difference from what is believed to be true

Question 25

What is the relationship between X^2 statistic, test statistic, and p-values?

Answer 25

X^2 and test statistics are proportionally related (goes up/down together) and are both inversely related to p-values (as the stats increase or decrease, p-values does the opposite)