EXAM REVIEW

Denotation Letters

100

what does n stand for?

sample size

200

σ stands for?

standard deviation 

300

1-a stands for

confidence level

400

define phat and qhat 

phat: sample proportion 

qhat: estimate of the proportion

500

p_o and q_o mean..

p_o: assumed population proportion in the null hypothesis

q_o: initial quantity or (1-p_o) 

Critical Value

100

define critical value 

critical value is the threshold area where we reject or fail to reject the null hypothesis

200

You are conducting a two-tailed z-test at a 5% significance level. What are the critical values, and how do you determine them? 

CV= +-1.96 

use qnorm (0.05/2) 

300

In a left-tailed t-test with 20 degrees of freedom and a significance level of 0.01, how do you find the critical value? 

using Rcode qt(a,df) 

=-2.528 

400

given that the alpha is .15 and the degrees of freedom is 18, what is the critical value? 

-1.067

500

You are conducting a right-tailed t-test with a sample size of 12 and a significance level of 0.005.
What is the critical t-value, and how do you find it? 

qt(0.005,11) = -3.105

Hypothesis Testing

100

what is the first step to hypothesis testing? 

formulate hypothesis

200

Draw on the board the hack we know to determine which tail is which

rtail: the alt points left

Ltail: the alt points right

two tail: = or not = signs 

300

how do we determine accepting or rejecting the null hypothesis?

whether or not the test value we calculate lands in the critical value area or not

400

A factory claims its light bulbs last 1,000 hours on average. A sample of 36 bulbs has a mean life of 980 hours. The population standard deviation is 60 hours. At α = 0.05, test the factory’s claim.

1: H₀: mu=1000.  H₁: mu not =1000

2: xbar-mu/sigma/√n= 980-1000/60/√36 = -2

3: CV= +-1.96

4. reject null accept alt

500

A nutritionist believes that a protein bar contains less than the advertised 20g of protein. A sample of 10 bars has a mean of 18.7g with a sample standard deviation of 1.5g. Test this claim at α = 0.01. 

1. H₀: mu>20 H₁: mu<20 (Ltail)

2. TV= t test= -2.74

3. tvalue/critical= -2.821

4. fail to reject H₀

What kind of test

100

the hypothesis is H_0: u=12 H_1: u not =12

what type of test?

two sided test

200

the null hypothesis points to the LEFT, which way is my tail going to point? 

LEFT TAIL (opposite of alt which is the opposite of Null)

300

How do we know we are running NORMAL distribution? 

Does the CLT apply? Is n greater than or = to 30? 

400

What variables does a chi-square test use? 

sum of(observed-expected)²/expected value 

observed: claim

expected: actual 

500

give me all 3 formulas 

-test value Z

-test value T

-Population proportion Z

test value z= xbar-m_o/sigma/√n

test value t=xbar-m_o/s/√n

population proportion Z= phat-p_o/√po*qo/n