Denotation Letters
what does n stand for?
sample size
define critical value
critical value is the threshold area where we reject or fail to reject the null hypothesis
what is the first step to hypothesis testing?
formulate hypothesis
the hypothesis is H0: u=12 H1: u not =12
what type of test?
two sided test
σ stands for?
standard deviation
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)
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
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)
1-a stands for
confidence level
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
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
How do we know we are running NORMAL distribution?
Does the CLT apply? Is n greater than or = to 30?
define phat and qhat
phat: sample proportion
qhat: estimate of the proportion
given that the alpha is .15 and the degrees of freedom is 18, what is the critical value?
-1.067
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
What variables does a chi-square test use?
sum of(observed-expected)2/expected value
observed: claim
expected: actual
po and qo mean..
po: assumed population proportion in the null hypothesis
qo: initial quantity or (1-po)
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
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
give me all 3 formulas
-test value Z
-test value T
-Population proportion Z
test value z= xbar-mo/sigma/√n
test value t=xbar-mo/s/√n
population proportion Z= phat-po/√po*qo/n