Unit 11 - Lesson 1 Flashcards
T interval
x̄ ± t* * (s/√n)
x̄ = sample mean
t* = critical value
s = sample SD
n = # of trials
Make sure the critical t value is multiplied by the s/√n instead of adding it to x̄ first!
When do we use a t statistic/table/distribution?
When we are trying to create confidence intervals for means where we don’t have access to the SD of the sampling distribution but we can compute the sample SD
What are the conditions for a t interval?
Random sample
Normal distribution
Independence
How do you meet the normal condition for a t interval?
n ≥ 30
or
the population/sample distribution is (at least roughly) normal/symmetric
How do you meet the independence condition for a t interval?
With replacement
Without replacement (10% rule)
What is sx (the x is subscript)
Standard error; the standard deviation of the sample
When do we use sx (standard error) for the σx̄ = σ/√n equation?
σx̄ is SD of the sample mean (x bar is in subscript)
When we don’t know the population SD. In that case, the SE (SD of the sample) is the best estimate of the population SD.
So use sx/√n instead of σ/√n
What is the degree of freedom (df)?
n-1
How do you calculate the test statistic?
t = (x̄ - Mo) ÷ (Sx/√n)
Mo = assumed mean from the null hypothesis
Sx = sample SD
How do you interpret the test (t) statistic?
If it is lower than the value on the t table, there isn’t enough evidence to reject the null hypothesis. If it is higher, there is enough evidence to reject the null.
How do you calculate the p-value from the t-statistic?
Press 2nd then vars on the calculator. Select tcdf(.
Input the upper and lower limits of the function (which should include at least 1 t statistic) and the degrees of freedom (df). There you have it, the p-value!
This p-value is for all values inside the area of the limit, so if you want the values outside the limit, you’d need to do 1 - your p-value.
How do you determine whether the null is rejected or not?
If the p-value is ≥ the alpha level, you fail to reject the null (H0, 0 in subscript). If it is < than the alpha level, you can reject the null.
This is because if the p-value is greater than or equal to the alpha level, you have exceeded the alpha value, which is essentially the cutoff point; the probability of the observed result is high enough that we can’t reject the null.
