Download Scenario 1: You are given raw data (a ratio variable) and asked to

Scenario 1: You are given raw data (a ratio variable)
and asked to find a 95% confidence interval.
Step 1. Find the mean of the data:
Step 2. Find the standard deviation using this formula
Step 3. Find the standard error using this formula
SE =
Step 4. Find the confidence interval using this formula
Lower Bound:
Upper Bound:
- 1.96 (SE)
+ 1.96 (SE)
Step 5: Write your confidence interval as follows (Lower bound, Upper Bound)
Scenario 2. You are given 2 sets of data (both ratio
variables) and asked to test for a difference of means
using the confidence interval method
Step 1. State the null hypothesis (H0) and Alternative hypothesis (HA) as follows
H0: : µ1
- µ2 = 0
HA: µ1- µ2 ≠ 0
Step 2. Find the means of each data set. Label as
1 and
2 accordingly
Step 3. Find the variance of each set of data (individually) using this formula. This
s2
s2
values are
1 and 2 accordingly (this is because s, standard deviation, is the square
root of variance. Thus, s2 is the variance)
s2 =
Step 4. Find the pooled standard error using this formula
Pooled SE=
Step 5. Find the confidence interval for the difference of means using this formula and
compute algebraically
Lower Bound:
1 -
1
- 1.96(Pooled SE)
2 + 1.96(Pooled SE)
2
Upper Bound:
Write the confidence interval as (Lower Bound, Upper Bound)
Step 6. If zero is within your confidence interval (meaning if falls above the lower bound
and below the upper bound), then you DO NOT reject the null hypothesis. If zero is not
within the confidence interval, you may reject the null hypothesis.
NOTE: If you are asked to do a difference of means test using the confidence interval
method and have already been given the means and standard deviations (or variances),
then you only need to do steps 1 and 4-6.
Scenario 3: You are given 2 sets of data and asked
to find the difference of means using the t-statistic
(t-test) method for a two-tailed test.
Step 1. State the null hypothesis that the means are the same (H0) and Alternative
hypothesis (H1) that the means are different as follows
H0: : µ1
- µ2 = 0
HA: µ1- µ2 ≠ 0
Step 2. Find the means of each data set. Label as
1 and
2 accordingly
Step 3. Find the variance of each set of data (individually) using this formula. This
values are s21 and s22 accordingly (this is because s, standard deviation, is the square root
of variance. Thus, s2 is the variance)
s2 =
Step 4. Find the t-statistic using this formula:
Step 5. If the t-statistic is greater than 1.96 or less than -1.96, than you can reject the null
hypothesis. This means that the means are in fact different.
Scenario 4: You are given 1 set of data and asked
to test the hypothesis of whether the mean is
different than zero (a two-tailed test)
Step 1: State the null and alternative hypotheses as follows:
H0: µ = 0
HA: µ ≠ 0
Step 2: Find the mean
Step 3: Find the standard deviation using the following formula
Step 4: Find the standard error using the following formula
SE =
Step 5. Find the t-statistic using the following formula:
Step 6. If the t-statistic is greater than 1.96 or less than -1.96, then you may reject the
null hypothesis with 95% confidence.
NOTATION GUIDE:
: Sample Mean
µ : Population Mean (the true mean you are approximating)
s : Standard Deviation
s2: Variance
SE: Standard Error
N: Number in your sample
T: T-statistic