In this section you learned how to compute a confidence interval and perform a hypothesis test for a mean difference for paired data.
In this section you learned how to compute a confidence interval and perform a hypothesis test for a mean difference for paired data.
• In this section you are dealing with _______ ________________ data.
• The symbol for the parameter in this section is _______.
• The symbol for the point estimate for that parameter is _______.
• What input screen do you use for the interval estimate? __________________________________
• What input screen do you use for the hypothesis test? __________________________________
Remember for bigger data sets you can copy and paste the columns of data into StatCrunch.
For smaller sets of data you should practice using your TI84 since that is the only technology you have available in the classroom when you take the departmental final exam.
Since these are computer-graded it is important that L3 is computed as L1 – L2.
Fill in the following as you work through your given problems in MyOpenMath
1. a.) Hypothesis Test
P:
μ? = The mean traffic count of all locations on a Friday the 6th
μ? = The mean traffic count of all locations on a Friday the 13th
H:
H0: μ???? = 0 cars
HA: μ???? > 0 cars
A:(Make sure you know how to make a normal prob plot and a modified boxplot of differences)
Since quantitative information was collected from each object, we need to check the following conditions:
Check all that apply.
The samples are dependent
Normal population of differences or at least 30 pairs of data
No outliers in the differences
σ is unknown for each group
There were two measurements taken on the same object, so these samples are dependent.
Is the value of σ unknown for each group? Yes
Are there any outliers in the differences?
No, the modified boxplot of the differences shows no outliers
N:
The conditions are met to use a Paired T-Test
T:
d? = 2185.3 cars
t = 3.80
O:
P value = 0.0034
M:
Since the p-value ≤ 0.02, we reject H?.
S:
There is significant evidence to conclude the mean traffic count of all locations on a Friday the 6th
is more than the mean traffic count of all locations on a Friday the 13th
b.) Confidence Interval
P: already stated in part a
A:already checked in part a
N:
Paired T-Interval
I:
C:
2. a.) Hypothesis Test
P:
μ? = The mean pulse rate of all smoker non-drinking males before they exercise
μ? = The mean pulse rate of all smoker non-drinking males after they exercise
H:
H0: μ???? = 0 bpm
HA: μ???? < 0 bpm
A: (Make sure you know how to make a normal prob plot and a modified boxplot of differences)
Since quantitative information was collected from each object, we need to check the following conditions:
Check all that apply.
The samples are dependent
Normal population of differences or at least 30 pairs of data
No outliers in the differences
σ is unknown for each group
There were two measurements taken on the same object, so these samples are dependent
Is the value of σ unknown for each group? Yes
Are there any outliers in the differences? No, the modified boxplot of the differences shows no outliers
n = 17 which is < 30
Is it reasonable to assume the population is normally distributed?
Yes since the normal probability plot of the differences is roughly linear with no outliers.
N:
The conditions are met to use a Paired T-Test
T:
The symbol and value of the random variable on this problem are as follows:
This computation assumes you calculated L3 as L3= L1 – L2.
Round your answers to 2 decimal places.
d? = -51.05 bpm
t= -10.40
O:
P value = 0.0000
M:
Since the p-value ≤ 0.02 , we reject H?.
S:
b.) Confidence Interval
P: already stated in part a
A: already checked in part a
N:
Paired T-Interval
I:
C:
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