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Created: Nov 30, 2016
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Lab 4, Misti Cepeda
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  1. Determine whether the four samples are from a normally distributed population.  Use the chart of critical values found in the file Looney Gulledge QQ Critical Values Extended.pdf with α = 0.05.  Save and submit your four QQ plot results. Interpret your results to answer the question in the text of your report.

 

0.987 = empirical critical value
Since all four Audible and Visible are greater than the empirical value it is reasonable to conclude the data is approximately normal. 

 

  1. The population mean response time for the auditory stimuli is known to be 600 ms.  Is there enough evidence to indicate that the mean auditory response time Before medication is greater than 600 ms.?  Use and one-sample hypothesis test for this question.  Save and submit your hypothesis test results. Interpret your results to answer the question in the text of your report.

 

Yes, there is enough evidence to interpret since the mean is 640 which is higher than 600 it can be interpreted that the sample provides an acceptable representation of the population and the response time before medication is true.

 

  1. Is there enough evidence to indicate that the mean auditory response time After medication is less than the mean auditory response time Before medication?  Use a two-sample hypothesis test for this question.  Do not pool variances.  Save and submit your hypothesis test results.  Interpret your results to answer the question in the text of your report.

 

Yes, the mean after medication is 548 and less than the population mean of 600 which suggests with medication the auditory response did not improve significantly from the sample without medication. 

 

  1. Is there enough evidence to prove that the variation in auditory response times is reduced by the medication?  Use a two-sample hypothesis test for this question.  Save and submit your hypothesis test results.  Interpret your results to answer the question in the text of your report.

 

Yes, there is enough evidence because the P value is less than the level of significance.  The p-value measures the compatibility of the data with the null hypothesis, but does not necessarily mean it is correct.  The results from testing did not prove there was an improvement after medication and shows the results are better without medication.

 

  1. Now we will look at the visual test results.  The population mean response time for visual stimuli is known to be 440 ms.  Is there enough evidence Before medication to indicate that this patient's mean visual response time is greater than 440 ms?  Save and submit your hypothesis test results.  Interpret your results to answer the question in the text of your report.

 

No there is not enough evidence to indicate patient’s visual response time is greater because mean 385.54 is less than the population mean 440.  Also the P-Value is 1 which is greater than level of confidence 0.05.

 

  1. Is there enough evidence to indicate that the mean visual response time After medication is less than the mean visual response time Before medication?  Use a two-sample hypothesis test for this question.  Do not pool variances.  Save and submit your hypothesis test results.  Interpret your results to answer the question in the text of your report.

 

Since the P-Value is 0.0017 reject the hypothesis because it is less than level of significance 0.05 there is sufficient evidence. 

 

  1. Now let's look at the overall test results.  What you should have found is that the test results are consistent and provide a fairly clear diagnosis for the auditory spectrum whereas the visual spectrum diagnosis is less obvious.  Which result is inconsistent with the ADHD diagnosis in the visual spectrum? Explain your answer.

 

The mean result is inconsistent with the ADHD diagnose because even though the result from question #6 P-value was less than level of significance 0.05 stating the response times improved with medication but instead the response time were longer than without medication.  Even though the parameters were the same on QQ Plot for visual before and after the findings from the analysis were not consistent.

 

  1. Does the patient appear to respond well to the prescribed medication?  Despite the inconsistency you discussed in #7, do you think the doctor should continue to medicate the patient?  Explain your answer.

 

The doctor should not continue to medicate the patient because auditory response time was faster for a few tests but not continually and visual response time decreased.  The patient responded better without medication.  Even though the results agreed with null hypothesis the findings from each test did not show any improvements.

 

Result 1: Lab 4 Brand New Question 6 Two Sample T   [Info]
Two sample T hypothesis test:
μ1 : Mean of Vis-Before
μ2 : Mean of Vis-After
μ1 - μ2 : Difference between two means
H0 : μ1 - μ2 = 0
HA : μ1 - μ2 > 0
(without pooled variances)

Hypothesis test results:
DifferenceSample Diff.Std. Err.DFT-StatP-value
μ1 - μ228.7741949.7197452233.088512.96038560.0017

Result 2: Lab 4 New Question 5 One Sample T   [Info]
One sample T hypothesis test:
μ : Mean of variable
H0 : μ = 440
HA : μ > 440

Hypothesis test results:
VariableSample MeanStd. Err.DFT-StatP-value
Vis-Before385.540327.6389944123-7.12916841

Result 3: Lab 4 Brand New Question 3 Two Sample T   [Info]
Two sample T hypothesis test:
μ1 : Mean of Aud-Before
μ2 : Mean of Aud-After
μ1 - μ2 : Difference between two means
H0 : μ1 - μ2 = 0
HA : μ1 - μ2 > 0
(without pooled variances)

Hypothesis test results:
DifferenceSample Diff.Std. Err.DFT-StatP-value
μ1 - μ292.15411615.459202195.015815.9611172<0.0001

Result 4: Lab 4 New Question 4 Two Sample Variance   [Info]
Two sample variance hypothesis test:
σ12 : Variance of Aud-Before
σ22 : Variance of Aud-After
σ1222 : Ratio of two variances
H0 : σ1222 = 1
HA : σ1222 > 1

Hypothesis test results:
RatioNum. DFDen. DFSample RatioF-StatP-value
σ12221201242.78916932.7891693<0.0001

Result 5: Lab4 New Question 2 One Sample T   [Info]
One sample T hypothesis test:
μ : Mean of variable
H0 : μ = 600
HA : μ > 600

Hypothesis test results:
VariableSample MeanStd. Err.DFT-StatP-value
Aud-Before640.0661213.319691203.00803660.0016

Result 6: Lab 4 QQ Plot   [Info]
Right click to copy

HTML link:
<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=65151">Lab 4, Misti Cepeda</A>

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By leachk1979
Dec 9, 2016

I think your interpretation is off, but your test results are great. The only indication that the patient should not be medicated is that the visual data before medication already shows better than average response times, so medication may not be needed. However, since the auditory symptom is clearly present and both auditory and visual results are positively impacted, medication is still reasonable.

Always Learning