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(Solved) Hypothesis test for a Population Mean, Sigma Known If the population standard deviation is known, we can directly calculate the standard deviation of...


For this practical application assignment, you will use the daily adjusted closing price data you downloaded in Module 1. You may use the Hypothesis Tester â Single Sample document, linked in Resources, to complete both scenarios. You may also want to review the SAS One Sample T-Test tutorial, also located in the Resources.


Practical Application Scenario 1

Often, it is interesting to know whether mean adjusted closing prices have changed from some base value. Suppose you are interested in whether the mean adjusted daily closing price for the stock you downloaded in Module 1 has increased from some base price (for example, $4 or $10 or . . .). For our purposes, we will assume that you are interested in whether the mean daily adjusted closing price has increased from the oldest daily adjusted closing price in your dataset (for example, the one from five years ago). Conduct a hypothesis test that the mean adjusted daily closing price has increased from the base price. Assume that the stock price is sufficiently normal to conduct a t-test. Note: you might also transform the stock to normality, that is, applying the natural logarithm.

To successfully complete this hypothesis test, do the following:

  1. State the null and alternative hypotheses via both an explanation and a math equation.
  2. Identify the appropriate statistical test. State this clearly.
  3. Conduct the test and state whether to accept or reject the null hypothesis using the p-value and an alpha of .05. You may solve the equation manually, use the Hypothesis Tester â Single Sample file, provided in Resources, or use the SAS Enterprise Guide. You may also use the Hypothesis Tester multimedia piece provided in Resources to review the process for this equation.
  4. Report the rejection or acceptance of the null in terms of the scenario results using laymen's terms. For this scenario, write a three-sentence paragraph that details why you can be statistically confident that the mean adjusted closing price has increased, decreased, or remained the same, and what would happen if alpha was .01.
  5. Would the results of your hypothesis test be different if you used a Z-test rather than a t-test? Why or why not?
Practical Application Scenario 2

To explore your stock dataset, you decide that you want to know whether your stock's mean daily volume has increased or decreased from the oldest closing value in your data set (in other words, the closing volume from five years ago). Often, you would conduct a test like this with two samples, but for now, we will just use the oldest closing value as the baseline. Conduct a hypothesis test to see if the mean daily volume differs from the oldest daily volume in your dataset. Complete the following.

  1. State the null and alternative hypotheses via both an explanation and a math equation.
  2. Identify the appropriate statistical test. State this clearly.
  3. Conduct the test and state whether to accept or reject the null hypothesis using the p-value and an alpha of .05. You may solve the equation manually: use the Hypothesis Tester â Single Sample file provided in Resources, or use the SAS Enterprise Guide. You may also use the Hypothesis Tester multimedia piece provided in Resources to review the process for this equation.
  4. Report the rejection or acceptance of the null in terms of the scenario results using laymen's terms. For this scenario, write a three-sentence paragraph that details why you can be statistically confident that the mean adjusted closing price has increased, decreased, or remained the same, and what would happen if alpha was .01.

Hypothesis test for a Population Mean, Sigma Known
If the population standard deviation is known, we can directly calculate the
standard deviation of the sampling distribution (the standard error of the estimate),
and use the standardized normal distribution to get a z multiple, using the Excel
function NORMSINV.
We can then calculate p for each of the three possible test conditions, and compare it to
each level of alpha to see whether the null hypothesis should be rejected. Inputs -Hypothesized Population Mean:
Population Standard Deviation (sigma):
Sample size (n):
Sample Mean (X-bar) 295 <-- Input the appropriate number for your situation
12 <-- Input the appropriate number for your situation
50 <-- Input the appropriate number for your situation
297.6 <-- Input the appropriate number for your situation Intermediate Calculations -Standard Error of the Estimate: 1.69705627
Test Statistic (z): 1.53206469
Results -- For the Alpha level given, H0 should be
Alpha:
0.01
not rejected One tailed, H0: Mu =>295, p= 0.9372 One tailed, H0: Mu <=295, p= 0.0628 not rejected Two-tailed, H0: Mu = 295, p = 0.1255 not rejected timate),
cel mpare it to ate number for your situation
ate number for your situation
ate number for your situation
ate number for your situation pha level given, H0 should be
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not rejected not rejected Rejected not rejected not rejected Hypothesis test for a Population Mean, Sigma Unknown
If the population standard deviation is not known, we must use the sample standard
deviation as an estimate and use it to calculate the standard deviation of the sampling
distribution (the standard error of the estimate). We also use the t distribution to get a
multiple corresponding to the desired confidence level, using the Excel function TINV.
We can then calculate p for each of the three possible test conditions, and compare it to
each level of alpha to see whether the null hypothesis should be rejected. Inputs -Hypothesized Population Mean:
Sample Standard Deviation (s):
Sample size (n):
Sample Mean (X-bar) 7 <-- Input the appropriate number for your situation
1.05 <-- Input the appropriate number for your situation
60 <-- Input the appropriate number for your situation
7.25 <-- Input the appropriate number for your situation Intermediate Calculations -Standard Error of the Estimate: 0.135554
Test Statistic (t): 1.844278
Degrees of Freedom (d.f.):
59
Results -- For the Alpha level given, H0 should be
Alpha:
0.01
0.05
not rejected
not rejected One tailed, H0: Mu =>7, p= 0.9649 One tailed, H0: Mu <=7, p= 0.0351 not rejected Rejected Two-tailed, H0: Mu = 7, p = 0.0702 not rejected not rejected our situation
our situation
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0.1
not rejected
Rejected
Rejected Hypothesis Tester – Single Sample
Hypothesis test for a population proportion From a sample proportion, we can calculate the standard deviation of the
sampling distribution (the standard error of the estimate) and use the standardized
normal distribution to get a z multiple, using the Excel function NORMSINV.
We can then calculate p for each of the three possible test conditions and compare it to
each level of alpha to see whether the null hypothesis should be rejected. Inputs:
Hypothesized population proportion: 0.35
Sample Proportion (p-bar) 0.4
Sample Size (n) 30 <-- Input the appropriate number for your situation
<-- Input the appropriate number for your situation
<-- Input the appropriate number for your situation Intermediate Calculations:
Standard Error of the Estimate: 0.0871
Test statistic (z): 0.5741692518 Results:
One tailed, H0: P => 0.35, p = 0.7171 For the Alpha level given, H0 should be
0.01
not rejected One tailed, H0: P <= 0.35, p = 0.2829 not rejected Two-tailed, H0: P = 0.35, p = 0.5659 not rejected Alpha: ate number for your situation
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ate number for your situation he Alpha level given, H0 should be:
0.05
0.1
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not rejected not rejected not rejected not rejected

 


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