National open university of nigeria introduction to econometrics I eco 355

and Sample Frequency Distribution for SAT Math
Statistics & Parameters Sample Frequency Distribution 
Sample Statistics
Samp. Mean = 589.39
Samp. Stand. Dev. = 94.35
Population Parameters
  
Pop. Mean = 460
Pop. Stand. Dev. = 100
Note that red is for males, blue for females.
The same four steps are involved in both directional and non-directional hypothesis 
testing. However, some details are different. Here is what we do for directional 
hypothesis testing:
4. State the Hypotheses:
(a). Alternative Hypothesis
: Students in this class are sampled from a restricted 
selection population whose SAT Math Scores are above the unrestricted population's 
mean of 460. There is a restrictive selection process for admitting students to UNC that 
results in SAT Math scores above the mean: Their mean SAT score is greater than 460.
(b). Null hypothesis
: Students in this class are not sampled from a restricted selection 
population whose SAT Math Scores are above the unrestricted population's mean of 460. 
There is an unrestrictive selection process for admitting students to UNC: Their mean 
SAT score is not greater than 460.
Symbols
:
 
 
5. Set the decision criteria:

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Specify the significance level. We specify:
Determine the standard error of the mean (standard deviation of the distribution of 
sample means) for samples of size 41. The standard error is calculated by the formula:
The value is
To determine how unusual the mean of the sample we will get is, we will use the Z 
formula to calculate Z for our sample mean under the assumption that the null hypothesis 
is true. The Z formula is:
Note that the population mean is 460 under the null hypothesis, and the standard error is 
15.6, as we just calculated. All we need to calculate Z is a sample mean. When we get the 
data we will calculate Z and then look it up in the Z table to see how unusual the obtained 
sample's mean is, if the null hypothesis Ho is true.
6. 
Gather Data
:
We gathered the data on the first day of class and observed that the class's mean on SAT 
Math was 589.39.