Download Lab 11: Inferential Statistics and Hypothesis Testing

Lab 10: Instructions and Questions for Excel 2003
Inferential Statistics and Hypothesis Testing
NAME_________________________LAB TIME_________LAB BLDG___________________
This lab will carry out hypothesis tests and will examine the conditions which result in rejection of
the null hypothesis.
1.
Go to the course webpage and open the lab10data file.
2.
Suppose we are interested in a variable whose mean is supposed to be 100. The distribution
of this variable is believed to be normal with a standard deviation = 0.8 mm based on
previous surveys. We want to detect a shift in the mean in either direction.
3.
The null hypothesis should be: __Ho:_______________________________
4.
5.
The alternate hypothesis should be: __Ha:___________________________
To examine the effect of sample size, we will use two sample sizes, n=30 and n = 6. The
first sample of 30 observations is given in column B, and the first sample of 6 observations
is given in Column K.
Use A45 through A49 for labels as follows: A45: sample size, A46: sample mean, A47:
test statistic, z, A48: 1-side P Value, A49: 2-side P Value.
In B45 enter =30 for sample size.
In B46 use the AVERAGE function to calculate the sample mean for B10:B39.
In B47 calculate the test statistic, z, using the formula: z = (sample mean – hypothesized
mean) / (0.8/ sqrt of sample size). Enter = (B46-100) / (0.8/SQRT(B45))
In B48 use the NORMSDIST function to calculate the 1-side P Value. Enter =
NORMSDIST(B47).
In B49 use the NORMSDIST function to calculate the 2-side P Value. Enter =
2*NORMSDIST(B47)
6.
7.
8.
9.
10.
11.
CALCULATE 7 NEW COLUMNS OF HYPOTHETICAL SAMPLES OF SIZE = 30:
12.
In Column C generate a new sample of n= 30 items using excel to deduct 0.1 from each data
value in the column B. ie, in C10 use the formula: =B10-0.1. Copy this formula down to
generate 30 new values.
13.
Repeat the above instructions to generate 6 new data samples in columns D through I except
deduct 0.05 instead of .1 from the column on the left.
14.
Copy the formulas in B45:B49 across to column I.
15.
The sample means in line 46 should be 100, 99.9, 99.85, 99.80, 99.75, 99.70, 99.65, 99.60,
and the corresponding test statistics and P Values should be descending also.
CALCULATE 8 NEW COLUMNS OF HYPOTHETICAL SAMPLES OF SIZE =6
16.
In Column K a sample of n=6 items is given. In Column L generate a new sample of size
n=6 using excel to deduct 0.15 from each data value in column K.
17.
Repeat the above instructions to generate 7 new samples in columns M through S except
deduct 0.10 instead of 0.15 from the column on the left.
18.
In K45 enter = 6. Copy K45 across to columns L through S. Copy the formulas in I46:I49
over to columns K through S.
19.
20.
The sample means from K46 through S46 should be 100, 99.85, 99.75, 99.65…..99.15.
There should be two graphs between lines 51 and 102 showing the sample means and the
associated P Values which you just generated. The second plot just expands the y axis of
the first plot to aid in interpretation.
INTERPRETATION OF SAMPLES 1-8 WHEN SAMPLE SIZE = 30
21.
The first sample of n=30 in Column B has a mean = 100, exactly as expected in the null
hypothesis. Samples 2 - 8 in Columns C through I have descending means. Note that the P
Values are also descending from Column B through I.
22.
Remember that you can reject the null hypothesis only when the P Value is equal to or less
than the significance level, α.
23.
Sample 1 in Column B supports which hypothesis? Null______ Alternate_______
24.
As the sample mean decreases, going from Column B toward Column I the null hypothesis
becomes: Easier to believe_______ Harder to believe________
25.
If α = .10, and with a two-side Ha, rejection of the null hypothesis would begin with what
sample mean? ______________
26.
If α = .01, and with a two-side Ha, rejection of the null hypothesis would begin with what
sample mean? ______________
27.
If α = .10, and with a one-side Ha, rejection of the null hypothesis would begin with what
sample mean? ______________
28.
If α = .01, and with a one-side Ha, rejection of the null hypothesis would begin with what
sample mean? ______________
29.
In general, is it easier (more likely) or harder (less likely) to reject a 2-side hypothesis than it
is to reject a one-side hypothesis? _____________
COMPARISON OF SAMPLE SIZE N=30 WITH N=6
30.
Comparing sample size n=30 with n=6, for a given value of the sample mean, and for a
given set of hypotheses, the P Value is always lower for which sample size? __________
31.
For detecting small shifts in the population mean, it would be better to use a large sample
size or a small sample size? ______________________
COMPARISON OF α = .10 VS α = .01
32.
In general, which value of α would result in rejection of Ho more often, α = .10 or α = .01?
________________________________
33.
Which value of α would be regarded as the most rigorous criteria (most difficult to achieve)
for rejection of Ho,
α = .10 or α = .01? _________________________________
34.
The P Value represents the probability that the particular value of the sample mean (or a
value more extreme) could occur by chance alone WHEN THE NULL HYPOTHESIS IS
ACTUALLY TRUE. Knowing this, which value of α would result is more cases where Ho
is rejected when Ho is actually true, ie: the mean is actually = 100, α = .10 or α = .01?
____________________________________________________________
Print the spreadsheet including the plots of P Values, A1:S104 using landscape with a page break
after line 43, and turn in with your answers to the questions.