Hello.
My process here is basically the same as what I did in Question #
185193.
Again, I'm assuming normal distribution.
To calculate the p-values, we must consult a standard normal table,
such as this one from San Jose State University.
http://www.sjsu.edu/faculty/gerstman/EpiInfo/z-table.htm
a. Left-tail test and Z = -1.62
When we look up the absolute value of -1.62 (i.e., 1.62) in the normal
table, we see a value of 0.9474 , which is equal to the entire area
under the normal curve to the left of 1.62. The p-value for the left
tail test is the area to the left of -1.62 (which is also equal to the
area to right of 1.62 because the normal curve is symetrical. Thus,
calculating the area to the left of -1.62 is simply a matter of
subtracting 0.9474 from 1.
p-value = 1 - 0.9474 = 0.0526
b. Right-tail test and Z = 1.43 .
When we look up 1.43 in the normal table, we see a value of 0.9236 ,
which is equal to the entire area under the normal curve to the left
of 1.43. The p-value for the right tail test is the area to the right
of 1.43. Thus, calculating the area to the right of 1.43 is simply a
matter of subtracting 0.9236 from 1.
p-value = 1 - 0.9236 = 0.0764
c. Two-tail test and Z = 1.27 .
When we look up 1.27 in the normal table, we see a value of 0.8980 ,
which is equal to the entire area under the normal curve to the left
of 1.27. The p-value for the two tail test is the area to the left of
-1.27, plus the area to the right of 1.27. Thus, calculating the area
to the right of 1.27 and the left of -1.27 is simply a matter of
subtracting 0.8980 from 1, and then multiplying by 2.
p-value = 2 * (1 - 0.8980) = 2 * (0.102) = 0.204
sources for the concepts discussed:
San Jose State University: Normal Table
http://www.sjsu.edu/faculty/gerstman/EpiInfo/z-table.htm
"In a left-tail test, the P-value is the area under the normal curve
to the left of x: had we chosen the significance level p so that zp =
x, we would have rejected the null hypothesis, but we would not have
rejected it for any smaller value of p, because for all smaller values
of p, xp < x. Similarly, for a right-tail z test, the P-value is the
area under the normal curve to the right of x. For a two-tail z test,
the P-value is the sum of the area under the normal curve to the left
of -|x| and the area under the normal curve to the right of |x|."
Source: "Approximate Hypothesis Tests: the z-test and the t-test,"
hosted by Berkeley.edu:
http://stat-www.berkeley.edu/users/stark/SticiGui/Text/ch22.htm
"Lesson 19 - Part II: Testing Hypotheses," hosted by southwestern.edu
http://www.southwestern.edu/~owensp/Statintro/Lectures/19b/19b.htm
search strategy: "left tail", "right tail", "two tail"
I hope this helps. |
