Download Homework 5

MIME 4100
Hwk 5
Due 2/26/2014
1. Study section C6 of the book and your class notes
2/17/2014
2. Complete the statements below:
a) The objective of a hypothesis test is to _____________________________
b) Type I error is _________________________________________
c) Type II error is ________________________________________
d) p-value from a hypothesis test is the probability of ______________________
e) If the following decision rule is used to test the null hypothesis, then the
probability of type I error is equal to _________________ :
if p - value of the test   do not reject null hypothesis
if p - value of the test   reject null hypothesis
f) A very small p-value (i.e. 10-3) in a hypothesis test means that there is strong
evidence for _____________
3.
a) Test hypothesis that the probability of failure of failure of an electronic circuit is
0.01. We tested 500 nominally identical circuits and observed one failure. Use a
significance level   0.1.
b) Is this test a one-tailed or two tailed test?
c) Find the probability that you could reject a hypothesis that is actually true in this
test.
Hint: The test statistic for a sample proportion is,
Pˆ ( A)  P ( A)
ˆ
Pˆ ( A)
Pˆ ( A){1  Pˆ ( A)}
is the
nA
standard deviation of the sample proportions. The statistic in Equation (1) follows the
standard normal distribution.

where Pˆ ( A) is the observed proportions, and ˆ ˆ
P ( A)
(1)
4. We inspected two shipments consisting of nA=334 and nB=116 ball bearings from
two factories. We found xA=14 defectives in the first shipment and xB=36 in the second.
Test the null hypothesis that the proportions of defective bearings from the two factories
are equal. Use a level of significance equal to 0.05.
Hint: The test statistic for two sample proportions is,
Pˆ ( A)  Pˆ ( B)
ˆ 2ˆ
P( A)
 ˆ 2ˆ
(2)
P( B)

where Pˆ ( A) and Pˆ ( B) are the observed proportions, and ˆ ˆ
P ( A)
Pˆ ( A){1  Pˆ ( A)}
nA
Pˆ ( B){1  Pˆ ( B)}
the standard deviations of these proportions. The statistic in
nB
Equation (2) follows the standard normal distribution.
ˆ ˆ

P( B)
5. Answer the following true-false questions:
a) The smaller the p-value the more likely it is to reject the null hypothesis. (T-F)
b) The probability of type I error is equal to the level of significance,  . (T-F)
c) Type I error occurs when we fail to reject a truly false hypothesis. (T-F)
d) When we increase the sample size we reduce the probability of Type II error. (T-F)
e) A hypothesis test is easy to pass when the sample size is small. (T-F)
f) If the alternative hypothesis is that the mean values of two populations are
different, 1   2 , then the test is called two-tailed test. (T-F)