Recent coffee research Coffee reduces the risk of diabetes
Hypothesis Testing H a : p < Coffee does not reduce the risk of
diabetes H 0 : p >
Slide 3
Subways FOOTLONG is not a foot long Subways FOOTLONG is a foot
long H 0 : = H a : Hypothesis Testing Coffee reduces the risk of
diabetes H a : p < Coffee does not reduce the risk of diabetes H
0 : p >
Slide 4
is normally distributed provided OR x s distribution is not
heavily skewed and n > 30 x is normally distributed OR x s
distribution is heavily skewed and n > 50 one mean test known
Hypothesis Testing 2 is some value that only Deity knows
Slide 5
is normally distributed provided x is normally distributed one
mean test known Hypothesis Testing What do you do if Deity wont
reveal to you the value of 2 ? one mean test unknown OR x s
distribution is not heavily skewed and n > 30 OR x s
distribution is heavily skewed and n > 50
Slide 6
The t distribution is the exact distribution if one mean test
unknown Hypothesis Testing x is normally distributed What do you do
if Deity wont reveal to you the value of 2 ?
Slide 7
x is normally distributed The t distribution is the approximate
distribution if OR n > 30 and x is NOT heavily skewed OR n >
50 and x is HEAVILY skewed one mean test unknown Hypothesis Testing
What do you do if Deity wont reveal to you the value of 2 ?
Slide 8
one proportion test is approximately normally distributed if n
p 0 > 5 and n (1 p 0 ) > 5 Hypothesis Testing What do you use
for 2 when you test a proportion?
Slide 9
1960s Chips Ahoy cookie TV commercial claim Hypothesis
Testing
Slide 10
the cookies have 16 chips H 0 : = 16 Hypothesis Testing The
null hypothesis is assumed to be true The sample says the cookies
do not have 16 chips when they actually do. This error is costly
because the production line will be shutdown to fix a problem that
does not exist Rejecting a true H 0 is a Type I error
Slide 11
the cookies have 16 chips H 0 : = 16 Hypothesis Testing
Rejecting a true H 0 is a Type I error Rejecting a true H a is a
Type II error The alternative hypothesis is the opposite The sample
says the cookies have 16 chips when they really do not. The error
will upset Chips Ahoys customers if there are too few OR increase
Chips Ahoys costs if there are too many the cookies do not have 16
chips H a : 16
Slide 12
The alternative hypothesis is the opposite Rejecting a true H 0
is a Type I error is rejected? Hypothesis Testing Rejecting a true
H a is a Type II error What conclusion is appropriate when H 0 the
cookies have 16 chips H 0 : = 16 the cookies do not have 16 chips H
a : 16
Slide 13
The alternative hypothesis is the opposite cannot be rejected?
Hypothesis Testing Rejecting a true H 0 is a Type I error Rejecting
a true H a is a Type II error What conclusion is appropriate when H
0 the cookies do not have 16 chips H a : 16 the cookies have 16
chips H 0 : = 16 We cannot conclude that
Slide 14
Example: Chips Ahoy Chocolate Chip Cookies Perform a hypothesis
test, at the 5% level of significance, to determine if Chips Ahoy
cookies have an average of 16 chips per cookie. Hypothesis Testing
mean test known one mean test unknown 2 = p (1 p ) mean test
proportion test
Slide 15
Bottle Number of Chips deviation from mean 114 -2.5 215 -1.5
315 -1.5 417 0.5 518 1.5 616 -0.5 715 -1.5 2919 2.5 3017 0.5
Total495 0 one mean test unknown Hypothesis Testing
Slide 16
1. Determine the hypotheses. H a : 16 2. Compute the test
statistic one mean test unknown Hypothesis Testing H 0 : = 16
Slide 17
degrees of freedom.200.100.050.025.010.005
28.8551.3131.7012.0482.4672.763 29.8541.3111.6992.0452.4622.756
30.8541.3101.6972.0422.4572.750 31.8531.3091.6962.0402.4532.744
32.8531.3091.6942.0372.4492.738 33.8531.3081.6922.0352.4452.733
34.8521.3071.6912.0322.4412.728 df = 30 1 = 29 =.050 /2 =.025 H a :
16 one mean test unknown 3. Determine the critical value(s).
Hypothesis Testing
Slide 18
degrees of freedom.200.100.050.025.010.005
28.8551.3131.7012.0482.4672.763 29.8541.3111.6992.0452.4622.756
30.8541.3101.6972.0422.4572.750 31.8531.3091.6962.0402.4532.744
32.8531.3091.6942.0372.4492.738 33.8531.3081.6922.0352.4452.733
34.8521.3071.6912.0322.4412.728 t.0250 = 2.045 -t.0250 = -2.045 one
mean test unknown 3. Determine the critical value(s). Hypothesis
Testing =.050 H a : 16
Slide 19
-2.045 2.045.025 1.91 t-stat 0 t.025 Do Not Reject H 0 : 4.
Conclude the cookies do not have 16 chips We cannot conclude that
one mean test unknown Hypothesis Testing
Slide 20
Example: National Safety Council (NSC) The National Safety
Council claimed that more than 50% of the accidents are caused by
drunk driving. A sample of 120 accidents showed that 67 were caused
by drunk driving. Perform a hypothesis test, at the 2.5% level of
significance, to determine if NSCs claim is valid. one proportion
test Hypothesis Testing
Slide 21
one proportion test 2. Compute the test statistic Hypothesis
Testing 1. Determine the hypotheses.
Slide 22
Z.00.01.02.03.04.05.06.07.08.09
-2.2.0139.0136.0132.0129.0125.0122.0119.0116.0113.0110
-2.1.0179.0174.0170.0166.0162.0158.0154.0150.0146.0143
-2.0.0228.0222.0217.0212.0207.0202.0197.0192.0188.0183
-1.9.0287.0281.0274.0268.0262.0256.0250.0244.0239.0233
-1.8.0359.0351.0344.0336.0329.0322.0314.0307.0301.0294
-1.7.0446.0436.0427.0418.0409.0401.0392.0384.0375.0367 H a : p
>.5 =.0250 / 1 =.0250 one proportion test 3. Determine the
critical value(s). Hypothesis Testing -z.0250 -1.96 z.0250
1.96