STAT 200 Week 5: Assignment – Hypothesis Testing & Type I and II Error
STAT 200 Week 5: Assignment – Hypothesis Testing & Type I and II Error
#1 Points possible: 2. Total attempts: 3 At most 70% of Internet users pay bills online. Express the null and alternative hypotheses in symbolic
form for this claim (enter as a percentage).
H0 : p
H1 : p
Use the following codes to enter the following symbols:
? enter >=
? enter <=
? enter !=
#2 Points possible: 2. Total attempts: 3 A commonly cited standard for one-way length (duration) of school bus rides for elementary school
children is 30 minutes. A local government office in a rural area randomly samples 100 elementary
school children in their district and find an average one-way commute time of 38 minutes with a
standard deviation of 8 minutes.
Which of the following is the correct set of hypotheses for testing if the average commute time of
elementary school students in this district is different than the commonly cited standard of 30 minutes?
H0: µ = 30; HA: x = 38
H0: µ = 30; HA: µ > 30
HA: µ = 30; H0: x ? 30
H0: x = 38; HA: µ = 30
H0: µ = 30; HA: µ ? 30 #3 Points possible: 2. Total attempts: 3 A New York Times article titled For Runners, Soft Ground Can Be Hard on the Body considered two
perspectives on whether runners should stick to hard surfaces or soft surfaces following an injury. One
position supported running on soft surfaces to relieve joints that were in recovery from injury. The
second position supported running on hard surfaces since soft surfaces can be uneven, which may make
worse those injuries a soft surface was intended to help.
Suppose we are given sufficient funds to run an experiment to study this topic. With no studies to
support either position, which of the following hypotheses would be appropriate?
The first position is more sensible, so this should be a one-sided test. In this case, we should form
the alternative hypothesis around the second position.
Because we would be interested in any difference between running on hard and soft surfaces, we
should use a two-sided hypothesis test.
Because there is uncertainty, we should postpone defining the hypotheses until after we collect
data to guide the test.
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The second position makes the more sense, so this should be a one-sided test. In this case, we
should form the alternative hypothesis around the first position. #4 Points possible: 2. Total attempts: 3 If your null and alternative hypothesis are:
H0 : µ = 2
H1 : µ > 2 Then the test is:
left tailed
two tailed
right tailed #5 Points possible: 2. Total attempts: 3 A commonly cited standard for one-way length (duration) of school bus rides for elementary school
children is 30 minutes.
A local government office in a rural area conducts a study to determine if elementary schoolers in their
district have a longer average one-way commute time. If they determine that the average commute time
of students in their district is significantly higher than the commonly cited standard they will invest in
increasing the number of school busses to help shorten commute time. What would a Type 2 error mean
in this context?
The local government decides that the average commute time is 30 minutes.
The local government decides that the data provide convincing evidence of an average commute
time higher than 30 minutes, when the true average commute time is in fact 30 minutes.
The local government decides that the data do not provide convincing evidence of an average
commute time higher than 30 minutes, when the true average commute time is in fact higher than
30 minutes.
The local government decides that the data do not provide convincing evidence of an average
commute time different than 30 minutes, when the true average commute time is in fact 30
minutes. #6 Points possible: 2. Total attempts: 3 Food inspectors inspect samples of food products to see if they are safe. This can be thought of as a
hypothesis test with the following hypotheses.
H0: the food is safe
Ha: the food is not safe
The following is an example of what type of error?
The sample suggests that the food is safe, but it actually is not safe.
type I
type II
not an error #7 Points possible: 2. Total attempts: 3 If your claim is in the null hypothesis and you fail to reject the null hypothesis, then your conclusion
would be:
There is not sufficient sample evidence to support the original claim
There is sufficient evidence to warrant rejection of the original claim
The sample data support the original claim
There is not sufficient evidence to warrant rejection of the original claim