Unit 7.1 Developing Hypothesis and
understanding Possible Conclusions
Question: Which type of test is used in the following scenario:
The mean cutting rate of two competing table saws is to be compared. Fourteen cuts are randomly
selected and measured for cutting speed to test if the speeds were different from each other. Both
populations have normal distributions with known standard deviation.
Answer: The hypothesis is two-tailed because the alternative hypothesis is Ha:μ1≠μ2.
In order for saw 1 to have the same cutting speed as saw 2, the mean cutting rate of saw 1 must be equal
to the mean cutting rate of saw 2: μ1=μ2. The null hypothesis must have some form of equality,
so Ha is μ1−μ2≠0 and H0 is μ1−μ2=0. Since the test is used to determine if the difference μ1−μ2 is
significantly different from 0, the test is two-tailed.
Question
Determine the Type I error if the null hypothesis, H0, is: researchers claim that 65% of college students
will graduate with debt.
Answer: The researchers think that greater than or less than 65% of college students will graduate with
debt when, in fact, 65%will graduate with debt.
A Type I error is the decision to reject the null hypothesis when it is true. In this case, the Type I error is
when the researchers think that greater than or less than 65% of college students will graduate with debt
when it actually will be 65%.
Question: A consumer protection company is testing a seat belt to see how much force it can hold. The
null hypothesis, H0, is that the seat belt can hold at least 5000 pounds of force. The alternative
hypothesis, Ha, is that the seat belt can hold less than 5000pounds of force.
What is a Type II error in this scenario?
Answer: The researchers conclude that the seat belt holds at least 5000 pounds of force, but the seat belt
actually holds less than 5000 pounds.
Remember that a Type I error is rejecting the null hypothesis when the null hypothesis is true.
A Type II error is not rejecting the null hypothesis when it is false.
We are asked for the Type II error in this scenario. Failing to reject the null hypothesis means failing to
reject the statement that the seat belt can hold more than 5000 pounds. Therefore, a Type II error is:
The researchers conclude that the seat belt holds at least 5000 pounds when in reality it holds less
than 5000 pounds.
Question
A city claims that the mean number of public transportation users per day is at least 4,800. A group of
researchers think this is not accurate and want to show that the number of public transportation users is
less than 4,800.
Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter μ.
Answer: H0: μ≥4,800; Ha: μ<4,800
Let the parameter μ be used to represent the mean.
Remember that the null hypothesis is the statement that the researchers are trying to reject. So, in this
case, the null hypothesis is the city's claim that μ is at least 4,800. In symbols, H0 is μ≥4,800.
The alternative hypothesis is the statement that the researchers are trying to show. So Ha is μ<4,800.
Question
, A study claims that the mean age of online dating service users is 40 years. Some researchers think this is
not accurate and want to show that the mean age is not 40 years.
Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter μ.
Answer: H0: μ=40; Ha: μ≠40
Let the parameter μ be used to represent the mean.
Remember that the null hypothesis, H0, is the claim that researchers are trying to reject. In this case, the
null hypothesis is the study's claim that μ=40.
The alternative hypothesis Ha is the opposite of this, μ≠40.
Question
Which of the following results in a null hypothesis p=0.3 and alternative hypothesis p≠0.3?
Answer: An insurance company claims that 30% of adults between the ages of 30 and 40 are overweight.
A group of doctors think that is not accurate, and wants to show that the percent of these adults that are
overweight is not 30%.
Remember that the null hypothesis, p=0.3, is the claim that the researchers (in this case, the doctors) are
trying to reject. So the insurance company's claim should be that p=0.3 and the group of doctors should
try to show that p≠0.3. This is the fourth answer choice.
Question
A car magazine claims that 68% of car owners follow a normal maintenance schedule. A mechanic does
not think this is accurate, and so he wants to show that the percentage of people who follow a normal
maintenance schedule is not equal to 68%.
Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter p.
Answer: H0: p=0.68; Ha: p≠0.68
The null hypothesis is the stated or claimed fact that the researcher is trying to refute or reject. In this
case, this is the claim of the car magazine that 68% of car owners follow a normal maintenance schedule.
So H0 is p=0.68.
The alternative hypothesis Ha is what the researcher (the mechanic in this case) is trying to show. It is the
opposite of the null hypothesis. Namely, Ha is p≠0.68.
Question
Which of the following results in a null hypothesis p≤0.48 and alternative hypothesis p>0.48?
Answer: A car magazine claims that at most 48% of car owners follow a normal maintenance schedule. A
mechanic thinks this is incorrect and wants to show that the percent of car owners who follow a normal
maintenance schedule is more than 48%.
Remember that the null hypothesis is the claim that the researcher (in this case the mechanic) is trying to
reject. So the null hypothesis, p≤0.48, corresponds to the claim of the car magazine, and the alternative
hypothesis p>0.48 corresponds to what the mechanic is trying to show.
Thus, the car magazine claim should be that the percent is at most 48%, and the mechanic should be
trying to show the percent is greater than 48%, which is the second answer choice.
understanding Possible Conclusions
Question: Which type of test is used in the following scenario:
The mean cutting rate of two competing table saws is to be compared. Fourteen cuts are randomly
selected and measured for cutting speed to test if the speeds were different from each other. Both
populations have normal distributions with known standard deviation.
Answer: The hypothesis is two-tailed because the alternative hypothesis is Ha:μ1≠μ2.
In order for saw 1 to have the same cutting speed as saw 2, the mean cutting rate of saw 1 must be equal
to the mean cutting rate of saw 2: μ1=μ2. The null hypothesis must have some form of equality,
so Ha is μ1−μ2≠0 and H0 is μ1−μ2=0. Since the test is used to determine if the difference μ1−μ2 is
significantly different from 0, the test is two-tailed.
Question
Determine the Type I error if the null hypothesis, H0, is: researchers claim that 65% of college students
will graduate with debt.
Answer: The researchers think that greater than or less than 65% of college students will graduate with
debt when, in fact, 65%will graduate with debt.
A Type I error is the decision to reject the null hypothesis when it is true. In this case, the Type I error is
when the researchers think that greater than or less than 65% of college students will graduate with debt
when it actually will be 65%.
Question: A consumer protection company is testing a seat belt to see how much force it can hold. The
null hypothesis, H0, is that the seat belt can hold at least 5000 pounds of force. The alternative
hypothesis, Ha, is that the seat belt can hold less than 5000pounds of force.
What is a Type II error in this scenario?
Answer: The researchers conclude that the seat belt holds at least 5000 pounds of force, but the seat belt
actually holds less than 5000 pounds.
Remember that a Type I error is rejecting the null hypothesis when the null hypothesis is true.
A Type II error is not rejecting the null hypothesis when it is false.
We are asked for the Type II error in this scenario. Failing to reject the null hypothesis means failing to
reject the statement that the seat belt can hold more than 5000 pounds. Therefore, a Type II error is:
The researchers conclude that the seat belt holds at least 5000 pounds when in reality it holds less
than 5000 pounds.
Question
A city claims that the mean number of public transportation users per day is at least 4,800. A group of
researchers think this is not accurate and want to show that the number of public transportation users is
less than 4,800.
Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter μ.
Answer: H0: μ≥4,800; Ha: μ<4,800
Let the parameter μ be used to represent the mean.
Remember that the null hypothesis is the statement that the researchers are trying to reject. So, in this
case, the null hypothesis is the city's claim that μ is at least 4,800. In symbols, H0 is μ≥4,800.
The alternative hypothesis is the statement that the researchers are trying to show. So Ha is μ<4,800.
Question
, A study claims that the mean age of online dating service users is 40 years. Some researchers think this is
not accurate and want to show that the mean age is not 40 years.
Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter μ.
Answer: H0: μ=40; Ha: μ≠40
Let the parameter μ be used to represent the mean.
Remember that the null hypothesis, H0, is the claim that researchers are trying to reject. In this case, the
null hypothesis is the study's claim that μ=40.
The alternative hypothesis Ha is the opposite of this, μ≠40.
Question
Which of the following results in a null hypothesis p=0.3 and alternative hypothesis p≠0.3?
Answer: An insurance company claims that 30% of adults between the ages of 30 and 40 are overweight.
A group of doctors think that is not accurate, and wants to show that the percent of these adults that are
overweight is not 30%.
Remember that the null hypothesis, p=0.3, is the claim that the researchers (in this case, the doctors) are
trying to reject. So the insurance company's claim should be that p=0.3 and the group of doctors should
try to show that p≠0.3. This is the fourth answer choice.
Question
A car magazine claims that 68% of car owners follow a normal maintenance schedule. A mechanic does
not think this is accurate, and so he wants to show that the percentage of people who follow a normal
maintenance schedule is not equal to 68%.
Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter p.
Answer: H0: p=0.68; Ha: p≠0.68
The null hypothesis is the stated or claimed fact that the researcher is trying to refute or reject. In this
case, this is the claim of the car magazine that 68% of car owners follow a normal maintenance schedule.
So H0 is p=0.68.
The alternative hypothesis Ha is what the researcher (the mechanic in this case) is trying to show. It is the
opposite of the null hypothesis. Namely, Ha is p≠0.68.
Question
Which of the following results in a null hypothesis p≤0.48 and alternative hypothesis p>0.48?
Answer: A car magazine claims that at most 48% of car owners follow a normal maintenance schedule. A
mechanic thinks this is incorrect and wants to show that the percent of car owners who follow a normal
maintenance schedule is more than 48%.
Remember that the null hypothesis is the claim that the researcher (in this case the mechanic) is trying to
reject. So the null hypothesis, p≤0.48, corresponds to the claim of the car magazine, and the alternative
hypothesis p>0.48 corresponds to what the mechanic is trying to show.
Thus, the car magazine claim should be that the percent is at most 48%, and the mechanic should be
trying to show the percent is greater than 48%, which is the second answer choice.
