Stat Test Practice Test 4 Rated A+
A 2014 study by the reputable Gallup organization estimates that 44% of U.S. adults are
underemployed. Underemployed means the person wants to work full time but is
employed part time or unemployed. We want to know if the proportion is smaller this
year. We select a random sample of 100 U.S. adults this year and find that 40% are
underemployed.
After carrying out the hypothesis test for p = 0.44 compared to p < 0.44, we obtain a
P-value of 0.21. Which of the following interpretations of the P-value is correct? -
ANSWER-There is a 21% chance that a sample of 100 U.S. adults will have 40% or
fewer underemployed if 44% of the population is underemployed this year.
A group of 71 college students from a certain liberal arts college were randomly
sampled and asked about the number of alcoholic drinks they have in a typical week.
The purpose of this study was to compare the drinking habits of the students at the
college to the drinking habits of college students in general. In particular, the dean of
students, who initiated this study, would like to check whether the mean number of
alcoholic drinks that students at his college in a typical week differs from the mean of
U.S. college students in general, which is estimated to be 4.73.
The group of 71 students in the study reported an average of 3.91 drinks per with a
standard deviation of 3.88 drinks.
Find the p-value for the hypothesis test - ANSWER-
A medical researcher is studying the effects of a drug on blood pressure. Subjects in the
study have their blood pressure taken at the beginning of the study. After being on the
medication for 4 weeks, their blood pressure is taken again. The change in blood
pressure is recorded and used in doing the hypothesis test.
Change: Final Blood Pressure - Initial Blood Pressure
The researcher wants to know if there is evidence that the drug affects blood pressure.
At the end of 4 weeks, 36 subjects in the study had an average change in blood
pressure of 2.4 with a standard deviation of 4.5.
Find the p-value for the hypothesis test. - ANSWER-
A politician claims that a larger proportion of members of the news media are
Democrats when compared to the general public. Let p1 represent the proportion of the
news media that is Democrat and p2 represent the proportion of the public that is
Democrat. What are the appropriate null and alternative hypotheses that correspond to
this claim? - ANSWER-H0: p1 - p2 = 0; Ha: p1 - p2 > 0
A quality control engineer at a potato chip company tests the bag filling machine by
weighing bags of potato chips. Not every bag contains exactly the same weight. But if
more than 15% of bags are over-filled then they stop production to fix the machine.
They define over-filled to be more than 1 ounce above the weight on the package.
The engineer weighs 100 bags and finds that 21 of them are over-filled. He plans to test
the hypotheses H0:p=0.15 versus Ha:p>0.15.
,What is the test statistic? - ANSWER-z = 1.68 (multiple choice)
A quality control engineer at a potato chip company tests the bag filling machine by
weighing bags of potato chips. Not every bag contains exactly the same weight. But if
more than 15% of bags are over-filled then they stop production to fix the machine.
They define over-filled to be more than 1 ounce above the weight on the package.
The engineer weighs 102 bags and finds that 32 of them are over-filled. He plans to test
the hypotheses H0: p = 0.15 versus Ha: p > 0.15. What is the test statistic? - ANSWER-
z=
A researcher conducts an experiment on human memory and recruits 15 people to
participate in her study. She performs the experiment and analyzes the results. She
uses a t-test for a mean and obtains a p-value of 0.17.
Which of the following is a reasonable interpretation of her results? - ANSWER-If there
is a treatment effect, the sample size was too small to detect it.
A scientist claims that a smaller proportion of members of the National Academy of
Sciences are women when compared to the proportion of women nationwide. Let p1
represent the proportion of women in the National Academy of Sciences and p2
represent the proportion of women nationwide. Which is the correct alternative
hypotheses that corresponds to this claim? - ANSWER-Ha: p1 - p2 < 0
A teacher is experimenting with computer-based instruction. In which situation could the
teacher use a hypothesis test for a population mean? - ANSWER-She gives each
student a pretest. Then she teaches a lesson using a computer program. Afterwards,
she gives each student a posttest. The teacher wants to see if the difference in scores
will show an improvement.
A tire manufacturer has a 60,000 mile warranty for tread life. The manufacturer
considers the overall tire quality to be acceptable if less than 5% are worn out at 60,000
miles. The manufacturer tests 250 tires that have been used for 60,000 miles. They find
that 3.6% of them are worn out. With this data, we test the following hypotheses.
H0: The proportion of tires that are worn out after 60,000 miles is equal to 0.05.
Ha: The proportion of tires that are worn out after 60,000 miles is less than 0.05.
In order to assess the evidence, which question best describes what we need to
determine? - ANSWER-NEED ANSWER Incorrect. In a hypothesis test we are trying to
estimate the chance that random sampling produces sample results are as or more
extreme than the result observed in the data if the null hypothesis is true. The statement
you chose asks, in essence, "What is the chance that the population proportion is less
than the null value?" In other words, the statement you chose asks, "What is the chance
that the alternative hypothesis is true?" But a hypothesis test cannot determine this.
A tire manufacturer has a 60,000 mile warranty for tread life. The manufacturer
considers the overall tire quality to be acceptable if less than 5% are worn out at 60,000
miles. The manufacturer tests 250 tires that have been used for 60,000 miles. They find
, that 9 of them are worn out. With this data, we test the following hypotheses at the 5%
significance level. The p-value is 0.15.
H0: The proportion of tires that are worn out after 60,000 miles is equal to 0.05.
Ha: The proportion of tires that are worn out after 60,000 miles is less than 0.05.
Which of the following conclusions is correct? - ANSWER-Fail to reject H0
According to a Pew Research Center study, in May 2011, 33% of all American adults
had a smart phone (one which the user can use to read email and surf the Internet). A
communications professor at a university believes this percentage is higher among
community college students. She selects 349 community college students at random
and finds that 138 of them have a smart phone. In testing the hypotheses:
H0: p = 0.33 versus
Ha: p > 0.33,
she calculates the test statistic as z = 2.5990.
Then the p-value = - ANSWER-
According to a Pew Research Center study, in May 2011, 39% of all American adults
had a smart phone (one which the user can use to read email and surf the Internet). A
communications professor at a university believes this percentage is higher among
community college students. She selects 341 community college students at random
and finds that 163 of them have a smart phone. Then in testing the hypotheses:
H0: p = 0.39 versus
Ha: p > 0.39,
what is the test statistic? - ANSWER-
According to the National Institute on Drug Abuse, a U.S. government agency, 17.3% of
8th graders in 2010 had used marijuana at some point in their lives. A school official
hopes to show the percentage is lower in his district, testing H0: p = 0.173 versus Ha: p
< 0.173.
The health department for the district uses anonymous random sampling and finds that
10% of 80 eighth graders surveyed had used marijuana.
Is the sample size condition for conducting a hypothesis test for a population proportion
satisfied? - ANSWER-Yes, because (80)(.173) and (80)(1 - 0.173) are both at least 10.
This means we can use the normal distribution to model the distribution of sample
proportions.
Cheating: According to a report on academic cheating by ETS, the Educational Testing
Service, college students majoring in Business and Engineering are more likely to cheat
than students in other majors. For a statistics project, a community college student at
Diablo Valley College (DVC) decides to investigate cheating in two popular majors at
DVC: business and nursing. She convinces professors who teach business and nursing
courses to distribute a short anonymous survey in their classes. The question about
cheating is one of many other questions about college life.
From this data, the student plans to calculate a confidence interval for the difference in
two population proportions. Which is the most reasonable description of the two
populations for her conclusion? - ANSWER-
A 2014 study by the reputable Gallup organization estimates that 44% of U.S. adults are
underemployed. Underemployed means the person wants to work full time but is
employed part time or unemployed. We want to know if the proportion is smaller this
year. We select a random sample of 100 U.S. adults this year and find that 40% are
underemployed.
After carrying out the hypothesis test for p = 0.44 compared to p < 0.44, we obtain a
P-value of 0.21. Which of the following interpretations of the P-value is correct? -
ANSWER-There is a 21% chance that a sample of 100 U.S. adults will have 40% or
fewer underemployed if 44% of the population is underemployed this year.
A group of 71 college students from a certain liberal arts college were randomly
sampled and asked about the number of alcoholic drinks they have in a typical week.
The purpose of this study was to compare the drinking habits of the students at the
college to the drinking habits of college students in general. In particular, the dean of
students, who initiated this study, would like to check whether the mean number of
alcoholic drinks that students at his college in a typical week differs from the mean of
U.S. college students in general, which is estimated to be 4.73.
The group of 71 students in the study reported an average of 3.91 drinks per with a
standard deviation of 3.88 drinks.
Find the p-value for the hypothesis test - ANSWER-
A medical researcher is studying the effects of a drug on blood pressure. Subjects in the
study have their blood pressure taken at the beginning of the study. After being on the
medication for 4 weeks, their blood pressure is taken again. The change in blood
pressure is recorded and used in doing the hypothesis test.
Change: Final Blood Pressure - Initial Blood Pressure
The researcher wants to know if there is evidence that the drug affects blood pressure.
At the end of 4 weeks, 36 subjects in the study had an average change in blood
pressure of 2.4 with a standard deviation of 4.5.
Find the p-value for the hypothesis test. - ANSWER-
A politician claims that a larger proportion of members of the news media are
Democrats when compared to the general public. Let p1 represent the proportion of the
news media that is Democrat and p2 represent the proportion of the public that is
Democrat. What are the appropriate null and alternative hypotheses that correspond to
this claim? - ANSWER-H0: p1 - p2 = 0; Ha: p1 - p2 > 0
A quality control engineer at a potato chip company tests the bag filling machine by
weighing bags of potato chips. Not every bag contains exactly the same weight. But if
more than 15% of bags are over-filled then they stop production to fix the machine.
They define over-filled to be more than 1 ounce above the weight on the package.
The engineer weighs 100 bags and finds that 21 of them are over-filled. He plans to test
the hypotheses H0:p=0.15 versus Ha:p>0.15.
,What is the test statistic? - ANSWER-z = 1.68 (multiple choice)
A quality control engineer at a potato chip company tests the bag filling machine by
weighing bags of potato chips. Not every bag contains exactly the same weight. But if
more than 15% of bags are over-filled then they stop production to fix the machine.
They define over-filled to be more than 1 ounce above the weight on the package.
The engineer weighs 102 bags and finds that 32 of them are over-filled. He plans to test
the hypotheses H0: p = 0.15 versus Ha: p > 0.15. What is the test statistic? - ANSWER-
z=
A researcher conducts an experiment on human memory and recruits 15 people to
participate in her study. She performs the experiment and analyzes the results. She
uses a t-test for a mean and obtains a p-value of 0.17.
Which of the following is a reasonable interpretation of her results? - ANSWER-If there
is a treatment effect, the sample size was too small to detect it.
A scientist claims that a smaller proportion of members of the National Academy of
Sciences are women when compared to the proportion of women nationwide. Let p1
represent the proportion of women in the National Academy of Sciences and p2
represent the proportion of women nationwide. Which is the correct alternative
hypotheses that corresponds to this claim? - ANSWER-Ha: p1 - p2 < 0
A teacher is experimenting with computer-based instruction. In which situation could the
teacher use a hypothesis test for a population mean? - ANSWER-She gives each
student a pretest. Then she teaches a lesson using a computer program. Afterwards,
she gives each student a posttest. The teacher wants to see if the difference in scores
will show an improvement.
A tire manufacturer has a 60,000 mile warranty for tread life. The manufacturer
considers the overall tire quality to be acceptable if less than 5% are worn out at 60,000
miles. The manufacturer tests 250 tires that have been used for 60,000 miles. They find
that 3.6% of them are worn out. With this data, we test the following hypotheses.
H0: The proportion of tires that are worn out after 60,000 miles is equal to 0.05.
Ha: The proportion of tires that are worn out after 60,000 miles is less than 0.05.
In order to assess the evidence, which question best describes what we need to
determine? - ANSWER-NEED ANSWER Incorrect. In a hypothesis test we are trying to
estimate the chance that random sampling produces sample results are as or more
extreme than the result observed in the data if the null hypothesis is true. The statement
you chose asks, in essence, "What is the chance that the population proportion is less
than the null value?" In other words, the statement you chose asks, "What is the chance
that the alternative hypothesis is true?" But a hypothesis test cannot determine this.
A tire manufacturer has a 60,000 mile warranty for tread life. The manufacturer
considers the overall tire quality to be acceptable if less than 5% are worn out at 60,000
miles. The manufacturer tests 250 tires that have been used for 60,000 miles. They find
, that 9 of them are worn out. With this data, we test the following hypotheses at the 5%
significance level. The p-value is 0.15.
H0: The proportion of tires that are worn out after 60,000 miles is equal to 0.05.
Ha: The proportion of tires that are worn out after 60,000 miles is less than 0.05.
Which of the following conclusions is correct? - ANSWER-Fail to reject H0
According to a Pew Research Center study, in May 2011, 33% of all American adults
had a smart phone (one which the user can use to read email and surf the Internet). A
communications professor at a university believes this percentage is higher among
community college students. She selects 349 community college students at random
and finds that 138 of them have a smart phone. In testing the hypotheses:
H0: p = 0.33 versus
Ha: p > 0.33,
she calculates the test statistic as z = 2.5990.
Then the p-value = - ANSWER-
According to a Pew Research Center study, in May 2011, 39% of all American adults
had a smart phone (one which the user can use to read email and surf the Internet). A
communications professor at a university believes this percentage is higher among
community college students. She selects 341 community college students at random
and finds that 163 of them have a smart phone. Then in testing the hypotheses:
H0: p = 0.39 versus
Ha: p > 0.39,
what is the test statistic? - ANSWER-
According to the National Institute on Drug Abuse, a U.S. government agency, 17.3% of
8th graders in 2010 had used marijuana at some point in their lives. A school official
hopes to show the percentage is lower in his district, testing H0: p = 0.173 versus Ha: p
< 0.173.
The health department for the district uses anonymous random sampling and finds that
10% of 80 eighth graders surveyed had used marijuana.
Is the sample size condition for conducting a hypothesis test for a population proportion
satisfied? - ANSWER-Yes, because (80)(.173) and (80)(1 - 0.173) are both at least 10.
This means we can use the normal distribution to model the distribution of sample
proportions.
Cheating: According to a report on academic cheating by ETS, the Educational Testing
Service, college students majoring in Business and Engineering are more likely to cheat
than students in other majors. For a statistics project, a community college student at
Diablo Valley College (DVC) decides to investigate cheating in two popular majors at
DVC: business and nursing. She convinces professors who teach business and nursing
courses to distribute a short anonymous survey in their classes. The question about
cheating is one of many other questions about college life.
From this data, the student plans to calculate a confidence interval for the difference in
two population proportions. Which is the most reasonable description of the two
populations for her conclusion? - ANSWER-
