Download Unit 3 Review Questions (Ch. 5 and Ch. 6) A random sample of 250

Unit 3 Review Questions (Ch. 5 and Ch. 6)
1. A random sample of 250 voters were asked if they planned to vote in the next midterm
elections. Using the results, researchers formed the following 95% confidence interval
estimate of the proportion of voters who plan to vote: 0.38 ± .05. If a pundit claims that
less than half of the public plans to vote in the coming midterm elections, does the
interval support the pundit's statement?
2. A biologist wishes to estimate the average amount of nitrogen in a certain canal to
within 4 ppm and with 90% reliability. Initial tests indicate that the standard deviation
for nitrogen levels is 19 ppm. How many samples of canal water must be sampled for
the biologist to get the information she desires?
3. A business owner randomly samples 25 days of sales. The data is used to create the
following 99% interval which estimates the average daily sales total: $250 to $600. The
business owner is not happy with the resulting interval because it is very wide. If the
business owner decides she is going to collect new data and try again, what steps can
she take to ensure the interval has a smaller margin of error?
4. A sports writer is trying to estimate the average amount of stoppage time that is added
to the end of MLS soccer games. The writer randomly samples 50 games. He finds that
the average amount of stoppage time added to those games is 3.2 minutes. The
population standard deviation for the data is 1.2 minutes. Using this data, construct a
99% confidence interval to estimate the mean amount of stoppage time added to the
end of MLS games.
5. A professor wants to estimate the average amount of hours his working students work
per week. The professor sampled a random selection of 15 students who work. The
average number of hours worked per week for the sample of students was 21.3 hours.
The sample standard deviation was 5.1 hours. Form a 95% confidence interval to
estimate the true mean number of hours worked per week for working students.
6. A professor wants to estimate the average amount of hours his working students work
per week. The professor sampled a random selection of 15 students who work. The
average number of hours worked per week for the sample of students was 21.3 hours.
The sample standard deviation was 5.1 hours. Form a 95% confidence interval to
estimate the true mean number of hours worked per week for working students
7. A random sample of 500 students were asked about the costs of traditional textbooks.
Three hundred ninety-five of the students stated that traditional textbooks are too
expensive. Using the data from the sample, construct a 98% interval estimate of the
true proportion of students who believe traditional textbooks are too expensive.
8. In the past, the mean running time for a certain type of flashlight battery has been 8.5
hours. The manufacturer has introduced a change in the production method, which they
hope has increased the mean running time. The mean running time for a random
sample of 22 light bulbs was 8.65 hrs with a standard deviation of 0.4 hrs. Use this data
to find the margin of error that would be used to construct a 98% confidence interval
estimate of the true mean running time.
9. A chef wishes to estimate the average amount of time it takes to prepare for each
dinner service. He wants to form a 95% interval estimate of the mean time to prepare.
He believes the standard deviation is 16 minutes. How many dinner preps must he
randomly sample and time to estimate the true mean time to within 5 minutes?
10. For problems 1 – 3, examine the given statement and express the null and alternative
hypothesis in symbolic form:
1. The average weight loss obtained on the Atkins Diet is greater than 4 pounds. VS
2. The average grade in this class will be at least a 74. VS
3. The average waist circumference of adult males is 36.5 inches. VS
11. A consumer group claims that the Doritos snack pack size has an average weight below
1.75 ounces which is the weight labeled on the bags. A random sample of 49 bags had
an average weight of 1.71 ounces and a standard deviation of 0.13 ounces. At the 5%
significance level, test the consumer group’s claim. Give the practical interpretation of
the outcome of the test.
12. A professor claims that it takes the average student no more than 40 minutes to finish
his final exam. A random selection of 39 students was timed while taking the final. The
students had an average completion time of 41.6 minutes and a standard deviation of 6
minutes. Use a 1% significance level to test the professor’s claim. Give the practical
interpretation of the outcome of the test.
13. The CEO of Equifax credit reporting agency claims the average credit rating has dropped
below 675 points. A study of 20 randomly selected credit scores had an average of 660
points and a standard deviation of 95.3 points. Use a 5% significance level to test the
claim that credit scores are now on average below 675 points. The CEO claims the
results are not valid since they came from too small a sample. Is there any merit to his
argument?
14. A senatorial candidate claims that most of the people in the country feel they are worse
off today than they were two years ago. A poll of 500 people in the country reveals that
255 feel they are worse off today than two years ago. At the 10% significance level, test
the senatorial candidates claim.
15. Some researchers think that divorce is more likely when a couple marries at a young
age. One researcher claims that the average divorced male was younger than 25 on the
day of his wedding. A study of 33 divorced males shows their average age on the day of
their wedding was 24.3 with a standard deviation of 2.5 years. At the 3% significance
level, use the p-value method to test the researcher’s claim.
16. An accountant claims that the hourly wage for pizza delivery drivers is more than ten
dollars. If a sample of 28 pizza delivery driver’s paychecks has a mean of $9.25 and a
standard deviation of $1.00, why is it not necessary to conduct a formal hypothesis test
on the accountant’s claim?
17. Nationally 60% of Ph.D. students have paid assistantships. An FIU professor thinks at FIU
the rate is lower than this. In a random sample of 50 Ph.D. students, 26 have
assistantships. Using a 5% significance level, test the FIU professor’s claim.
18. The government mint claims that at least 77% of the public is against changing dollar
coins for dollar bills. In a survey of 800 people, 550 said they were opposed to the
change. At the 5% level of significance, test the mint’s claim.