QUESTIONS
Question 1
According to a survey, the average American person watches TV for 3 hours per week. To test if the amount of TV in New York City is less than the national average, a researcher decides to do a hypothesis test, at a 10% significance level. She surveys 26 New Yorkers randomly and asks them about their amount of TV each week, on average. From the data, the sample mean time is 2.5 hours per week, and the sample standard deviation (s) is 1.1 hours.
- H0: μ≥3; Ha: μ<3.
- α=0.1(significance level)
What is the test statistic (t-value) of this one-mean hypothesis test (with σ unknown)?
- Round your final answer to two decimal places.
Question 2
If a hypothesis test were to be performed, in which of the following contexts would a t-test be appropriate?
- A simple random sample of 19students is taken from a school of 1,188 students with approximately normally distributed heights. The sample mean is 61 inches and the sample standard deviation is 2
- A sample mean of 19miles per gallon and a standard deviation of 2 miles per gallon are obtained using a convenient sample of 10 vehicles from a large group of vehicles, which have approximately normally distributed fuel consumption rates.
- A sample mean of 84and sample standard deviation of 2 are obtained using a simple random sample of size 14 from a large population.
- A sample mean of 112minutes and a standard deviation of 9 minutes are obtained using a simple random sample of 10 movies from the collection of movies at a rental store having approximately normally distributed time lengths. The population standard deviation is 6 minutes.
Question 3
For which of the following is a t-test appropriate for performing a hypothesis test?
- A convenient sample of 23individuals is taken from the residents of a city with approximately normally distributed commute times. The sample mean is 19 minutes and the sample standard deviation is 2
- A population is used to obtain a sample mean of 53and a sample standard deviation of 7 based on a convenient sample of size 19.
- A sample mean of 70and sample standard deviation of 7 are obtained using a simple random sample of size 19 from a normally distributed population.
- A sample mean of 194pages and a standard deviation of 37 pages are obtained using a simple random sample of 30 books from a public library having approximately normally distributed numbers of pages. The population standard deviation is 4 pages.
Question 4
If a hypothesis test were to be performed, in which of the following contexts would a t-test be appropriate?
- A simple random sample of 29books is taken from a public library and the lengths (pages) were collected. The sample mean is 166 pages and the population standard deviation is 27
- A sample mean of 30pounds and a sample standard deviation of 5 pounds are obtained using a simple random sample of 27 dogs from the dogs within a county, which have approximately normally distributed weights.
- A sample mean of 31,994dollars and a standard deviation of 4,658 dollars are obtained using a simple random sample of 22 individuals from the residents of a town having approximately normally distributed incomes. The population standard deviation is 3,959.3
- A convenience sample of 16vehicles is taken from a large group of vehicles with approximately normally distributed fuel consumption rates. The sample mean is 20 miles per gallon and the sample standard deviation is 2 miles per gallon.
ANSWERS:
Question 1
According to a survey, the average American person watches TV for 3 hours per week. To test if the amount of TV in New York City is less than the national average, a researcher decides to do a hypothesis test, at a 10% significance level. She surveys 26 New Yorkers randomly and asks them about their amount of TV each week, on average. From the data, the sample mean time is 2.5 hours per week, and the sample standard deviation (s) is 1.1 hours.
- H0: μ≥3; Ha: μ<3.
- α=0.1(significance level)
What is the test statistic (t-value) of this one-mean hypothesis test (with σ unknown)?
- Round your final answer to two decimal places.
Answer
Test Statistic = −2.32
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