Chapter 9 Homework
A Type II error is made when we reject the null hypothesis and the null hypothesis is actually false.
FALSE
For a given sample size, any attempt to reduce the likelihood of making one type of error (Type I or Type II) will increase the likelihood of the other error.
TRUE Explanation It is not always easy to determine which of two errors has more serious consequences. For a given evidence, there is a trade-off between these errors; by reducing Type I error, we implicitly increase Type II error, and vice versa.
It is generally believed that no more than 0.50 of all babies in a town in Texas are born out of wedlock. A politician claims that the proportion of babies born out of wedlock is increasing. In testing the politician's claim, how does one define the population parameter of interest?
The current proportion of babies born out of wedlock.
In general, the null and alternative hypotheses are __________.
mutually exclusive Explanation We use hypothesis testing to resolve conflicts between two competing hypotheses on a particular population parameter of interest, and these competing hypotheses are mutually exclusive.
The hypothesis statement H: µ = 25 is an example of a(an) ________ hypothesis.
null Explanation In general, the null hypothesis regarding a particular population parameter of interest is specified with one of the following signs: =, ≥, ≤; the alternative hypothesis is then specified with the corresponding opposite sign: ≠, >, <.
We define the allowed probability of making a Type I error as α, and we refer to 100α% as the ____________.
significance level
A statistics professor works tirelessly to catch students cheating on his exams. He has particular routes for his teaching assistants to patrol, an elevated chair to ensure an unobstructed view of all students, and even a video recording of the exam in case additional evidence needs to be collected. He estimates that he catches 95% of students who cheat in his class, but 1% of the time that he accuses a student of cheating he is actually incorrect. Consider the null hypothesis, "the student is not cheating." What is the probability of a Type I error?
1% Explanation A Type I error is committed when we reject the null hypothesis when the null hypothesis is actually true.Type I: provided at 1%
A schoolteacher is worried that the concentration of dangerous, cancer-causing radon gas in her classroom is greater than the safe level of 4pCi/L. The school samples the air for 36 days and finds an average concentration of 4.4pCi/L with a standard deviation of 1pCi/L. To test whether the average level of radon gas is greater than the safe level, the appropriate hypotheses are _____________________.
Ho:μ≤4.0,HA:μ>4.0 Explanation The competing hypotheses are Ho: μ ≤ μo,HA: μ > μo. It is referred to as a right-tailed test.
When conducting a hypothesis test, which of the following decisions represents an error?
Rejecting the null hypothesis when it is true Explanation -A Type I error is committed when we reject the null hypothesis when the null hypothesis is actually true. -A Type II error is made when we do not reject the null hypothesis and the null hypothesis and the null hypothesis is actually false.
Which of the following types of tests may be performed?
Right-tailed, left-tailed, and two-tailed tests Explanation A hypothesis test can be one-tailed or two-tailed.
A Type I error is committed when we reject the null hypothesis, which is actually true.
TRUE
The null hypothesis typically corresponds to a presumed default state of nature.
TRUE
As a general guideline, we use the alternative hypothesis as a vehicle to establish something new, or contest the status quo, for which a corrective action may be required.
TRUE Explanation As a general guideline, we use the alternative hypothesis as a vehicle to establish something new, that is, to contest the status quo. In general, the null hypothesis regarding a particular population parameter of interest is specified with one of the following signs: =, ≥, ≤; the alternative hypothesis is then specified with the corresponding opposite sign: ≠, >, <.
The national average for an eighth-grade reading comprehension test is 73. A school district claims that its eighth-graders outperform the national average. In testing the school district's claim, how does one define the population parameter of interest?
The mean score on the eighth-grade reading comprehension test. Explanation Hypothesis testing is used to resolve conflicts between two competing hypotheses on a particular population parameter of interest.
A(n) ______ error is committed when we reject the null hypothesis when the null hypothesis is true.
Type I
The alternative hypothesis typically ___________.
contests the status quo, for which a corrective action may be required
A Type II error occurs when we ___________.
do not reject the null hypothesis when it is actually false Explanation A Type II error is made when we do not reject the null hypothesis and the null hypothesis and the null hypothesis is actually false.
A Type I error occurs when we ___________.
reject the null hypothesis when it is actually true Explanation A Type I error is committed when we reject the null hypothesis when the null hypothesis is actually true.
A fast-food franchise is considering building a restaurant at a busy intersection. A financial advisor determines that the site is acceptable only if, on average, more than 300 automobiles pass the location per hour. If the advisor tests the hypotheses Ho: μ ≤ 300 versus HA: μ > 300, μ stands for ____________.
the average number of automobiles that pass the intersection per hour Explanation Hypothesis testing is used to resolve conflicts between two competing hypotheses on a particular population parameter of interest.
It is generally believed that no more than 0.50 of all babies in a town in Texas are born out of wedlock. A politician claims that the proportion of babies born out of wedlock is increasing. When testing the two hypotheses, H0>: p ≤ 0.50 and HA: p > 0.50, p stands for _____________.
the current proportion of babies born out of wedlock Explanation Hypothesis testing is used to resolve conflicts between two competing hypotheses on a particular population parameter of interest. It is an example of the hypothesis testing regarding the population proportion.
The null hypothesis in a hypothesis test refers to _____________.
the default state of nature Explanation We can think of a null hypothesis as corresponding to a presumed default state of nature or status quo. An alternative hypothesis, on the other hand, contradicts the default state of nature or status quo.
A fast-food franchise is considering building a restaurant at a busy intersection. A financial advisor determines that the site is acceptable only if, on average, more than 300 automobiles pass the location per hour. The advisor tests the following hypotheses: Ho: μ ≤ 300. HA: μ > 300. The consequences of committing a Type I error would be that____________________________.
the franchiser builds on an unacceptable site Explanation A Type I error is committed when we reject the null hypothesis when the null hypothesis is actually true.
A fast-food franchise is considering building a restaurant at a busy intersection. A financial advisor determines that the site is acceptable only if, on average, more than 300 automobiles pass the location per hour. The advisor tests the following hypotheses: Ho: μ ≤ 300. HA: μ > 300. The consequences of committing a Type II error would be that__________________________.
the franchiser does not build on an acceptable site Explanation A Type II error is made when we do not reject the null hypothesis and the null hypothesis and the null hypothesis is actually false.
A local courier service advertises that its average delivery time is less than 6 hours for local deliveries. When testing the two hypotheses, Ho: μ ≥ 6 and HA: μ < 6, μ stand for _____________.
the mean delivery time Explanation Hypothesis testing is used to resolve conflicts between two competing hypotheses on a particular population parameter of interest.
