Hypothesis Testing with One Sample

In hypothesis testing, what is the null hypothesis (H0)?

What does the alternative hypothesis (Ha) represent in hypothesis testing?

A medical trial is conducted to test whether a new medicine reduces cholesterol by 25 percent. What are the correct null and alternative hypotheses?

What is a Type I error in the context of hypothesis testing?

In the scenario where the null hypothesis is 'a patient is not sick,' which type of error has the greater consequence?

What is the Power of the Test?

When performing a hypothesis test for a single population mean where the population standard deviation is unknown and the sample size is less than 30, which distribution should be used?

In a hypothesis test for proportions, what conditions must be met to approximate the binomial distribution with the normal distribution?

If a hypothesis test is conducted where H0: μ = 100 and the resulting test statistic Zc is -2.8, with a critical value Zα of -1.96 for a left-tailed test at a 5 percent significance level, what is the correct decision?

Using the p-value approach, when do you reject the null hypothesis?

A test of a claim, such as a car manufacturer claiming their new model gets 'greater than' 25 miles per gallon, would be what type of test?

In Example 9.8, Jeffrey's dad, Frank, tests if new goggles help Jeffrey swim the 25-yard freestyle faster than his established mean of 16.43 seconds. What is the correct null hypothesis (H0)?

In Example 9.8, the p-value for Jeffrey's swim time was 0.0187 and the significance level was 0.05. What was the correct decision?

In the salad dressing example (Example 9.10), why was a two-tailed test used?

In the salad dressing example (Example 9.10), the calculated test statistic was -3.07 and the critical value was 2.575. What was the conclusion?

According to the systematic approach for testing a hypothesis outlined in Section 9.4, what is typically the hardest part of the process?

For a test of a single population mean, what are the fundamental assumptions for a Student's t-test to work properly?

If a test of the mean entry-level salary of an employee is stated as being '$58,000' and you believe it is 'higher for IT professionals', what is the alternative hypothesis (Ha)?

What is the primary reason the scientific method, and by extension hypothesis testing, puts the 'burden of proof' on the alternative hypothesis?

In a study of 420,019 cell phone users, 172 developed brain cancer. The rate for non-cell phone users is 0.0340 percent. What is the correct null hypothesis to test the claim that cell phone users develop cancer at a GREATER rate?

If a hypothesis test is described as 'left-tailed,' what does that imply about the alternative hypothesis (Ha)?

What is the test statistic for a hypothesis test of a single population proportion?

A sociologist claims the probability that a person picked at random in Times Square is visiting the area is 0.83. You want to test if the proportion is actually less. What is the random variable in this scenario?

In the consumer group example (Example 9.12), a survey of 150 households found that 43 had three or more cell phones. The test was for a proportion of 30 percent. Calculate the sample proportion, p'.

If you are performing a hypothesis test of a single population mean and you find out that np is less than five, what must you do?

A test for a single population mean is conducted. The sample mean is 12.8, the hypothesized population mean is 13, the sample size is 20, and the population is assumed to be normal. Which distribution should be used?

What is the consequence of committing a Type I error when testing the hypothesis that a new drug is unsafe (H0: The drug is unsafe)?

For the data in Problem 84 (page 409), a sample of a college math class resulted in a mean family size of 3.826. The national average is 3.13. The test is conducted at an alpha of 0.05. If the calculated p-value is 0.0005, what is the correct conclusion?

What is the primary reason for creating a graph of the distribution and marking the critical value and test statistic during a hypothesis test?

A test is conducted to see if the mean time spent in jail by a first-time convicted burglar has increased from the previous mean of 2.5 years. What is the null hypothesis (H0)?

A study is conducted on Jasmine, a new salesperson. A sample of 16 sales calls has a mean value of 108 dollars and a standard deviation of 12 dollars. The test is to see if her population mean is less than 100 dollars. What is the correct test statistic to use?

In Example 9.9, the calculated test statistic (t-score) is 2.67. With 15 degrees of freedom and a 5 percent significance level for a right-tailed test, the critical value is 1.753. What is the correct decision?

If you are testing if a mean is 'at most 12', how would you write the alternative hypothesis (Ha)?

Why must you assume the underlying distribution of data is normal when performing a hypothesis test of a single population mean using a Student’s t-distribution with a small sample?

An article reports that teenagers spend 4.5 hours per week on the phone. An organization believes the mean is now higher. A sample of 15 teenagers had a mean of 4.75 hours. What is the null hypothesis (H0)?

What does it mean if the conclusion of a hypothesis test is 'do not reject the null hypothesis'?

In a study, the null hypothesis is that the mean lifespan of a brand of tires is at least 50,000 miles (H0: μ ≥ 50,000). A test is conducted and the p-value is found to be 0.0103. At a 5 percent significance level, what is the correct decision?

A test for a population mean is conducted, and the alternative hypothesis is Ha: μ ≠ 9. This indicates what kind of test?

In Problem 61 on page 395, a study tests if the mean work week for women has increased from 80 hours. The sample mean was 83 and the test was at the 5 percent significance level. If the conclusion was to reject the null hypothesis, what does this mean?

A bathroom scale claims to be accurate within a pound. You believe it cannot be that accurate. What kind of test would you use?

What is the probability of a Type II error denoted by?

If you perform a hypothesis test and your decision is to 'reject the null hypothesis', which type of error could you have possibly made?

A survey of 100 people in a town found that 7 suffered from depression. A test is conducted to see if the proportion in the town is lower than the national average of 9.5 percent. What is the correct alternative hypothesis?

What is the primary purpose of the scientific method as described in the introduction to Chapter 9?

In a test for a single mean, if the null hypothesis is H0: µ = 50, the alternative is Ha: µ ≠ 50, and the significance level is 0.05, how is the alpha risk distributed?

A particular brand of tires claims its deluxe tire averages at least 50,000 miles. What is the correct alternative hypothesis (Ha) for this test?

In Problem 79 (page 409), a report on homes heated by natural gas is being tested. The national rate is 51.7 percent. A sample of 221 homes in Kentucky found 115 were heated by gas. What is the sample proportion p'?

A study is conducted to see if the mean number of sick days an employee takes per year is ten. A sample of eight employees is surveyed. Why is a Student's t-distribution appropriate for this test, assuming the population of sick days is normal?

What is the power of a test if the probability of a Type II error (beta) is 0.019?

If a research claim is that a new teaching method helps 'more than 30 percent' of students, what is the corresponding null hypothesis (H0)?