Chapter 10
What is the meaning of "level of significance" in the context of hypothesis testing?
The probability of rejecting the null hypothesis when it is true
If we reject a false null hypothesis, what type of error would we be making?
no error was made
Which symbol represents the level of significance?
α
Hypothesis testing follows a six step procedure. Place these steps in order (first at the top)
1. State null and alternate hypothesis 2. Select a level of significance 3. Identify the test statistic 4. Formulate a decision rule 5. Take a sample, and use it to decide 6. Interpret the result
A soda bottling company fills bottles with 12 ounces of soda. Overfilling causes the company to give away free soda. Underfilling causes the company to cheat the customer. To test to see if the process is working correctly, the company conducts a hypothesis test using the following hypotheses: Ho: μ=12 H1: μ≠12 Which of the following is the result of a Type I error?
Concluding the population average is not 12 when it really is
Which of the following best summarizes the process of selecting a significance level for a hypothesis test of the mean?
The investigator should select the significance level before setting up the decision rule and taking the sample data
Why do many statisticians prefer the use of "fail to reject the null hypothesis" instead of "accept the null hypothesis"? Select all that apply
- Because only by rejecting the null hypothesis can we calculate the probability of a Type I error - To emphasize that there is always the possibility of a Type II error, which typically cannot be quantified
Which of the following statements of a test hypothesis uses the correct protocol for choosing a null hypotheses? Select all that apply
- H0: μ = 88 - H0: μ ≥ 27
Which of the following statements of a test hypothesis uses the correct protocol for stating an alternate hypothesis? Select all that apply
- H1: μ ≠ 24 - H1: μ < 30
Which of the following are essential elements of hypothesis testing? Select all that apply
- It uses probability theory to determine if a hypothesis is a reasonable statement - It makes use of sample data.
From the statements below, select all that are accurate descriptions of the null hypothesis=
- The null hypothesis is designated H0 - The purpose of the test is to prove the null hypothesis is false - The term "null" refers to no significant difference
Which of the following is a "hypothesis" in the statistical sense? Select all that apply
- The population mean miles per gallon of a particular car is 44 - The population mean lifetime of a particular brand of light bulb is at least 1000 hours
The probability of rejecting a true null is know as which of the following? Select all that apply
- Type I error - α
Calculate the test statistic z for a population mean of 30, a population standard deviation of 6, a sample mean of 27 and a sample size of 20
-2.24
Which one of the following best describes Hypothesis Testing?
A procedure based on sample evidence and probability to see if a hypothesis is a reasonable statement
Choose the best definition of "hypothesis" in the context of statistical analysis
A statement about a population parameter subject to verification
Which of the following is the best definition of the null hypothesis, H0?
A statement about a population parameter to be tested using sample measures
In the context of hypothesis testing, what is a test statistic?
A value, determined from sample information, used to test the null hypothesis
If the test statistic for a hypothesis test (H0: μ = 25) is z = 2.05 and the critical value for 5% significance is 1.96, what should our conclusion be?
Reject the null hypothesis and conclude the alternative is true
What is the "critical value" for a hypothesis test?
The dividing point between rejecting and failing to reject the null hypothesis