24 Questions
What is the primary goal of hypothesis testing in statistics?
To determine the value of a population parameter based on some preconceived ideas
What is the assumption about a population parameter that may or may not be true?
Hypothesis
In a criminal trial, what is the hypothesis that the jury initially assumes?
The defendant is innocent
What is the term used to describe the testing of a hypothesis to determine whether the data obtained are indicative of the general or future behavior of the phenomenon being studied?
Hypothesis Testing
What is the alternative hypothesis in a criminal trial?
The defendant is guilty
What is the purpose of looking at the context of a criminal trial in understanding hypothesis testing?
To understand the ideas of hypotheses testing
What is the outcome if the jury rejects the null hypothesis in a trial?
The defendant is guilty beyond reasonable doubt.
What does acquitting the defendant mean in a trial?
The evidence is insufficient to prove guilt.
What is the purpose of stating a null hypothesis in hypothesis testing?
To formulate a statement with the hope of it being rejected.
What is the first step in hypothesis testing?
Stating the null and alternative hypotheses.
What is the definition of β in hypothesis testing?
Power of a test.
What is the goal of hypothesis testing?
To make decisions about the population based on the sample characteristics.
What is the purpose of selecting a level of significance in a hypothesis test?
To determine the probability of rejecting the null hypothesis when it is true
What is the term for the set of values of the test statistic that result in the rejection of the null hypothesis?
Critical region
What is the purpose of formulating the decision rule in a hypothesis test?
To decide whether to reject or fail to reject the null hypothesis
What is the term for a test hypothesis where the alternative hypothesis is one-sided?
One-tailed test
What is the purpose of computing the value of the test statistic in a hypothesis test?
To evaluate the sample data using the test statistic formula
What does it mean if the value of the test statistic falls within the critical region?
The null hypothesis is rejected in favor of the alternative hypothesis
Which test is used when the data are normally distributed, the sample size is greater than or equal to 30, and the population variance or population standard deviation is known?
z-test
What is the reason for using the sample variance in the t-test?
The population variance is unknown
A survey was conducted among 25 employees, and the sample mean is 24000. If the population standard deviation is unknown, which test should be used to determine if there is a significant difference between the population mean and sample mean?
t-test
A sample of 8 measurements was randomly selected from a normally distributed population. Which test should be used to test for significant difference between the sample mean and the population mean?
t-test
Which of the following conditions is not a requirement for using the z-test?
The population variance is unknown
A factory owner claims that the average capacity of their bottled juice is 250 ml and a standard deviation of 5 ml. If a sample of 30 measurements is taken, which test should be used to test for significant difference between the sample mean and the population mean?
z-test
Study Notes
Hypothesis Testing
- Hypothesis: an assumption or conjecture about a population parameter, which may or may not be true
- Examples of hypotheses:
- The average of the final grades of Grade 11 Liceo Male Students is higher than those of the Female Students
- Coca-Cola contains 80% sugar
- A radio station selects the music it plays based on the assumption that the average age of its listening audience is 30 years old
Notations and Definitions
- H0: Null Hypothesis
- Ha: Alternative Hypothesis
- α: Significance Level (e.g. 5%, 1%)
- β: Power of a Test, Probability of a Type II error
- N: Population Size
- n: Sample Size
- μ: Population Mean
- σ: Population Standard Deviation
- σ2: Population Variance
- X̄: Sample Mean
- s: Sample Standard Deviation
- s2: Sample Variance
- z: z-value
- t: t-value
- c: Critical Value
Steps in Hypothesis Testing
- STEP 1: State the null and alternative hypotheses
- STEP 2: Select a Level of Significance (α)
- STEP 3: Select the Test Statistic
- STEP 4: Formulate the decision rule
- STEP 5: Compute the value of the test statistic
- STEP 6: Make a decision (reject or do not reject the null hypothesis)
Types of Tests
- One-tailed test: when the alternative hypothesis is one-sided
- Two-tailed test: when the alternative hypothesis is two-sided
- z-test: used when data are normally distributed, sample size ≥ 30, and population variance is known
- t-test: used when z-test cannot be used (e.g. sample size < 30, population variance unknown)
Examples of Hypothesis Testing
- Example 1: Testing the average income of customer service representatives (use t-test)
- Example 2: Testing the sample mean and population mean (use t-test)
- Example 3: Testing the average capacity of bottled juice (use t-test)
Test your understanding of essential terms in hypothesis testing, including hypotheses and hypothesis testing, with examples and scenarios. Learn how to define and apply these concepts in various situations.
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