Podcast
Questions and Answers
When do you commit a Type I error?
When do you commit a Type I error?
- When you reject a null hypothesis that is false.
- When you fail to reject a null hypothesis that is false.
- When you fail to reject a null hypothesis that is true.
- When you reject a null hypothesis that is true. (correct)
If a researcher wants to increase the possibility of making a correct decision in hypothesis testing, what should they do with the level of significance?
If a researcher wants to increase the possibility of making a correct decision in hypothesis testing, what should they do with the level of significance?
- Ignore the level of significance.
- Increase the level of significance.
- Maintain the level of significance at 5%.
- Decrease the level of significance, typically to 1%. (correct)
In hypothesis testing, what is the role of the null hypothesis?
In hypothesis testing, what is the role of the null hypothesis?
- It represents the alternative explanation that the researcher is trying to prove.
- It defines the level of significance for the test.
- It is a statement of no effect or no difference that is tested against the alternative hypothesis. (correct)
- It is used to determine the sample size for the experiment.
Which of the following is the correct symbolic representation of the null hypothesis stating that there is no difference between a parameter and a specific value?
Which of the following is the correct symbolic representation of the null hypothesis stating that there is no difference between a parameter and a specific value?
A researcher is conducting a hypothesis test where the alternative hypothesis suggests that the population mean is greater than a specified value. Which type of test is being used?
A researcher is conducting a hypothesis test where the alternative hypothesis suggests that the population mean is greater than a specified value. Which type of test is being used?
What is the purpose of hypothesis testing?
What is the purpose of hypothesis testing?
Which of the following examples illustrates a Type II error?
Which of the following examples illustrates a Type II error?
What distinguishes a directional test from a non-directional test?
What distinguishes a directional test from a non-directional test?
In the context of hypothesis testing, what does the 'level of significance' represent?
In the context of hypothesis testing, what does the 'level of significance' represent?
Which test statistic is most appropriate when testing a hypothesis about a population mean, given a sample size of 25 and an unknown population standard deviation?
Which test statistic is most appropriate when testing a hypothesis about a population mean, given a sample size of 25 and an unknown population standard deviation?
In hypothesis testing, what area is defined by the 'critical region'?
In hypothesis testing, what area is defined by the 'critical region'?
Given a computed test statistic of z = 2.5 and a critical value of 1.96 for a right-tailed test, what decision should be made regarding the null hypothesis?
Given a computed test statistic of z = 2.5 and a critical value of 1.96 for a right-tailed test, what decision should be made regarding the null hypothesis?
A researcher wants to test if the average height of students in a school is different from the national average. What type of test should they use?
A researcher wants to test if the average height of students in a school is different from the national average. What type of test should they use?
With a significance level ($\alpha$) of 0.05, what is the corresponding confidence level?
With a significance level ($\alpha$) of 0.05, what is the corresponding confidence level?
A study examines whether a new drug reduces blood pressure. The null hypothesis states the drug has no effect. If a Type I error occurs, what is the likely conclusion?
A study examines whether a new drug reduces blood pressure. The null hypothesis states the drug has no effect. If a Type I error occurs, what is the likely conclusion?
For a sample size of n = 10, what are the degrees of freedom (df) for a t-distribution?
For a sample size of n = 10, what are the degrees of freedom (df) for a t-distribution?
Given a population mean ($\mu$) of 50, a sample mean ($\bar{x}$) of 55, a population standard deviation ($\sigma$) of 10, and a sample size (n) of 25, what is the calculated z-score?
Given a population mean ($\mu$) of 50, a sample mean ($\bar{x}$) of 55, a population standard deviation ($\sigma$) of 10, and a sample size (n) of 25, what is the calculated z-score?
A student is testing the hypothesis that the average test score is greater than 70. They collect data and calculate a t-statistic of 2.1 with 15 degrees of freedom. Using a significance level of $\alpha=0.05$, and a one-tailed test, what critical t-value should they compare their t-statistic to, to make a decision?
A student is testing the hypothesis that the average test score is greater than 70. They collect data and calculate a t-statistic of 2.1 with 15 degrees of freedom. Using a significance level of $\alpha=0.05$, and a one-tailed test, what critical t-value should they compare their t-statistic to, to make a decision?
If you reject the null hypothesis, what does this indicate?
If you reject the null hypothesis, what does this indicate?
Explain what a 'hypothesis' is, in the context of statistics.
Explain what a 'hypothesis' is, in the context of statistics.
Flashcards
Hypothesis
Hypothesis
A proposed explanation about a population parameter or the distribution of a random variable.
Hypothesis Testing
Hypothesis Testing
A statistical method used to make decisions using experimental data.
Null Hypothesis
Null Hypothesis
A statement saying there is no difference between a parameter and a specific value. Denoted by H0.
Alternative Hypothesis
Alternative Hypothesis
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Non-directional Test
Non-directional Test
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Directional Test
Directional Test
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Left-tailed test
Left-tailed test
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Right-tailed test
Right-tailed test
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Level of Significance
Level of Significance
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Type I Error
Type I Error
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Type II Error
Type II Error
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μ (mu)
μ (mu)
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XÌ„ (x-bar)
XÌ„ (x-bar)
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σ (sigma)
σ (sigma)
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s
s
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Z-test
Z-test
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T-test
T-test
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Rejection Region
Rejection Region
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Critical Value
Critical Value
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Non-rejection Region
Non-rejection Region
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Study Notes
Null and Alternative Hypothesis
- A hypothesis is a proposed explanation or assumption about a population parameter or the distribution of a random variable.
- Hypothesis testing is a statistical method for making decisions using experimental data.
- The null hypothesis (H0) states that there is no difference between a parameter and a specific value, using symbols =, ≤, or ≥.
- The alternative hypothesis (Ha or H1) is the opposite or negation of the null hypothesis, using symbols <, >, or ≠.
Types of Tests
- A non-directional test is commonly referred to as a two-tailed test, indicated by ≠.
- A directional test is commonly referred to as a one-tailed test.
- A left-tailed test checks if a value is less than another, for example <.
- A right-tailed test checks if a value is more than another, for example >.
Types of Error
- The level of significance is the probability of making an incorrect decision about the null hypothesis; a 1% level is used for a higher chance of a correct decision.
- A Type I Error occurs when a true null hypothesis is rejected; a security system detecting a thief when there is none, a student suspended for cheating but is innocent, or a patient diagnosed with cancer who is healthy.
- A Type II Error occurs when a false null hypothesis is not rejected; a COVID-19 test incorrectly saying someone is negative, a fire alarm not ringing during a fire, or an airport scanner missing a weapon.
Identifying the Appropriate Test Statistic Involving Population Mean
- µ represents the population mean, which is the average of all values in the population.
- x represents the sample mean.
- σ represents the population standard deviation, measuring variability with a fixed value from each individual.
- s represents the sample standard deviation.
- A Z-test is used when n is 30 or more, and the population or sample standard deviation is known.
- A T-test is used when the population is normal, the sample standard deviation is known, and n is 29 or below.
Rejection Region for a Given Level of Significance
- The rejection region is also known as the critical region.
- The critical value is the boundary of the rejection region.
- The non-rejection region is also known as the acceptance region.
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