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Questions and Answers
What is the purpose of the null hypothesis in statistical hypothesis testing?
What is the purpose of the null hypothesis in statistical hypothesis testing?
- To provide a hypothesis of no difference. (correct)
- To calculate the critical value for test statistics.
- To determine if there is a significant difference between two means.
- To highlight the rejection region for hypothesis testing.
Which type of error occurs when true null hypothesis is incorrectly rejected?
Which type of error occurs when true null hypothesis is incorrectly rejected?
- Acceptance region error
- Type I error (correct)
- Critical value error
- Type II error
What is the alternative hypothesis in statistical hypothesis testing?
What is the alternative hypothesis in statistical hypothesis testing?
- It agrees with the null hypothesis.
- It disagrees with the null hypothesis. (correct)
- It states that there is no significant difference.
- It provides the critical value for test statistics.
What does the critical value in hypothesis testing determine?
What does the critical value in hypothesis testing determine?
What is the purpose of the test statistics in hypothesis testing?
What is the purpose of the test statistics in hypothesis testing?
What is the purpose of the assumption step in hypothesis testing?
What is the purpose of the assumption step in hypothesis testing?
In hypothesis testing, what defines whether the null hypothesis will be accepted or rejected?
In hypothesis testing, what defines whether the null hypothesis will be accepted or rejected?
When is the null hypothesis rejected in hypothesis testing?
When is the null hypothesis rejected in hypothesis testing?
What does the decision rule specify in hypothesis testing?
What does the decision rule specify in hypothesis testing?
Which test is commonly used to compare means of two different groups in hypothesis testing?
Which test is commonly used to compare means of two different groups in hypothesis testing?
What type of data is commonly used with the student (t) test in hypothesis testing?
What type of data is commonly used with the student (t) test in hypothesis testing?
In hypothesis testing, what does the distribution of test statistics help determine?
In hypothesis testing, what does the distribution of test statistics help determine?
What is the purpose of hypothesis testing?
What is the purpose of hypothesis testing?
In the context of hypothesis testing, what is a statement focused on?
In the context of hypothesis testing, what is a statement focused on?
What are the two types of hypothesis testing mentioned?
What are the two types of hypothesis testing mentioned?
What percentage of observations typically lies within plus or minus 1.96 standard deviation units in a normal distribution?
What percentage of observations typically lies within plus or minus 1.96 standard deviation units in a normal distribution?
If the sample size (n) is less than or equal to 30, what value is used instead of 1.96 for calculating the confidence interval in a normal distribution?
If the sample size (n) is less than or equal to 30, what value is used instead of 1.96 for calculating the confidence interval in a normal distribution?
Which measure of a normal distribution is zero by definition?
Which measure of a normal distribution is zero by definition?
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Study Notes
- Hypothesis testing involves a 9-step procedure including determining the nature of data, assumptions about normality and independence, setting up hypotheses (null or alternative), using test statistics to make decisions, drawing the distribution curve, setting a decision rule for accepting or rejecting the null hypothesis, calculating test statistics, making a statistical decision based on the calculated value, and finally reaching a conclusion.
- There are two types of errors in hypothesis testing: Type I error (α) involves incorrectly rejecting a true null hypothesis, while Type II error (β) is accepting a false null hypothesis.
- The normal distribution, also known as the Gaussian Distribution, is characterized by a mean, median, and mode that are all equal, with skewness and kurtosis being zero. It is symmetrical and the total area under the curve is 1.
- In the normal distribution, about 68% of observations fall within plus or minus one standard deviation (SD), 95% within plus or minus 1.96 SD units, 99% within plus or minus 2.58 SD units, and 99.7% within plus or minus 3 SD units.
- Confidence intervals for the mean provide a range in which the true population mean is likely to lie with a certain level of assurance, expressed as X ± 1.96√n for a 95% confidence interval and X ± 2.58√n for a 99% confidence interval when n > 30, and X ± t√n when n ≤ 30.
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