18 Questions
What is the purpose of the null hypothesis in statistical hypothesis testing?
To provide a hypothesis of no difference.
Which type of error occurs when true null hypothesis is incorrectly rejected?
Type I error
What is the alternative hypothesis in statistical hypothesis testing?
It disagrees with the null hypothesis.
What does the critical value in hypothesis testing determine?
The point that separates acceptance and rejection regions.
What is the purpose of the test statistics in hypothesis testing?
To provide a mathematical expression of the sample value.
What is the purpose of the assumption step in hypothesis testing?
To check for normality, equality, and independence of samples
In hypothesis testing, what defines whether the null hypothesis will be accepted or rejected?
The calculated value must be less than the critical value.
When is the null hypothesis rejected in hypothesis testing?
When the calculated value is less than the tabulated value
What does the decision rule specify in hypothesis testing?
Whether to accept or reject the null hypothesis
Which test is commonly used to compare means of two different groups in hypothesis testing?
$ ext{t-test}$
What type of data is commonly used with the student (t) test in hypothesis testing?
Numerical data
In hypothesis testing, what does the distribution of test statistics help determine?
Whether to accept or reject the null hypothesis
What is the purpose of hypothesis testing?
To help in decision-making regarding a population
In the context of hypothesis testing, what is a statement focused on?
Population parameters
What are the two types of hypothesis testing mentioned?
Research type and statistical type
What percentage of observations typically lies within plus or minus 1.96 standard deviation units in a normal distribution?
95%
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?
$t \sqrt{n}$
Which measure of a normal distribution is zero by definition?
Skewness
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.
Learn about the 9 steps involved in hypothesis testing, from analyzing the nature of data to making conclusions about the null and alternative hypotheses. Understand the significance of rejecting or failing to reject the null hypothesis based on the evidence from the test.
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