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Hypothesis Testing: Wrong Critical Z Score Explained
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In summary, the conversation discusses the critical z-values for different types of hypotheses in a statistical test. Question 2 is about a left-sided hypothesis and the critical z-value needed is typically -1.645. Question 3 is about a 2-sided hypothesis and the critical z-value needed is ±2.5758 for an alpha of 0.005. The individual also mentions their difficulty in finding the correct z-values on a table.
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I like Serena
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It looks as if question (2) asks about a left sided hypothesis.
The critical z-value should then typically be $-1.645$.
Where did you get the test statistic z?
To reject the null hypothesis, we need that the test statistic z is more negative than $-1.645$.
In question (3) we have a 2-sided hypothesis.
It means that we need to find the critical z-value for $\frac \alpha 2=0.005$, which is $\pm 2.5758$.
The critical z-value should then typically be $-1.645$.
Where did you get the test statistic z?
To reject the null hypothesis, we need that the test statistic z is more negative than $-1.645$.
In question (3) we have a 2-sided hypothesis.
It means that we need to find the critical z-value for $\frac \alpha 2=0.005$, which is $\pm 2.5758$.
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yelenaaa13
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Klaas van Aarsen said:
Thank you for your response!
I got the test statistic from this formula: ((p-hat - p)/(square root((p(1-p))/n) ( i attached an image of the formula i used since this is kind of hard to read).
It was cut off, but p-hat and n were given. p-hat is 0.75 and n = 90.
And my problem with question 3 is the z critical values. It says 2.33 and -2.33 are wrong, but on the table those are the values that correspond with an alpha of 0.01
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yelenaaa13 said:
Question 3 has a 2-sided hypothesis. We need the values that correspond to alpha/2=0.005.
Question 2 has a left-sided hypothesis. You probably need a minus sign in front of the critical z-value.
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yelenaaa13
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Okay that's exactly what was wrong. Thank you so much for your help!Klaas van Aarsen said:
FAQ: Hypothesis Testing: Wrong Critical Z Score Explained
What is a critical Z score in hypothesis testing?
A critical Z score in hypothesis testing is a value that is used to determine the level of significance in a statistical test. It is based on the standard normal distribution and is used to determine the probability of obtaining a particular result by chance. Generally, a critical Z score is used to identify the boundary between the rejection and acceptance regions in a hypothesis test.
How is a critical Z score calculated?
A critical Z score is calculated by taking the significance level (alpha) of the test and finding the corresponding Z score on a standard normal distribution table. For example, if the significance level is 0.05, the critical Z score would be 1.96. This means that any result with a Z score greater than 1.96 or less than -1.96 would be considered statistically significant and the null hypothesis would be rejected.
What happens if the wrong critical Z score is used in hypothesis testing?
If the wrong critical Z score is used in hypothesis testing, it can lead to incorrect conclusions about the data. Using a lower critical Z score than is appropriate can result in a higher chance of a Type I error (rejecting the null hypothesis when it is actually true). On the other hand, using a higher critical Z score than is appropriate can result in a higher chance of a Type II error (failing to reject the null hypothesis when it is actually false).
How can one avoid using the wrong critical Z score in hypothesis testing?
To avoid using the wrong critical Z score in hypothesis testing, it is important to clearly define the significance level (alpha) before conducting the test. This should be based on the research question and the desired level of confidence in the results. Additionally, it is important to double-check the calculations and ensure that the correct Z score is being used for the chosen significance level.
Can the critical Z score be adjusted in hypothesis testing?
Yes, the critical Z score can be adjusted in hypothesis testing. This can be done by changing the significance level (alpha) of the test. A lower significance level will result in a higher critical Z score, making it more difficult to reject the null hypothesis. Conversely, a higher significance level will result in a lower critical Z score, making it easier to reject the null hypothesis. However, it is important to note that the significance level should not be changed arbitrarily and should be based on the research question and the desired level of confidence in the results.