Answer :
Final answer:
In inferential statistics, the conditions for inference -Random, 10%, and Large Counts conditions- are used to validate the usage of statistical tests. The Random condition necessitates a randomly collected sample, the 10% condition mandates the sample size to be no more than 10% of the population, and the Large Counts condition requires both success and failure counts in the sample to be at least 10.
Explanation:
The conditions for inference, in the realm of inferential statistics, are used to determine if statistical tests, such as a hypothesis test, can be used. The three conditions you mentioned are the Random, 10% and Large Counts conditions.
Random condition requires that your data sample is collected randomly. This is necessary to remove any potential bias and to ensure that your sample accurately represents the population. In the case of hypothesis testing, your null hypothesis should be based on a random and representative sample.
The 10% condition is met when the sample size is less than or equal to 10% of the population. This condition assumes that each individual in the population is independent of others, which is important when you're drawing without replacement.
The Large Counts condition or the 'success-failure' condition is met when the sample size is large enough such that both 'successes' (n*p) and 'failures' (n*(1-p)) are at least 10. This condition is crucial for your sample proportion to be approximately normally distributed, helping to apply the Central Limit Theorem when conducting a hypothesis test.
So, to determine if the conditions for inference are met, you need to check if your sample is random, represents 10% or less of your population, and both successes and failures are greater than or equal to 10. If all these conditions are met, then the conditions for inference are satisfied.
Learn more about Inferential Statistics here:
https://brainly.com/question/30761414
#SPJ12
If Researcher like to know if data provide convincing evidence that the true proportion of American adults who work more than one job differs from 12% , then we can say that , (a) Yes, the conditions of inference are met .
The size of the random sample (n) = 100 ;
the number of persons that work on more than one job is (x) = 18 ;
the difference is 12% that means (p) = 0.12 ,
So , [tex]q=1-p = 1-0.12 = 0.88[/tex] ;
To check for the inference ,
we calculate , [tex]n\times p = 100\times 0.12 = 12 > 5[/tex] and
[tex]n\times q = 100\times 0.88 = 88 > 5[/tex] ,
Both the conditions are true .
Therefore , we can say that the Conditions for the inference are met .
The given question is incomplete , the complete question is
According to historical data, it is believed that 12% of American adults work more than one job. To investigate if this claim is still accurate, a random sample of 100 American adults is selected. It is discovered that 18 of them work more than one job. A researcher would like to know if the data provide convincing evidence that the true proportion of American adults who work more than one job differs from 12%. Are the conditions for inference met ?
(a) Yes, the conditions for inference are met.
(b) No, the 10% condition is not met.
(c) No, the Large Counts Condition is not met.
(d) No, the randomness condition is not met.
Learn more about Inference here
https://brainly.com/question/27751801
#SPJ4
