tatement I: When sampling from a population. irthe sample size is at least 30, t

Question

tatement I: When sampling from a population. irthe sample size is at least 30, t is possible the observed sample wiLnot be normally distrbuted. but e sampling distribution for the sample mean be normally distributed. statement ll: The Central Limit Theorem guarantees that if the sample size is at least 30, then the values observed in the sample wil be normaly distributed. Which of the following is correct? O A. Statement I only. O B. Statement ll only. O C. Both statements land ll O D. Neither statement or ll. Click to select your answer

Explanation / Answer

1)

If sample size is large ( at least 30 ) then according to central limit theorem distribution of sample mean is approximately normal.

Statement 1 is correct .

2)

If test statistics fall in rejection region then we reject null hypothesis.

According to p-value approach, we reject null hypothesis if p- value is less then level of significance.

and test statistics is used to finde p- value.

For right tailed test , P-value = P( t > test statistics )

For left tailed test , P value = P( t < test statistics )

For two tailed test , p-value = 2*P( t > | test statistics )

Option c is correct !

3)

Option c is correct.

For large sample size any distribution follows normal distribution. If large sample size then df is large so in this case t distribution convert to normal distribution. So we can not compare size of critical value without knowing sample size.

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