The interpretation given to the 95% confidence interval for the population mean

Question

The interpretation given to the 95% confidence interval for the population mean based on a random sample, is that; 95% of the sample means will fall within this interval 95% of the population means will fall within this interval 95% of the intervals based on such sample s will contain the population mean The probability is 95% that the observed sample mean equals the population mean None of the above.___When we reject the null hypothesis: We might commit a type I error, but couldn't commit a type II We might commit a type II error, but couldn't commit a type I We might commit both a type I and type II error We might commit either a type I or type II error, but not both None of the above___If the correlation coefficient r = -1, then: There is a perfect negative nonlinear correlation between the bivariate data. There is a perfect negative linear correlation between the bivariate data. There is No linear relationship between the data There is a weak linear correlation between the data We have made an error in calculation. John Doe is on trial for dognapping and is assumed to be innocent until proven guilty (if found guilty he will go to jail). The court makes the wrong decision and commits a type 1 error then, John is guilty and will be sent to jail. John is not guilty but is sent to jail. John is not guilty and not sent to jail. John is guilty but not sent to jail.___Suppose that X has a continuous uniform distribution over the interval [-1, 1]. Determine the variance of X: 1/2 1/3 1/4 0.57 None of the above

Explanation / Answer

11) Ans (b) 95% population mean will fall within the interval, confidence interval for the population mean is calculated based on sample mean.

12) (A) when we commit type 1 error but not type 2 error then we reject null hypothesis

because type 1 error is rejecting null hypothesis when it is true and when we commit type 1 error then we will reject null hypothesis.

13) (B) If correlation coefficient is -1 then there is perfect negative linear correlation between the bivariate data

if r=1 then there is perfect linear correlation between the bivariate data and if r=0 then there is no correlation between the bivariate data

15) (b) X follows uniform distribution (-1,1) then variance= (b-a)^2 /12 =(1+1)^2/12 =4/12=1/3

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