I use computer software to do the following. I generate ten random numbers from

Question

I use computer software to do the following. I generate ten random numbers from a N(500, 10) distribution. From these ten numbers I compute a 95% confidence interval for the mean using the formula 10 10 X ± 1.96 where X is the mean of the ten random numbers. I then repeat this process (generating a new set of 10 random numbers from a N(500, 100) distribution each time) until I have produced 1000 such intervals. Which of the following will be true? (a) Approximately 97.5 percent of the intervals will contain the true mean because the probability that a standard normal random variable is less than 1.96 is 0.975

Explanation / Answer

1) option B is correct; approximately 95% of the intervals will contain the value 500 ; as -/+1.96 is for 2.5 and 97.5 percentile and middle 95 percentile vlaues lies between them

2)for narrowest sample size should be high and confidence interval low

therefore option e) is correct n=400 and 80% CI

3) option (d) as sample size increases ; the width of confidence interval decreases.

4) option (ii) confidence level =99% and ME =0.01

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