Suppose the data are independent observations sampled from some population distribution. In which of the following circumstances we would NOT be safe to construct a one-sample t confidence nterval for a population mean based on a simple random sample from a huge population? (Select one answer.) (i) The sample size is 5, and we know from past experience that the population distribution is normal. (ii) The sample size is 10, and the observations are 0, 0, 0, 0, 0, 0, 0 ,1 ,1 ,18. (iii) The sample size is 45 and the boxplot of the data is 0 00 m @ @ m0000 O O 2 6. 10 14 18 (iv) The sample size is 1800 and the histogram of the data is 10 20 30 40 50 (v) It's not safe to construct t confidence intervals in any of the circumstances above.

#3

. Given a normal random variable X with mean μ = 100 and variance o² = 49 if we randomly observe X=30, is this an unusual observation? (a) This would be an unusual observation because it lies less than 3 standard deviations away from the mean. (b) This would not be an unusual observation because it lies less than 3 standard deviations away from the mean. (c) This would be an unusual observation because it lies more than 3 standard deviations away from the mean. (d) This would not be an unusual observation because it lies more than 3 standard deviations away from the mean.

Suppose we have two normal populations denoted A and B, and we want to compare their population variances by estimating the ratio: variance of population B divided by variance of population A.  We have an independent random sample of size 15 from population A and an independent random sample of size 9 from population B.  The sample variance for population B turns out to be 30 percent larger than that for population A.  What is the 99 percent confidence interval for the ratio:  population variance of population B divided by population variance of population A?  Use stattrek.org for finding the needed critical values.