Which the following is true about a confidence interval for the population mean?
ID: 3258240 • Letter: W
Question
Which the following is true about a confidence interval for the population mean? it is an estimate for the value of the population mean it always contains the sample mean it always contains the population mean it is a lower and an upper bound of an interval of values which always contains the population mean many numbers as possible When we build a 90% and a 9s% confidence interval the same data and the same method, using which of the following is true? The 90% confidence interval contains the 95% confidence interval The lower bound for the 90% confidence interval is larger than the lower bound for the 95% confidence interval The probability that both contain the population mean is very small The widths of these two intervals are not comparable Which confidence interval is wider depends on the random data We take 100 independent samples of size 4 from the same normally distributed population with mean 10 and known standard deviation 4 We build 90% two-sided z confidence interval using each sample. What is the expected number of intervals that will contain the value 10? 4 96 90 100 Cannot be decided In a test of hypotheses for the mean p, which of the following quantities depends on the distribution under the alternative hypothesis? Power of the test The critical value and the rejection regionExplanation / Answer
(5)
(d) It is a lower and upper bound of an interval of values which always contains the population mean.
The confidence interval gives a interval of values which is likely to contain the population mean.
(6)
(b) The lower bound for the 90% confidence interval is larger than the lower bound for the 95% confidence interval.
As the confidence level increases the confidence interval becomes wider and wider. Thus the lower bound of 90% CI will be greater than the 95% CI.
(7)
(c) 90.
A 90% confidence limit specifies that, on repeating the samples and computing the mean, 90 percent of the times the population mean will fall within the confidence limit. Therefore the expected no of intervals that will contain the value 10 is 90.
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