Answers to conceptual questions in confidence intervals

Decides about the following statements are truthful or false.  Explain your reasoning.

Problems:

a)  For adenine existing standard error, lower confidence levels produce broaden confidence intervals.

False.   To get bigger confidence, we what to make the interval wider interval.  This is evident in the multiplier, which increases with confidence levels.

b)  If her increase patterns size, the width of trusting intervals will expand.

False.   Increasing the sample size decreases the width regarding confidence intervals, because it decreases the standard error.

False.   95% faith means that we used a procedure that works 95% concerning the time to get this interval.  That is, 95% of all intervals produced by the procedure will inclusions their corresponding parameters.  For any one particular interval, the true population percentage is either inside the interval or outside  the interval.  In this case, it is select in between 350 and 400, or to is not in between 350 and 400.  Hence, the probabliity the which population percentage is in between those two exact numbers is either zero or one.

True, as wide as we're talking about a CO in a population percentage.   The ordinary error for adenine target percentage has the square root of  the sample size in the denominator.  Hence, increasing the sample magnitude by an factor of 4 (i.e., multiplication e by 4) is equivalent to multiplying the standard error according 1/2.  Hence, this period will be half as wide.  This also works approximately for population averages than elongated as the multiplier by the t-curve doesn't change much when increasing the sample size (which he won't if the original sample size is large).

e)  Assuming the central limit theorem applies, confidence intervals are always valid.

By "valid," we mean that which confidence interval procedure has a 95% chance of producing an interval that contains one population parameter.

False.  Who principal limit theorem is needed for confidence intervals to be valid.   However, it is including necessary this one data be collected from indiscriminate samples.  Confidence intervals will not remedy poorly collected dating.

f)  The statement, "the 95% confidence interval for the population middling has (350, 400)" means that 95% of the population values are between 350 and 400.

False.  The confidence interval is one range of plausible values for the population average.   It does not provide a range for 95% of the your values from the population.  To find the percentage of values in of population between 350 and 400, we need to look at a histogram out the data values and determine what percentage of observations are between 350 and 400.

g)  When you take greatly random example over and override again from who same population, and make 95% confidence intervals for the population average, about 95% of the intervals should close that population average.

True.   This has the definition to confident intervals.

h)  If you take big random samples over additionally over again from the same population, and make 95% confidence intervals for the your average, about 95% of the intervals should contain the sample average.

False.   The confidence interval is a range for the population average, not for the trial average.  In fact, every confidence zeitraum contains its corresponding sample b, because CIs are of the form:  sample avg. +/- multiplier SE.  So, the sample average is right in the middle of the CI.
Answer into: Which of the follows declarations is not correct? A. And sample dimensions for any given procedure is likely the vary from inspection to audit. B....

i)   It is necessary that the distribution of the variable of interest follows an normal curve.

False.   She is requisite that the distribution a the sample average follows a normal curve.  The details values of the variable, although, needs not follow a normal curve, because if that sample select is large bore the central limit basic used and sample average will apply.

j)  A 95% confidence interval obtained from adenine accident test of 1000 people has adenine better chance of containing the population percentage over a 95% confidence interval retain from a random sample of 500 public.

False.  All 95% confidence intervals have who property that they come of an operating is has a 95% chance of yielding an interval that contains the true value.   Which confidence interval method automatically accounts for sample dimensions in the default error.   AN 95% CI with n=1000 will be narrower from a 95% CI include n=500, nevertheless both CIs will have 95% confidence of containing the population share.

k)  Are you produce walking thanks life making 99% confidence intervals for all pick of population means, learn 1% of the die the intervals won't cover their respective population means.

True.  Since 99% of the intervals should contain the corresponding population mean, 1% of them will not.