Exam 8: Sampling Distributions and Estimation

A random sample of 160 commercial customers of PayMor Lumber revealed that 32 had paid their accounts within a month of billing.Can normality be assumed for the sample proportion?

As the sample size increases,the standard error of the mean:

A random sample of 160 commercial customers of PayMor Lumber revealed that 32 had paid their accounts within a month of billing.The 95 percent confidence interval for the true proportion of customers who pay within a month would be:

We could narrow a 95 percent confidence interval by:

The standard error of the sample proportion is largest when π = .50.

The confidence level refers to the procedure used to construct the confidence interval,rather than to the particular confidence interval we have constructed.

In a survey,858 out of 2600 homeowners said they expected good economic conditions to continue for the next 12 months.Construct a 95 percent confidence interval for "good times" in the next 12 months.

What is the approximate width of a 90 percent confidence interval for the true population proportion if there are 12 successes in a sample of 25?

In constructing confidence intervals,it is conservative to use the z distribution when n ≥ 30.

As long as the sample is more than one item,the standard error of the sample mean will be smaller than the standard deviation of the population.

What is the approximate width of an 80 percent confidence interval for the true population proportion if there are 12 successes in a sample of 80?

Ceteris paribus,the narrowest confidence interval for π is achieved when p = .50.

Why does σ pose a problem for sample size calculation for a mean? How can σ be approximated when it is unknown?

All estimators are biased since sampling errors always exist to some extent.

If σ = 12,find the sample size to estimate the mean with an error of ± 4 and 95 percent confidence (rounded to the next higher integer).

The statistic p = x/n may be assumed normally distributed when np ≥ 10 and n(1 - p)≥ 10.

In constructing a confidence interval for a mean with unknown variance with a sample of 25 items,Bob used z instead of t."Well,at least my interval will be wider than necessary,so it was a conservative error," said he.Is Bob's statement correct?

The sample standard deviation s is halfway between the lower and upper confidence limits for the population σ (i.e. ,the confidence interval is symmetric around s).

If a normal population has parameters μ = 40 and σ = 8,then for a sample size n = 4: