5 Estimation and Confidence Intervals Online Quiz Questions

The standard error usually increases.

The standard error usually decreases.

The critical value must increase.

The confidence interval becomes less precise.

True

False

$\bar{x} \pm z_{1-\alpha/2}\frac{s}{\sqrt{n}}$

$\bar{x} \pm t_{1-\alpha/2,\,n}\frac{\sigma}{\sqrt{n}}$

$\bar{x} \pm t_{1-\alpha/2,\,n-1}\frac{s}{\sqrt{n}}$

$\bar{x} \pm z_{1-\alpha/2}\frac{\sigma}{n}$

A small sample can make the normal approximation unreliable.

A large sample always makes the normal approximation reliable, regardless of the observed proportion.

A proportion near 0 or 1 can make the normal approximation perform poorly.

The approximation is appropriate only when the sample contains no failures.

Treat the before and after measurements as unrelated groups and ignore which observations came from the same store.

Analyze the within-store differences.

Use only the after-change measurements.

Estimate the difference by comparing the two sample standard deviations.

True

False

A regression slope interval estimates the change in the mean outcome associated with a one-unit increase in the predictor under the fitted model.

A regression slope interval estimates the change in the predictor associated with a one-unit increase in the mean outcome.

For normally distributed data, an interval for variance uses the chi-square distribution rather than the mean’s t-interval.

An interval for variance uses the same standard error and critical value as an interval for a population proportion.

The estimate is positive, so the campaign must be worthwhile regardless of the interval.

The interval includes zero, so the campaign can have no effect.

Compare the interval with the minimum effect that would justify the campaign cost; a plausible effect may be too small to matter financially.

Ignore the interval’s width if the point estimate is positive.

There is a 95% probability that the fixed parameter lies in this particular interval.

About 95% of intervals produced by this procedure over repeated samples capture the fixed parameter.

The sample estimate is correct 95% of the time.

The parameter changes from sample to sample, and 95% of its values lie in the interval.

A larger sample and a higher confidence level both usually make the interval narrower.

A larger sample usually makes the interval wider, while a higher confidence level makes it narrower.

A larger sample usually makes the interval narrower, while a higher confidence level makes it wider.

Neither sample size nor confidence level affects interval width.

Calculate each store's before-and-after difference and construct an interval for the mean of those differences.

Treat all before and after measurements as independent and compare the two sample means.

Construct separate intervals for the before and after means and infer the difference from their overlap.

Use a confidence interval for a population proportion.

Use a $z$-interval because the sample mean is always normally distributed, regardless of sample size or data shape.

Use a proportion interval because the sample contains multiple observations.

Use a $t$-interval regardless of outliers or severe skew, since it automatically handles them.

A $t$-interval is the usual choice when the population standard deviation is unknown, but strong skew or outliers can undermine it, especially with a small sample.

True

False