In constructing a contidence interval tor a population mean, which of the tollowing are true?

Select four $(4)$ true statements from the list below:

Note: A point is deducted for each incorrect selection.

For a confidence level of $97\%,$ the right$-$tail area $\frac{}{2}=0\mathrm{.}015.$

If the point estimate and lower limit for a confidence interval are $149\mathrm{.}1$ and $131\mathrm{.}1$ respectively, then the upper limit must be $167\mathrm{.}1.$

The width of the confidence interval depends on the size of the population mean.

If a particular $86\%$ confidence interval captures the population mean, then for the same sample data, the population mean will also be captured at the $82\%$ confidence level.

If a confidence interval does not contain the population parameter, then an error has been made in the calculation.

A confidence interval that fails to capture the population mean will also fail to capture the sample mean.

A $97\%$ confidence interval must capture $97\%$ of the sample values.

Increasing the sample size will not affect the width of the confidence interval.

Decreasing the confidence level will decrease the width of the confidence interval.

For the same sample data, a $95\%$ confidence interval will be wider than a $99\%$ confidence interval.