IXL - Interpret confidence intervals for population means (Algebra 2 practice)

Residents of a small fishing village are gathering the largest clams they can find for an upcoming clam festival. To investigate the environmental impact of this event, activists measured the widths of 75 randomly selected clams from a local beach (in centimeters). From their measurements, the activists calculated a

95%

confidence interval of

(

11.2

13.4

)

for the mean width of the clams from this beach.

Is the following conclusion valid?

There is a

95%

chance that the mean width of all clams from this beach is in the interval

(

11.2

13.4

)

yes

ref_doc_title.

Learn with an example

question

A major insurance company wants to estimate the effort it would take to completely switch to paper-free correspondence. The company randomly selected 275 customers and logged the number of letters sent to each last month. They found a

99%

confidence interval of

(

2.7

3.1

)

for the mean number of letters sent to each customer last month.

Is the following conclusion valid?

If 100 more samples are taken (with elements chosen randomly and independently), it is expected that exactly 99 of them will each produce a

99%

confidence interval that contains its sample mean.

yes

key idea

You can use a random sample to calculate a

confidence interval for the population mean. The population mean is the mean of all data values in a population.

confidence interval depends on the sample it is calculated from. Different samples can yield different

confidence intervals.

The center of any confidence interval is the sample mean. The sample mean is the mean of all data values in the sample.

A confidence interval may or may not contain the population mean. A

confidence interval will contain the population mean for

of samples whose elements were chosen randomly and independently.

solution

Look at the conclusion:

If 100 more samples are taken (with elements chosen randomly and independently), it is expected that exactly 99 of them will each produce a

99%

confidence interval that contains its sample mean.

The sample mean is the average number of letters sent to the selected customers last month.

A confidence interval for a sample always contains its sample mean. In fact, it is symmetric around the sample mean.

If 100 more samples are taken, it is guaranteed that all 100, not just 99 of them, will each produce a

99%

confidence interval that contains the sample mean.

So, the conclusion is not

valid.

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