Question

A sample of 140 Vopstra customers have had their annual phone charge recorded for the previous calendar year. The data were used to calculate a 92% confidence interval for the mean annual phone charge of all Vopstra customers. The confidence interval was calculated as $470 + $65. According to this confidence interval, it is most reasonable to conclude that:a.you are 92% confident the interval between $405 and $535 contains the mean phone charge of all Vopstra customers b.you are 92% confident the mean phone charge of all Vopstra customers is approximately $470 c.you are 92% confident the mean phone charge of all mobile phone customers is approximately $470 d.you are 92% confident the interval between $405 and $535 contains the mean phone charge of all mobile phone customers

Answer 1

Correct option: (a)

Explanation:

A confidence interval is an interval estimate of the parameter value.

A (1 - α)% confidence interval implies that the confidence interval has a (1 - α)% probability of consisting the true parameter value.

OR

If 100 such confidence intervals are made then (1 - α) of these intervals would consist the true parameter value.

The 92% confidence interval for the mean annual phone charge of all Vopstra customers is:

`\$470\pm \$65=(\$405, \$535)`

This confidence interval implies that true mean annual phone charge of all Vopstra customers is contained in the interval ($405, $535) with 0.92 probability.

Thus, the correct option is (a).