Question

refer to the accompanying data display that results from a simple random sample of times (minutes) between eruptions of the old faithful geyser. the confidence level of 95% was used. complete parts (a) and (b) below tinterval (85.74,91.76) x = 88.75 sx = 8.897431411 n = 36 a. express the confidence interval in the format that uses the \less than\ symbol. round the confidence interval limits given that the original times are all rounded to one decimal place. 85.74 min < μ < 91.76 min (round to two decimal places as needed.) b. identify the best point estimate of μ and the margin of error the point estimate of μ is □ minutes. (round to two decimal places as needed.)

Explanation:

Part (b)

Step 1: Recall the formula for confidence interval

The confidence interval for a population mean \(\mu\) is given by \(\bar{x}-E < \mu<\bar{x} + E\), where \(\bar{x}\) is the point estimate of \(\mu\) and \(E\) is the margin of error. From the data display, we have \(\bar{x}=88.75\) (the sample mean, which is the best point estimate of the population mean \(\mu\)).

Answer:

The point estimate of \(\mu\) is \(88.75\) minutes.