In Exercises 1–4, refer to the accompanying screen display tha...

Question

In Exercises 1–4, refer to the accompanying screen 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.

Degrees of Freedom

a. What is the number of degrees of freedom that should be used for finding the critical value ta/2?

calc

Refer to the accompanying screen display.

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.

Accepted Answer

Hi everyone, let's take a look at this practice problem. This problem says a researcher collects a simple random sample of waiting times in minutes for a popular amusement park ride. A confidence level of 95% was used. The researcher used a calculator for analysis, as shown in the figure. And in the figure we're given an interval from 33.49 to 37.41. And X is equal to 35.45, S of X is equal to 6.128, 321. 633 and N is equal to 40. Write the confidence interval in inequality notation. Round the upper and lower limits to two decimal places, given that the original times are all rounded to one decimal place. And we're given 4 answers as our possible answer choices. And for choice A, we have 33.49 minutes, is less than you, which is less than 37.41 minutes. For choice B, we have 32.50 minutes, is less than you, which is less than 37.40 minutes. For choice C, we have 33.50 minutes, is less than you, which is less than 37.40 minutes, and for choice D, we have 33.40 minutes is less than you, which is less than 37.30 minutes. So we need to write the confidence interval in inequality notation, and the interval that we were given and the problem is the confidence interval that we're interested in. So we just need to write this interval as an inequality. And we're also told that the waiting times are in minutes. So, that means that we're gonna have units of minutes for our upper and lower bounds. So writing this interval, And as an inequality, we will have 33.49 minutes. Is less than you. Which is less than 37.41 minutes. And we just need to round this to 2 decimal places, and these values are actually already rounded to 2 decimal places. So this here is going to be the final answer for our problem. And when we compare our answer here to our answer choices, we see that the correct answer choice corresponds to answer choice A. So, I hope that this explanation has been useful, and I'll see you in the next video.

Key Concepts

Confidence Interval

Sample Mean (x̄)

Sample Size (n)

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