A random sample of 10 colleges was taken. A 95% confidence interval for the mean admission rate was left parenthesis 52.8 % comma 75.0 % right parenthesis (52.8%, 75.0%). The rates of admission were Normally distributed. Which of the following statements is the correct interpretation of the confidence level, and which is the correct interpretation of the confidence interval? a. We are confident that the mean admission rate is between 52.8% and 75.0%. b. In about 95% of all samples of 10 colleges, the confidence interval will contain the population mean admission rate.

Question

Mathematics

Soren Bender

10 March, 21:34

A random sample of 10 colleges was taken. A 95% confidence interval for the mean admission rate was left parenthesis 52.8 % comma 75.0 % right parenthesis (52.8%, 75.0%). The rates of admission were Normally distributed. Which of the following statements is the correct interpretation of the confidence level, and which is the correct interpretation of the confidence interval? a. We are confident that the mean admission rate is between 52.8% and 75.0%. b. In about 95% of all samples of 10 colleges, the confidence interval will contain the population mean admission rate.

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Answers (1)

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Rubi Morse · Answer 1

a. We are confident that the mean admission rate is between 52.8% and 75.0%

Step-by-step explanation:

When you have an unknown population parameter you can use a sample to delimit an interval in which this parameter is, the interval is called confidence interval and the confidence level is the probability of the parameter being inside the interval. The confidence interval is represented by a pair of numbers, in this case, the pair is (52.8%, 75.0%) and the confidence level is 95%, with that level you can say that you're confident that the mean admission rate is between (52.8%, 75.0%).