Constructing a Confidence Interval In Exercises 25–28, use the...

Question

Constructing a Confidence Interval In Exercises 25–28, use the data set to (c) construct a 99% confidence interval for the population mean. Assume the population is normally distributed.

SAT Scores The SAT scores of 12 randomly selected high school seniors

Table displaying SAT scores of 12 randomly selected high school seniors, arranged in two rows and six columns.

Accepted Answer

Hello, everyone, let's take a look at this question together. A sample of 8 randomly selected students had the following chemistry test scores. 7885, 80, 90, 88, 82, 84, and 91. Construct a 99% confidence interval for the population mean score assuming normality, given that the sample mean is 84.75 and the sample standard deviation is 4.68. Is it answer choice A 68.9. 6 to 90.54. Answer choice B 68.96 to 92.54. Answer choice C 78.96 to 90.54 or answer choice D 58.96 to 80.54. So in order to solve this question, we have to recall how to construct a confidence interval so that we can Construct a 99% confidence interval for the population mean score assuming normality where we are given the sample mean, which is 84.75, the sample standard deviation is 4.68, and the sample of eight randomly selected students' test scores, which have the following values. And so in order to construct our 99%. Confidence interval, we'll use the T distribution since the population standard deviation is unknown and N is less than 30. So the first step in solving this problem is identifying the values that we are given, which include a sample mean of 84.75, a sample standard deviation of 4.68, our sample size N is 8. The degrees of freedom, which is calculated as n minus 1 is equal to 7, and our confidence level is 99%. So we know we need to find a T critical value for our degrees of freedom which is equal to 7 and an alpha divided by 2, which is equal to 0.005, and this gives us Plus a critical value of approximately 3.499. And then we use the following formula to construct our confidence interval, which is equal to the sample mean plus minus our T critical value multiplied by the sample standard deviation divided by the square root of the sample size. And then we can substitute the values into the formula, so that we have 84.75 plus minus 3.499 multiplied by 4.68 divided by the square root of 8, which is equal to 84.75 plus minus 5.79. Therefore, our 99% confidence. Interval for the population mean score is 78.96 to 90.54, which looking at our answer choices, we can identify is answer choice C. So answer choice C is the correct answer, and all other answer choices are incorrect. I hope you found this video to be helpful. Thank you and goodbye.

Constructing a Confidence Interval In Exercises 25–28, use the data set to (c) construct a 99% confidence interval for the population mean. Assume the population is normally distributed.
SAT Scores The SAT scores of 12 randomly selected high school seniors

Key Concepts

Confidence Interval

Normal Distribution

Sample Mean and Standard Deviation

Watch next