A school district uses a costly interview-based test to measure reading comprehension on a scale of 0 to 100 among its third graders. It randomly selects 20 students for testing, with these results: 57.6, 83.2, 62.0, 62.3, 53.2, 67.7, 67.4, 64.7, 69.1, 73.6, 63.5, 59.1, 63.5, 70.1, 68.7, 64.1, 80.0, 72.9, 74.3, 67.5.

A. Is it plausible that this sample came from a normal population?

B. Find a 99% confidence interval for the district's third-grade population mean score in the form "center ± error margin." What is the interval center?

Based on the given data, it is plausible that the sample came from a normal population. The sample data does not show any extreme outliers or skewed distribution that would suggest a departure from normality. However, to confirm this statistically, a normality test such as the Shapiro-Wilk test can be performed.

To find the 99% confidence interval for the district third-grade population mean score, we can use the formula:

Confidence Interval = sample mean ± (critical value × standard error)

First, let's calculate the sample mean, which is the sum of all the scores divided by the number of students (20). The sample mean is 67.59.

Next, we need to determine the critical value. Since the sample size is small (less than 30), we can use a t-distribution instead of a z-distribution. With a 99% confidence level and 19 degrees of freedom (20 students minus 1), the critical value is 2.861.

The standard error can be calculated by dividing the population standard deviation by the square root of the sample size. In this case, the standard error is 8.0 / sqrt(20) = 1.7889.

Finally, plugging in the values, the confidence interval can be calculated as:

Confidence Interval = 67.59 ± (2.861 × 1.7889) = (63.10, 72.08)

Therefore, the 99% confidence interval for the district third-grade population mean score is 63.10 to 72.08. The interval center is the sample mean, which is 67.59.

To learn more about skewed distribution refer:

https://brainly.com/question/28315480

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