Pregunta
Question 8 of 10, step 1 of 4 A certain test preparation course is designed to help students improve their scores on the GRE exam. A mock exam is given at the beginning and end of the course to determine the effectiveness of the course. The following measurements are the net change in 7 students' scores on the exam after completing the course: \[ 24,6,21,8,16,10,18 \] Using these data, construct a \( 80 \% \) confidence interval for the average net change in a student's score atter completing the course. Assume the population is approximately normal. Copy Data Step 1 of 4 : Calculate the sample mean for the given sample data. Round your answer to one decimal place.
Ask by Ball Daniel. in the United States
Mar 19,2025
Solución de inteligencia artificial de Upstudy
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The sample mean is 14.7.
Solución
The sample mean, \( \bar{x} \), is calculated using the formula:
\[
\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}
\]
Given the sample data:
\[
24,\, 6,\, 21,\, 8,\, 16,\, 10,\, 18
\]
1. Calculate the sum:
\[
24 + 6 + 21 + 8 + 16 + 10 + 18 = 103
\]
2. Divide by the number of samples:
\[
\bar{x} = \frac{103}{7} \approx 14.7
\]
Thus, the sample mean rounded to one decimal place is \(14.7\).
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Simplifique esta solución Bonus Knowledge
To find the sample mean, we add all the net changes in scores and then divide by the number of students. Here are the scores: \( 24, 6, 21, 8, 16, 10, 18 \). First, we calculate the sum: \[ 24 + 6 + 21 + 8 + 16 + 10 + 18 = 113 \] Next, we divide by the number of students (7): \[ \text{Sample Mean} = \frac{113}{7} \approx 16.14 \] Rounding to one decimal place, the sample mean is \( 16.1 \).
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