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.

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UpStudy AI · Accepted Answer

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 $$14.7$$.
The sample mean is 14.7.

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