Asurvey of 350 students is selected randomly on a large campus. they are asked if they use a laptop in class to take notes. suppose that based on the survey, 140 of the 350 students responded "yes."

a. what is the value of the sample proportion ^p?

b. what is the standard error of the sample proportation?

c. construct an approximate 95% confidence interval for the true proportion p by taking +- ses from the sample proportion.

A. The value of the sample proportion is 0.4

B. The standard error of the sample proportion is 0.02619

C. 0.3487 ≤ p ≤ 0.4513

Step-by-step explanation:

The value of the sample proportion p' is calculated as:

Where x is the number of success in the sample or the number of students that use a laptop in class to take notes and n is the size of the sample or 350 students.

On the other hand, the standard error SE of the sample proportion is calculated as:

so, replacing the values, we get:

Finally, an approximate 95% confidence interval for the true proportion p is calculate as:

Where 1-α is equal to 95%, so is equal to 1.96. Then, replacing the values we get:

0.4 - 0.0513 ≤ p ≤ 0.4 + 0.0513

0.3487 ≤ p ≤ 0.4513

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