Question

A survey will be given to high school students asking how many hours of TV they watch per week. To find the mean number of hours of TV per week, how many students must be sampled to get a 95% confidence interval with a maximum error of 0.3 hours? Use a standard deviation of 1.15 hours.

a.39 students
b.40 students
c.56 students
d.57 students

Answer 1

To achieve a 95% confidence interval with a maximum error of 0.3 hours and a standard deviation of 1.15 hours, 57 high school students must be sampled.

Step-by-step explanation:

To determine how many high school students must be sampled for a survey asking about weekly TV watching hours in order to find the mean number of hours with a 95% confidence interval and a maximum error of 0.3 hours, we can use the formula for sample size in a confidence interval estimation:

n = (Z*σ/E)^2

Where:

• Z is the Z-score corresponding to the desired confidence level, which is 1.96 for 95%.
• σ (sigma) is the population standard deviation, which is given as 1.15 hours.
• E is the maximum error of the estimate, which is 0.3 hours.

Now, we can plug in the values to the formula:

n = (1.96 * 1.15 / 0.3)^2

n ≈ (2.254 / 0.3)^2

n ≈ (7.513)^2

n ≈ 56.44

Since you cannot survey a fraction of a person, you need to round up to the nearest whole number. This gives us:

n = 57

So, you would need a sample of 57 students to achieve the desired accuracy in the confidence interval.