Final answer:
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.