In a recent study of 42 eighth graders, the mean number of hours per week that they watched television was 19.6. Assume the population standard deviation is 5.8 hours. Find the 98% confidence interval for the
Population mean.
A)(17.5, 21.7)
B)(14.1, 23.2)
C)(18.3, 20.9)
D)(19.1, 20.4)

Question

Quizplus · Accepted Answer

We can use the formula:

CI = (x̄ - z*(σ/√n), x̄ + z*(σ/√n))

where:
x̄ = sample mean = 19.6
σ = population standard deviation = 5.8
n = sample size = 42
z = z-score for a 98% confidence level = 2.33

Plugging in the values:

CI = (19.6 - 2.33*(5.8/√42), 19.6 + 2.33*(5.8/√42))
CI = (17.5, 21.7)

Therefore, the 98% confidence interval for the population mean is (17.5, 21.7). Choice A is the correct answer. To find the confidence interval, we use the formula:

CI = x̄ ± z* (σ/√n)

where x̄ is the sample mean, z* is the z-value from the standard normal distribution table for the desired confidence level (98% in this case), σ is the population standard deviation, and n is the sample size.

Substituting the given values, we get:

CI = 19.6 ± 2.33 * (5.8/√42)

CI = (17.5, 21.7)

So the best choice is A, because it contains the correct interval based on the given information.

In a Recent Study of 42 Eighth Graders, the Mean