A survey is being planned to determine the mean amount of time corporation executives watch television. A pilot survey indicated that the mean time per week is 15 hours, with a standard deviation of 3.5 hours. It is desired to estimate the mean viewing time within one-quarter hour. The 98 percent level of confidence is to be used.



How many executives should be surveyed?

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Suppose that a researcher is interested in estimating the mean systolic blood pressure, , of executives of major corporations. He plans to use the blood pressures of a random sample of executives of major corporations to estimate . Assuming that the standard deviation of the population of systolic blood pressures of executives of major corporations is mm Hg, what is the minimum sample size needed for the researcher to be confident that his estimate is within mm Hg of ?

Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements).

To determine how many executives should be surveyed, we can use the formula for sample size calculation for estimating the population mean:

n = (Z * σ / E)²

Where:
n = required sample size
Z = Z-value corresponding to the desired confidence level (in this case, 98% confidence level)
σ = population standard deviation
E = maximum error tolerance (one-quarter hour in this case)

First, let's find the Z-value corresponding to the 98% confidence level. We can use a standard normal distribution table or a statistical calculator. In this case, the Z-value for a 98% confidence level is approximately 2.33.

Plugging in the values into the formula:

n = (2.33 * 3.5 / 0.25)²

Calculating this, we get:

n ≈ (8.155 / 0.25)²
n ≈ 32.62²
n ≈ 1063.5844

Rounding up to the nearest whole number, we should survey at least 1064 executives to estimate the mean viewing time within one-quarter hour at a 98% confidence level.