The college president asks the statistics teacher to estimate the average age of the students at their college. How large a sample is necessary? The statistics teacher decides the estimate should be accurate within half year and be 92% confident. From a previous study, the standard deviation of the ages is known to be 3 years.
my garden last year was a square with sides 28 ft. this year i added a section that is an isosceles triangle at one end of my square garden to form the figure below. if each of the two equal sides of the triangle is 18 feet. i'm having a problem with deer this year and therefore want to fence the garden. how many feet of fencing will i need to buy?
What is the domain of 5x^2+21x+4
110
To determine the sample size required to estimate the average age of the college students accurately within half a year and with 92% confidence, we need to use the formula for sample size in estimation problems.
The formula for sample size in estimation, also known as the minimum sample size formula, is:
n = (Z * σ / E)^2
Where:
n = sample size
Z = Z-score corresponding to the desired confidence level (92% confidence corresponds to a Z-score of 1.75)
σ = standard deviation of the population (known to be 3 years)
E = margin of error (half a year)
Plugging in the given values into the formula:
n = (1.75 * 3 / 0.5)^2
Simplifying this equation gives us:
n = (5.25 / 0.5)^2
n = 10.5^2
n = 110.25
Rounded up to the nearest whole number, the sample size required is 111.
Therefore, the statistics teacher needs a sample size of at least 111 to estimate the average age of the college students accurately within half a year and with 92% confidence, assuming the standard deviation of the ages is 3 years based on a previous study.