Question

# Suppose that you are interested in estimating the average number of miles per gallon of gasoline...

Suppose that you are interested in estimating the average number of miles per gallon of gasoline your car can get. You calculate the miles per gallon for each of the next ten times you fill the tank. Suppose that in truth, the values for your car are bell-shaped, with a mean of 25 miles per gallon and a standard deviation of 1. Find the possible sample means you are likely to get based on your sample of ten observations. Consider the intervals into which 68%, 95%, and almost all of the potential sample means will fall, using the Empirical Rule. (Round all answers to the nearest thousandth.)

About 68% of possible sample means will be in the range between  and  .

About 95% of possible sample means will be in the range between  and  .

About 99.7% of possible sample means will be in the range between  and  .

The weights of men in a particular age group have mean μ = 154 pounds and standard deviation σ = 30 pounds.

(a) For randomly selected samples of n = 9 men, what is the standard deviation, s.d., of the sampling distribution of possible sample means?

s.d.(x)

=

(b) For randomly selected samples of n = 36 men, what is the standard deviation, s.d., of the sampling distribution of possible sample means?

s.d.(x)

=

A randomly selected sample of n = 85 individuals over 65 years old takes a test of memorization skills. The sample mean is x = 53, and the standard deviation is s = 6.8. Give the numerical value of the standard error of the mean, s.e. (Round your answer to two decimal places.)

s.e.(x) =

Suppose that you are interested in estimating the average number of miles per gallon of gasoline your car can get. You calculate the miles per gallon for each of the next ten times you fill the tank. Suppose that in truth, the values for your car are bell-shaped, with a mean of 25 miles per gallon and a standard deviation of 1. Find the possible sample means you are likely to get based on your sample of ten observations. Consider the intervals into which 68%, 95%, and almost all of the potential sample means will fall, using the Empirical Rule. (Round all answers to the nearest thousandth.)

About 68% of possible sample means will be in the range between  and  .

About 95% of possible sample means will be in the range between and. .

About 99.7% of possible sample means will be in the range between  and  .

Suppose the population of IQ scores in the town or city where you live is bell-shaped, with a mean of 109 and a standard deviation of 17. Describe the distribution of possible sample means that would result from random samples of 100 IQ scores.
The distribution will be approximately a normal curve with mean  and standard deviation  .

1)

about 68% of observation of data lie within 1 std dev away from mean
about 95% of observation of data lie within 2 std dev away from mean
about 99.7% of observation of data lie within 3 std dev away from mean

µ=25

σx=σ/√n = 1/√10 = 0.316

About 68% of possible sample means will be in the range between X̄ ± 1 * s = (   24.684   ,   25.316   )

About 95% of possible sample means will be in the range between  X̄ ± 2 * s = (   24.368       25.632   )

About 99.7% of possible sample means will be in the range between  and  .X̄ ± 3 * s = (   24.051       25.949   )

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2)

a) σx = std error = σ/√n= 30/√9 = 10

b) σx = std error = σ/√n= 30/√36 = 5

c) s.e.(x) =std error = σ/√n= 6.8/√85 = 0.74