Question

1. The mean cholesterol levels of women age 45-59 in Ghana, Nigeria, and Seychelles is 5.1 mmol/l and the standard deviation is 1.0 mmol/l. Assume that cholesterol levels are normally distributed and a random sample of 25 women are selected.

It is possible with rounding for a probability to be 0.0000.

a) Identify the individual, variable, type of variable and the random variable X in the context of this problem.

The individual is _____

Select an answer:

(a) 25 randomly selected women age 45-59 in Ghana, Nigeria, and Seychelles

(b) all women age 45-59 in Ghana, Nigeria, and Seychelles

(c) a randomly selected woman age 45-59 in Ghana, Nigeria, or Seychelles

(d) the mean cholesterol level of all women age 45-59 in Ghana, Nigeria, and Seychelles

(e) the cholesterol level

(f) the mean cholesterol level of 25 randomly selected women age 45-59 in Ghana, Nigeria, and Seychelles

The variable information collected from each individual is ______

Select an answer:

(a) 25 randomly selected women age 45-59 in Ghana, Nigeria, and Seychelles

(b) the cholesterol level all women age 45-59 in Ghana, Nigeria, and Seychelles

(c) a randomly selected woman age 45-59 in Ghana, Nigeria, or Seychelles

(d) the mean cholesterol level of 25 randomly selected women age 45-59 in Ghana, Nigeria, and Seychelles

(e) the mean cholesterol level of all women age 45-59 in Ghana, Nigeria, and Seychelles

This variable is a ______ Select an answer:

(a) qualitative

(b) qualitative -- discrete

(c) quantitative -- continuous

The random variable X is as follows:

  Select an answer:

(a) rv X = all women age 45-59 in Ghana, Nigeria, and Seychelles

(b) rv X = a randomly selected woman age 45-59 in Ghana, Nigeria, or Seychelles

(c) rv X = the cholesterol level of a randomly selected woman age 45-59 in Ghana, Nigeria, or Seychelles

(d) rv X = the mean cholesterol level of all women age 45-59 in Ghana, Nigeria, and Seychelles

(e) rv X = the mean cholesterol level of 25 randomly selected women age 45-59 in Ghana, Nigeria, and Seychelles

(f) rv X = cholesterol level is normally distributed

b) List the givens with the correct symbols.
(which symbol goes with the number?)
  ? n p X μ X̄ σ s N  = 5.1 mmol/l

  ? s N X σ p X̄ μ n  = 1 mmol/l

  ? s X̄ N p n σ X μ  = 25

c) Identify the random variable ¯¯¯XX¯ in the context of this problem.

  Select an answer:

(a) rv X̄ = a randomly selected woman age 45-59 in Ghana, Nigeria, or Seychelles

(b) rv X̄ = the mean cholesterol level of 25 randomly selected women age 45-59 in Ghana, Nigeria, and Seychelles

(c) rv X̄ = cholesterol level is normally distributed

(d) rv X̄ = the cholesterol level of 25 randomly selected women age 45-59 in Ghana, Nigeria, and Seychelles

(e) rv X̄ = the cholesterol level of a randomly selected woman age 45-59 in Ghana, Nigeria, or Seychelles

(f) rv X̄ = the mean cholesterol level of all women age 45-59 in Ghana, Nigeria, and Seychelles

d) Find the mean of the sampling distribution of the sample mean.

Put the numeric value in the first box and the correct units in the second box.

e) Find the standard deviation of the sampling distribution of the sample mean.

Put the numeric value rounded to two decimal places in the first box and the correct units in the second box.

f) What is the shape of the sampling distribution of the sample mean?

  Select an answer:

(a) left-skewed

(b) uniform

(c) unknown

(d) right-skewed

(e) normal or approximately normal   

Why? Check all that apply:

• n is at least 30
• σσ is known
• σσ is unknown
• population is not normal
• population is normal
• n is less than 30

g) Find the probability that the sample mean cholesterol level of the 25 randomly selected women age 45-59 in Ghana, Nigeria, and Seychelles is less than 4.8 mmol/l.

    Round final answer to 4 decimal places.

    DO NOT use the rounded standard deviation from part e in this computation.

    Use the EXACT value of the standard deviation with the square root.

    

h) Find the probability that the sample mean cholesterol level of the 25 randomly selected women age 45-59 in Ghana, Nigeria, and Seychelles is more than 5.64 mmol/l.

    Round final answer to 4 decimal places.

    DO NOT use the rounded standard deviation from part e in this computation.

    Use the EXACT value of the standard deviation with the square root.

    

i) Is a mean cholesterol level of 5.64 mmol/l unusually high for 25 randomly selected women age 45-59 in Ghana, Nigeria, and Seychelles?

  Select an answer:

(a) Yes, the probability of having a sample mean cholesterol level of at least 5.64 mmol/l is less than or equal to 0.05

(b) Yes, the probability of having a sample mean cholesterol level of at least 5.64 mmol/l is more than 0.05

(c) Yes, the probability of having a sample mean cholesterol level of at most 5.64 mmol/l is less than or equal to 0.05

(d) Yes, the probability of having a sample mean cholesterol level of at most 5.64 mmol/l is more than 0.05

(e) No, the probability of having a sample mean cholesterol level of at least 5.64 mmol/l is less than or equal to 0.05

(f) No, the probability of having a sample mean cholesterol level of at least 5.64 mmol/l is more than 0.05

(g) No, the probability of having a sample mean cholesterol level of at most 5.64 mmol/l is less than or equal to 0.05

(h) No, the probability of having a sample mean cholesterol level of at most 5.64 mmol/l is more than 0.05

j) If you found a mean cholesterol level for a sample of 25 women age 45-59 in Ghana, Nigeria, and Seychelles as high as 5.64 mmol/l, what might you conclude?

  Select an answer:

(a) There is evidence that the mean cholesterol level of all women age 45-59 in Ghana, Nigeria, and Seychelles may now be higher than 5.1 mmol/l

(b) There is no evidence that the mean cholesterol level of all women age 45-59 in Ghana, Nigeria, and Seychelles has changed from 5.1 mmol/l

(c) There is evidence that the mean cholesterol level of all women age 45-59 in Ghana, Nigeria, and Seychelles may now be lower than 5.1 mmol/l

Answer 1

a.

The individual is a randomly selected woman age 45-59 in Ghana, Nigeria, or Seychelles

b.

The variable information collected from each individual is the cholesterol level all women age 45-59 in Ghana, Nigeria, and Seychelles.

c.

This variable is a quantitative -- continuous.

d.

rv X = the cholesterol level of a randomly selected woman age 45-59 in Ghana, Nigeria, or Seychelles

e.

rv X̄ = the mean cholesterol level of 25 randomly selected women age 45-59 in Ghana, Nigeria, and Seychelles