Topic 4 Flashcards

1
Q

What is the sampling distribution of a statistic?

A
  • considered as a random variable, when derived from a random sample of size n
  • it may also be considered as the distribution of the statistic for all possible samples from the same population of a given size
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2
Q

The mean of the sampling distribution of X bar is the same as what?

A
  • the same as the mean of the random variable that is sampled
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3
Q

The variance of the sampling distribution of X bar is the what?

A
  • the variance of the sampled random variable, divided by the sample size, n
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4
Q

What does the sampling distribution depend on?

A
  • underlying distribution of the parent population
  • statistic being considered
  • sampling procedure employed
  • sample size used
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5
Q

If X is exactly normally distributed then X bar has what?

A
  • it has an exactly normal distribution, no matter what the sample size is
  • i.e., if X~N(μ,σ2), then:
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6
Q

Regardless of the distribution of the sampled random variable, if the sample size is sufficiently large, X bar has what?

A
  • it has an approximately normal distribution
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7
Q

What happens if the sample size exceeds 30?

A
  • then it is large enough for the result of the Central Limit Theorem to be applied
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8
Q

The sampling distribution of the proportion, p, is an application of what?

A
  • the Central Limit Theorem
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9
Q

What is the parental population, X?

(sampling distribution of the sample proportion, p)

A
  • a categorical variable with only two possible outcomes.
  • also referred to as Yes/No variables
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10
Q

What is the mean and the variance of the proportion of X?

A
  • π (mean)
  • π (1 - π) (variance)
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11
Q

Is the X variable normal?

A
  • the X variable is definitely not normal but, if the sample size is large enough, p, is approximately normally distributed
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12
Q

What do we use to evaluate the sampling distribution of the proportion, p?

A
  • we use Z, the standard normal distribution:
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13
Q

What are the three steps to obtain probabilities for X bar?

A
  • convert value of X bar using the transformation formula:
  • draw a diagram and shade the appropriate area under the curve
  • read the appropriate value from Table E2
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14
Q

What are the three steps to obtain probabilities for p?

A
  • convert value of p, using the transformation formula:
  • draw a diagram and shade the appropriate area under the curve
  • read the appropriate value from Table E2
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15
Q

A random sample of 36 is drawn from a normal population with mean equal to 50 and standard deviation 12.

(a) Give the mean and the standard deviation of the sampling distribution of X bar.
(b) Find the value of:
i. P(X bar > 45.5)
ii. P(X bar < 54)
iii. P(X bar > 58)
(c) Find P(X bar > X bar0) = 0.60

A
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16
Q

For a large population of normally distributed account balances, the mean balance is µ = $150 with standard deviation σ = $35.

(a) What is the probability that one randomly sampled account has a balance that exceeds $160?
(b) What is the probability that the mean random sample of n = 40 accounts will exceed $160?

A
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