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AMS 102 > FINAL > Flashcards

FINAL Flashcards

1
Q

What is the estimate of a population parameter given by a single number called?

A

point estimate

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2
Q

What will ALWAYS be the point estimate?

A

the sample mean

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3
Q

What is a interval estimate for the mean at a specific confidence level?

A

confidence interval

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4
Q

The 95% CI for the mean is given by what value:

A

1.96,-1.96

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5
Q

The 99% CI for the mean is given by what value:

A

2.576, -2.576

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6
Q

The 80% CI for the mean is given by what value:

A

1.282, -1.282

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7
Q

What are probability mass functions?

A

Discrete

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8
Q

What are probability density functions?

A

Continuous

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9
Q

What type of variable takes on an infinite number of values?

A

Continuous

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10
Q

What is represented by an area under the curve?

A

Probability

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11
Q

What type of function is the continuous random variable X is a function such that the area under the curve f (x) between any 2 points a and b is equal to the probability that the random variable X takes on an value such that it is P(a<x<b)?

A

Probability density function (p.d.f)

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12
Q

What does a uniform distribution indicate?

A

that all values have the same probability

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13
Q

A continuous probability density function ALWAYS satisfies the following 2 conditions:

A
  1. f (x) is NEVER EVER NEGATIVE
  2. The total area under f(x) is ALWAYS 1
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14
Q

What are the 4 qualities of the normal distribution?

A
  1. bell-shaped
  2. symmetrical about mean (u symbol)
  3. unimodal
  4. continuous
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15
Q

X ~ N (μ, σ^2) says what?

A

This distribution is normal

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16
Q

What is the mean and std. dev for a standard normal distribution?

A

mean of 0; std. dev. of 1

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17
Q

What function is for the random variable X evaluated at the point a that it is defined as the probability that X will take on values less than or equal to A?

A

cumulative distribution function (cdf)

18
Q

How do I use the calculator for this type of problem?: P (z <1.28)

A
  1. 2nd
  2. VARS
  3. NormCDF
  4. input lower value: any very negative value
  5. input upper value: value you’re given
  6. input std. normal distribution mean and sigma
19
Q

How do I use the calculator for this type of problem?: P(0<z<1.53)
hint: for the endpoints: just use the values you’re given

A
  1. 2nd
  2. VARS
  3. NormCDF
  4. input lower value
  5. input higher value
  6. input std. normal distribution mean and sigma
20
Q

How do I use the calculator for this type of problem: P(z>2.13)

A
  1. 2nd
  2. VARS
  3. NormCDF
  4. input lower value: given value endpoint
  5. input higher value: very high positive value
  6. input std. normal distribution mean and sigma
21
Q

How do I use the calculator for this type of problem: X ~ N (50,25), find P(X>58.5)

A
  1. 2nd
  2. VARS
  3. NormCDF
  4. input lower value: given value endpoint
  5. input higher value endpoint: high positive value
  6. Input mean you’re given; input square root of variance you’re given
22
Q

How do I use the calculator for this type of problem: find P(8.5<x<12)
hint: for the endpoints: just use the values you’re given

A
  1. 2nd
  2. VARS
  3. NormCDF
  4. input lower value
  5. input higher value endpoint
  6. Input mean you’re given; input square root of variance you’re given
23
Q

How do I use the calculator for this type of problem:
If X ~ N (25.7, 5.88), what is the minimum value of X required to be in the top 10% of the distribution?

AKA how to find the value that is in a certain percentile?

A
  1. 2nd
  2. VARS
  3. invNORM
  4. input (percentile, mean, std. dev)
  5. tail: left
24
Q

How do I use the calculator to find for this type of problem: find z .025

A

1, 2nd
2. VARS
3. InvNORM
4. input (1-percentile, mean std. dev)
5. tail: left

25
Q

How do I use the calculator to find this type of problem:
Find the probability that an exact amount will be in this interval.

A
  1. find the probability of a single prob. being within that range
  2. 2nd
  3. VARS
  4. BinomPDF
  5. input # trials, probability that correlates, and exact amount you’re trying to find
26
Q

How do I use the calculator to find this type of problem:
Find the probability that an at most amount will be in this interval.

A
  1. find the probability of a single prob. being in that range
  2. 2nd
  3. VARS
  4. BinomCDF
  5. input # trials, probability that correlates, and exact amount you’re trying to find
27
Q

How do I use the calculator to find this type of problem:
Find the probability that an at least amount will be in this interval.

A

same as at most, BUT subtract 1 from the value you get at the end

28
Q

What is the key difference in finding the exact amount in an interval vs. finding the at most or at least amount?

A

EXACT amount uses BINOMPDF; EXACT AMOUNT uses BINOMCDF

29
Q

How do I find the sample standard deviation of the mean (formula):

This is known as the SEM formula

A

σ/ √n

30
Q

As n (the sample size increases), what decreases?

A

STANDARD DEVIATION

31
Q

What is the new standard error formula?

A

(√n old / √n new)

32
Q

What does the central limit theorem tell us?

A

That if X possesses ANY distribution, with mean and std. deviation, then the sample mean based on samples of size n will have a distribution which is appromixately normal, AS LONG AS n > = 30

33
Q

What is the central limit theorem z score formula?

A

Z = (x-μ) / (σ/√n)

34
Q

Small confidence levels and large confidence levels are not desirable-T or F

A

False; small confidence levels and LARGE CONFIDENCE LEVELS are desirable

35
Q

How do I use the calculator to find this type of problem: Find a 99% confidence level for U (T-Interval)

A
  1. STAT
  2. Tests
    3.T Interval
  3. Stats
  4. Input Values
36
Q

How do I use the calculator to find this type of problem: Gives us list of data*

A
  1. STAT
  2. Calc
  3. 1-VAR stats
37
Q

What is the formula for Confidence Intervals?

A

x̄ n ± z alpha/2 * (s/ √n)

could also be t alpha/2

38
Q

What is the formula for E?
hint* confidence intervals

A

z alpha/2 * (s/ √n)

or t alpha/2

39
Q

What is the formula for Length?

A

2E

40
Q
A

AMS 102 (2 decks)

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