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Stats 1 > Chapter 6 & 7 > Flashcards

Chapter 6 & 7 Flashcards

1
Q

Descriptors of normal distribution of random variables

A
  1. Graph centered around the mean
  2. Graph of distribution is symmetric
  3. Graph of distribution is bell-shaped
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2
Q

Which groups can be used interchangeably when working with normal distributions?

A
  1. Area
  2. Probability
  3. Percentages
  4. Relative Frequencies
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3
Q

A continuous random variable has a __________ distribution of its values are spread evenly over the range of possibilities.

A

Uniform

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4
Q

Requirements of density curve

A
  1. Total area under curve must be 1
  2. Every point on the curve must have a vertical height that is 0 or greater
  3. Curve cannot fall below horizontal axis
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5
Q

Standard normal distribution

A
  1. Area under curve must equal 1
  2. Mean is 0 and standard deviation is 1
  3. Graph is symmetric
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6
Q

Finding probabilities associated with distributions that are standard normal distributions is equivalent to _________.

A

Finding the area of the shaded region representing that probability

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7
Q

The _________ tells us that for a population with any distribution, the distribution of the sample means approaches a normal distribution as the sample size increase.

A

Central limit theorem

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8
Q

What conditions produce a negative z-score?

A

Value left of the mean

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9
Q

If you are being asked to find the 85th percentile, you are being asked to find ___________.

A

A data value associated with an area of 0.85 to its left

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10
Q

What does the notation z (a) indicate?

A

Denotes the z score with an area of a to it’s right

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11
Q

The __________ states that if, under a given assumption, the probability of a particular observed event is exceptionally small, we conclude that the assumption is probably not correct.

A

Rare event rule for inferential statistics

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12
Q

A critical value. z(a), denotes the _______.

A

Z-score with an area of a to its right

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13
Q

Population proportion concepts

A
  1. Using sample statistic to estimate population proportion is using inferential statistics.
  2. Sample proportion is best point estimate of population proportion.
  3. We can use a sample proportion to construct a confidence interval to estimate the true value of a population proportion.
  4. Knowing the sample size necessary to estimate a population proportion is important.
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14
Q

Which of the following groups has terms that can be used interchangeably with the others?

A

Percentage, probability, and proportion

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15
Q

A ___________ is a single value used to approximate a population parameter.

A

Point estimate

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16
Q

Confidence interval

A

Gives range of values to estimate population parameter rather than a single value.

17
Q

What is needed to determine minimum sample size to estimate population proportion?

A
  1. Margin of error
  2. a
  3. Z a/2
18
Q

Confidence interval for estimating a population proportion p: Notation

A

p= population proportion
^p= sample proportion
n= number of sample values (sample size)
E= margin of error
Za/2= critical value
^q= found from evaluating 1-^p

19
Q

Confidence interval requirements

A
  1. Sample is a simple random sample
  2. Conditions for the binomial distribution are satisfied.
  3. There are at least 5 successes and at least 5 failures
20
Q

Properties of student t distribution

A
  1. Same general shape & symmetry as the standard normal distribution with more variability expected with small samples
  2. Mean of t=0
  3. Standard deviation > 1
  4. Student t distribution is different for different sample sizes
21
Q

The ________ is the best point estimate of the population mean.

A

Sample mean

22
Q

Derived from confidence level

A
  1. Point estimate of mean
  2. Margin of error
  3. Difference between the limits
23
Q

Requirements for constructing confidence interval to estimate mean with sigma unknown

A
  1. Sample is simple random sample
  2. Sample measures quantitative value
  3. Either population is normally distributed or n> 30, or both
24
Q

The __________ distribution is used to develop confidence interval estimates of variances or standard deviations.

A

Chi square

25
Q

Properties of chi-square distribution

A
  1. Different for each number of degrees of freedom
  2. Values can be 0 or positive, but not negative
  3. Not symmetric
26
Q

Best point estimate of the population variance is the ___________.

A

Sample variance, s^2

27
Q

Requirements of constructing confidence interval estimate for population variance

A
  1. Population must have normally distributed values
  2. Histogram of data must be bell-shaped
  3. Sample is a simple random sample

Stats 1 (3 decks)

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