How to find the point estimate given a confidence interval

Suppose a confidence interval is (A, B): The point estimate is the average of A and B $$\frac{A+B}{2}$$ (It is the exact center of the interval)

How to find the margin of error given a confidence interval

Suppose a confidence interval is (A, B): To find the margin of error, subtract the point estimate from the upper bound of the confidence interval: ME = B - (pt. est.) OR $$ME=\frac{A+B}{2}$$

Type I and Type II errors

A Type I error occurs when the null hypothesis is true and is rejected (false positive). A Type II error occurs when the alternative hypothesis is true and the null hypothesis is not rejected (false negative).

The power of a test is the probability a test will correctly reject the null hypothesis, given the alternative hypothesis is true. *Remember! P(Type II error) = 1 – P(power)

Interpret the confidence interval

We are C % confident that the interval from lower to upper units captures the true population parameter in context .

Interpret the confidence level

After many, many random samples of size n , approximately C % of confidence intervals created will capture the population parameter in context.

Interpret the P-value

Assuming H 0 is true , there is a p probability of getting a parameter of stat or more/less/more extreme purely by chance.

What is an unbiased estimator?

When estimating a population parameter, a statistic is unbiased if the center of the sampling distribution for the statistic is equal to the population parameter.

Conditions for a one-sample t-test and t-interval for μ

Random : Data come from a random sample Independent : When sampling without replacement, n < 10% of the population size Normal : Population distribution is normal, large sample (n ≥ 30), or a dotplot of the sample data shows no strong skewness or outliers.

Conditions for a one-sample z-test and z-interval for p

Random : Data come from a random sample Independent : When sampling without replacement, n < 10% of the population size Normal : • Test: np 0 ≥ 0 and n(1-p 0 ) ≥ 0 • Interval: np̂ ≥ 10 and n(1-p̂) ≥ 10

Conditions for a two-sample t-test and t-interval for μ1– μ2

Random : Data come from independent random samples or 2 groups in a randomized experiment. Independent : when sampling without replacement: n < 10% of the population size for both samples. Normal : For both populations, either the population distribution is normal, large sample (n ≥ 30), or a dotplot of the sample data shows no strong skewness or outliers

Conditions for a two-sample z-test and z-interval for p1– p2

Random : Data come from independent random samples or 2 groups in a randomized experiment. Independent : when sampling without replacement: n < 10% of the population size for both samples. Normal : • Test: n 1 p̂ c ≥ 10, n 1 (1 - p̂ c ) ≥ 10, n 2 p̂ c ≥ 10, n 2 (1 - p̂ c ) ≥ 10 • Interval: n 1 p̂ 1 ≥ 10, n 1 (1 - p̂ 1 ) ≥ 10, n 2 p̂ 2 ≥ 10, n 2 (1 - p̂ 2 ) ≥ 10

Conditions for a chi-square test

Random : Data from a random sample, separate random samples, or groups in a randomized experiment. Independent : when sampling without replacement: n < 10% of the population size for all samples. Large Counts : All expected counts must be at least 5

Conditions for a t-test or t-interval for slope

Linear : True relationship between the variables is linear. Independent observations : 10% condition when sampling without replacement Normal : Responses vary normally around the regression line for all x-values Equal Variance around the regression line for all x-values Random : Data from a random sample or randomized experiment

Why do we check the Random, 10%, and Normal/Large Sample conditions?

Random …so we can generalize to the population from which the sample was selected. 10% condition …so sampling without replacement is OK and we can use the stated formula for standard deviation. Normal/Large Sample …so the sampling distribution is approximately Normal.

What is the difference between a parameter and a statistic?

A parameter is a number that describes the population. Ex: μ, p, σ A statistic is a number that describes the sample. Ex: x̄, p̂, s

What is the difference between the population distribution, the sample distribution, and the sampling distribution?

The population distribution is the distribution of responses for every individual of the population. The sample distribution is the distribution of responses for a single sample. The sampling distribution is the distribution of values for the statistic for all possible samples of a given size from a given population.

What is the Central Limit Theorem?

The central limit theorem (CLT) states that when the sample size is sufficiently large, a sampling distribution of the mean of a random variable will be approximately normally distributed.

What calculator function is used for a one-sample t-interval for μ?

1-Sample tInterval STAT -> INTR -> t -> 1-S

What calculator function is used for a one-sample t-test for μ?

1-Sample tTest STAT -> TEST -> t -> 1-S

What calculator function is used for a one-sample z-interval for p?

1-Prop zInterval STAT -> INTR -> Z -> 1-P

What calculator function is used for a one-sample z-test for p?

1-Prop zTest STAT -> TEST -> Z -> 1-P

What factors affect the width of a confidence interval?

The width of a confidence interval: • Decreases as n increases • Increases as the confidence level increases

How do I make a decision based on a P-value?

If the P-value ≤ a, reject the null hypothesis. If the P-value > a, fail to reject the null hypothesis.

What does it mean if we reject (or fail to reject) the null hypothesis?

Rejecting the null hypothesis means there is convincing statistical evidence to support the alternative hypothesis. Failing to reject the null means there is not convincing statistical evidence to support the alternative hypothesis.

What is the probability that a specific confidence interval captures the population parameter?

0 or 1 A confidence interval, calculated from sample data either does or does not capture the population parameter! Don’t say there is a 95% chance/probability of capturing the population parameter!!! (say 95% confident )

How to calculate expected counts in a chi-square test for homogeneity/independence

$$epected\ count=\frac{\left(row\ total\right)\left(column\ total\right)}{table\ total}$$ (The calculator will put expected counts in Matrix B)

How to choose the right inference procedure?

Ask yourself : • Does the scenario describe mean(s) [t], proportion(s) [z], counts [χ 2 ], or slope [t]? • Does the scenario describe one sample [1-S], two samples [2-S], or paired data [1-S]? • Does the scenario describe a test [TEST] or a confidence interval [INTR]?

Exploring Data! Describe a Distribution

C-SOCS ! C ontext - Where did the data come from? S hape – Skewed right? Skewed left? Fairly symmetric? Two distinct peaks? O utliers – If you are estimating, call them “potential outliers.” C enter – What is the mean? If the distribution is skewed, identify the median. S pread – Remember, SD goes with the mean and IQR goes with the median.

Exploring Data! Compare two distributions

C-SOCS ! (context, shape, outliers, center, spread) Remember to use COMPARISON words when describing the center and spread (variability). "is similar to" "is less than" "is greater than"

Exploring Data! Outlier Rule

An outlier is any value that falls more than 1.5 IQR above Q3 or below Q1. $$Lower\ outlier\ $$Upper\ outlier\ >\ Q_3+1.5\left(IQR\right)$$ Note: This is a rule of thumb, some consider any value that is more than 2 SD away from the mean to be an outlier.

Exploring Data! How do we describe the relationship between two variables (like in a scatterplot)?

DUFS : D irection – positive or negative U nusual values – outliers, influential observations F orm – Linear or curved S trength – Weak -> Strong

Exploring Data! How to find the mean, SD, and 5-number summary using a graphing calculator

STAT -> (enter data into table) -> CALC -> 1-Var *Before choosing 1-Var, you should select SET (F6) to ensure your setting are correct

Exploring Data! How to calculate a LSRL using a graphing calculator.

STAT -> (enter data into List 1 and List 2) -> CALC -> SET (make sure setting are correct) -> EXIT -> REG -> X -> a+bx a = y-int b = slope r = correlation coefficient R 2 = coefficient of determination

Exploring Data! What is the IQR?

The interquartile range (IQR) is defined as the difference between the third and first quartiles: Q 3 − Q 1 . Q 1 and Q 3 form the boundaries for the middle 50% of values in an ordered data set.

Exploring Data! How do I calculate the percentile of a particular value in a data set?

• Order the data • Count the number of values that are less than or equal to the value of interest. • Count the number of values in the data set. $$Percentile=\frac{Number\ of\ values\ less\ than\ or\ equal\ to\ the\ value\ of\ interest}{Number\ of\ values\ in\ the\ data\ set}$$ Express the decimal as a percentile. Ex: 0.58 is the 58th percentile.

AP Stats Flashcards (Set A) Flashcards

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50 questions

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1.

FLASHCARD QUESTION

Front

Formula

One-Sample t-interval for μ

Back

2.

FLASHCARD QUESTION

Front

Formula

One-sample t-test for μ

Back

3.

FLASHCARD QUESTION

Front

Formula

One-sample z-test for p

Back

4.

FLASHCARD QUESTION

Front

Formula

One-sample z-interval for p

Back

5.

FLASHCARD QUESTION

Front

Formula

Two-sample t-interval for μ_{1 -}μ₂

Back

6.

FLASHCARD QUESTION

Front

Formula

Two-sample t-test for μ_{1 -}μ₂

Back

7.

FLASHCARD QUESTION

Front

Formula

Two-sample z-interval for p_{1 - p2}

Back

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