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Statistics Test 3

Terms in this set (43)

1) The sample contains an outlier.

2) The sample exhibits a large degree of skewness.

3) The sample is has more than one distinct mode.
We will reject the assumption that a population is approximately normal if a sample has any of the following features: otherwise it is considered normal
Normal quantile plots
plots are somewhat more complex than dotplots, histograms, and stem-and-leaf plots.
Point Estimate
a single number that is used to estimate the value of an unknown parameter (sample mean, xbar, is an example)
These all Depend on Margin of Error:

1) Level of confidence: as the level of confidence increases, the margin of error increases
**

2) Sample size: if the sample size increases, then the margin of error decreases (due to the law of large numbers)
**

3) Standard Deviation: the more spread (more SD) in the population, the wider the intervals for the sample size & level of confidence
Three things that depend on Margin of error:
critical values
in a 90% confidence level, the z score that bind the middle 90% of the area of the curve are called
margin of error
standard error (sigma / squarer of sample size) x critical value = _______
confidence interval
an interval that is used to estimate the value of a paramete: point estimate (+ and -) the margin of error is called the ________
confidence level
a percentage between 0% and 100% that measures the success rate of the method used to construct the confidence interval
0.04 to the left and 0.04 to the right...find the z score for 0.04 to the left
find critical value of 92% confidence interval:
step 1) find point estimate
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step 2) find critical value for confidence level (table A.2 - area of left tail)
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step 3) find margin of error
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step 4) use point estimate and margin of error to construct confidence interval
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step 5) interpret result
Steps for constructing a confidence interval when POPULATION mean and SD are known (what table?):
Students T Distribution
the distribution when the population SD and mean are unknown
degree of freedom
how much more spread out the T distribution is than then Normal distribution depends on the ________ (n-1)
Use table A.3 with DOF column
finding critical values for t-distributions (t alpha /2):
If the desired number is less than 200, use the next smaller number that is in the table.
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If the desired number is greater than 200, use the z-value found in the last row of Table A.3, or use Table A.2.
If the desired number of degrees of freedom isn't listed in Table A.3, then
**
If the desired number is less than 200, what do you do?
**
If the desired number is greater than 200, what do you do?
step 1) find sample mean / point estimate (xbar) and sample SD (s)
**

step 2) find DOF (n-1) and CV (t alpha/2) [table A.3 w/ DOF column]
**

step 3) find margin of error (s/root n ) x (CV)
**

step 4) construct interval with point estimate and margin of error

step 5) interpret result
Steps for constructing a confidence interval when population mean and SD are UNKNOWN (only sample jawns are given no population jawns) (what table?):
population proportion of individuals who are in a specified category
what is p?
number of individuals in a sample who are in a specified category
what is x?
the sample proportion and the point estimate, formula (x/n)
what is p hat?
square root [p(1-p) / n]
standard error for population proportions
Check to be sure the assumptions are satisfied

Step 1) Compute the value of the point estimate 𝑝 ̂= x/n.
**
Step 2) Find the critical value 𝑧_(𝛼/2) for the desired confidence level (using table A.3 last column) .
**
Step 3) Compute the standard error √(𝑝 ̂(1−𝑝 ̂ )/𝑛) and multiply it be the critical value to obtain the margin of error 𝑧_(𝛼/2)∙√(𝑝 ̂(1−𝑝 ̂ )/𝑛).
**
step 4) construct confidence interval using point estimate and margin of error
**
step 5) interpret result
Procedure for Constructing a Confidence Interval for population proportion (p) (only x and n are given to find p, or percentages, no sample or population mean or sample SD):
use equations on sheet ! (chapter 8 top right 2)
finding sample size when given confidence level, p hat, and margin of error (also equation for no p hat):
Use when it says to use small sample method!

(p with ~) = x+2 / n+4

standard error = √p(1-p) / n+4
Small sample methodusing adjusted sample proportion (p with ~): formula and when to use
Null Hypothesis
states that the parameter is equal to a specific value, μ_0
Denoted as H_0
Alternate Hypothesis
states that the parameter differs from the value specified by the null hypothesis, μ_0
Denoted as H_1
Left-tailed
One Tailed: States that the parameter is less than the value specified by the null hypothesis, for example, H_1: µ<μ_0
Right-tailed
One Tailed: States that the parameter is greater than value specified by the null hypothesis, for example, H_1: µ>μ_0
Two-tailed
States that the parameter is not equal to the value specified by the null hypothesis, for example, H_1: µ≠μ0
conclude that the alternate hypothesis, H_1, is true
If the null hypothesis is rejected, what do you conclude?
There is not enough evidence to conclude that the alternate hypothesis, H_1, is true and H_0 MIGHT be true
If the null hypothesis is not rejected, what do you conclude?
A type I error occurs when we reject H_0 (the null hypothesis) when it is actually true
What is a Type 1 error?
A type II error occurs when we do not reject H_0 (the null hypothesis) when it is actaully false
What is a Type 2 error?
Test statistic
The z-score of the sample mean
critical value
Critical value method: the _______ forms a boundary between values that are considered unusual and values that are not
critical region
Critical value method: The region that contains the unusual values is called the _______
significance level
The probability that we use to determine whether an event is unusual is called the _________ (denoted by α)
P value
The ______ is the probability that a number drawn from the distribution of the sample mean would be as extreme as or more extreme than our observed value of xbar

**the smaller this value is the stronger the evidence against H_0
statistically significant
If P ≤ α we say that H_0 is rejected at the α level, or that the result is _________ at the α level
Step 1) state H_0 and H-1
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Step 2) chose a level of significance (α)
**
Step 3) compute test statistic using formula on sheet (top left in chapter 9)
**
Step 4) FIND Critical value(s) z_α, -z_α or z_α/2 (Use table A.3 last column)
**
Step 5) COMPARE CV TO TEST STATISTIC If Left tailed: reject if z ≤ -z_α, If Right Tailed: reject is z ≥ z_α, if Two Tailed: reject if z ≥ z_α/2 or z ≤ -z_α/2
**
Step 6) state conclusion
Doing a Hypothesis Test when we know population mean and SD using the critical value method
Probability of a type 1 error
The probability of a______ error is equal to the significance level which is denoted by α
practical significance
Sometimes statistically significant results do not have any practical importance or __________
T-test
When the null hypothesis is true, the t statistic has a student' t distribution with n - 1 degrees of freedom. When we perform a test using a t statistic we call this a __________
Step 1) state H_0 and H-1
**
Step 2) chose a level of significance (α)
**
Step 3) compute test statistic using formula on sheet (bottom left in chapter 9)
**
Step 4) FIND Critical value(s) t_α, -t_α or t_α/2 (use table A.3 with α and DOF column)
**
Step 5) COMPARE CV TO TEST STATISTIC If Left tailed: reject if t ≤ -t_α, If Right Tailed: reject if t ≥ t_α, if Two Tailed: reject if t ≥ t_α/2 or t ≤ -t_α/2
**
Step 6) state conclusion
Doing a Hypothesis Test when we DO NOT know population mean and SD using the critical value method (we are only given xbar and s which are sample mean and SD)
Step 1) state H_0 and H-1
**
Step 2) chose a level of significance (α)
**
Step 3) compute test statistic using formula on sheet (Top right in chapter 9 but don't square root n)
**
Step 4) FIND Critical value(s) z_α, -z_α or z_α/2 (Use table A.3 last column)
**
Step 5) COMPARE CV TO TEST STATISTIC If Left tailed: reject if z ≤ -z_α, If Right Tailed: reject if z ≥ z_α, if Two Tailed: reject if z ≥ z_α/2 or z ≤ -z_α/2
**
Ste 6) state conclusion
Doing a Hypothesis Test about a population proportion (only percentages given or x and n, no population / sample means or SDs)
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