Reference 1-9 PDF

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has formulas and charts to help you get ready for the exam...

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Chapter 1  To create a histogram on the TI -84 calculator: o Push STAT then select option 1: Edit. o Enter the data set in L1. o Push 2nd Y= (for Stat Plot). o Turn on Plot1 (press ENTER twice). o Use the down arrow, followed by the right arrow, to select Type that looks like histogram and push ENTER. o Make sure Xlist is set to L1. o Push GRAPH > ZOOM followed by the number 9 (for option 9: Zoom Stat) to see the histogram. o Use TRACE and the arrow keys to navigate about the graph (you will see relevant information on the screen).

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A Pareto chart is a bar graph in which the bars are arranged from tallest to shortest. \ Appropriate Graphs

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Appropriate Measures

o Chapter 3  When dealing with numerical data, you need to describe the distribution using these 3 characteristics:

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To find the mean on the TI-84 calculator: o Push STAT then select option 1: Edit. o Enter the data set in L1. o Push STAT and arrow over to Calc. o Choose option 1: 1-var stats (press ENTER). o The mean is given at the top (x). To find the standard deviation on the TI-84 calculator: o Push STAT then select option 1: Edit. o Enter the data set in L1. o Push STAT and arrow over to Calc. o Choose option 1: 1-var stats (press ENTER). o The standard deviation for a sample is given by sx The Empirical Rule  Guidelines: (% of data within __ standard deviation of the mean)  68% of the data is within 1 standard deviation.  95% of the data is within 2 standard deviations.  Almost all of the data is within 3 standard deviations. To find the median on the TI-84 calculator: o Push STAT then select option 1: Edit. o Enter the data set in L1. o Push STAT and arrow over to Calc. o Choose option 1: 1-var stats (press ENTER). o Arrow down to see the median (Med). To find the IQR on the TI-84 calculator: o Push STAT then select option 1: Edit. o Enter the data set in L1. o Push STAT and arrow over to Calc. o Choose option 1: 1-var stats (press ENTER). o Arrow down to see the first and third quartiles (Q1 and Q3). o Calculate the IQR: IQR = Q3 – Q1. When dealing with numerical data, you need to describe the distribution using these 3 characteristics:

o Choosing a Measure

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General Rule for finding outliers: o Find the fences (“cutoffs” ) for usual data values:  Lower fence = Q1 – 1.5 (IQR)  Upper fence = Q3 + 1.5 (IQR)  To create a boxplot on the TI-84 calculator: o Push STAT then select option 1: Edit. o Enter the data set in L1. o Push 2nd Y= (for Stat Plot). o Turn on Plot1 (press ENTER twice). o Use the down arrow , followed by the right arrow, to select Type that looks like a boxplot with outliers (first boxplot option) and push ENTER. o Make sure Xlist is set to L1. o Push GRAPH > ZOOM followed by the number 9 (for option 9: Zoom Stat) to see the boxplot. o Use TRACE and the arrow keys to navigate about the graph (you will see relevant information on the screen).  Computing r Using StatCrunch

o Enter the data into StatCrunch. o STAT > Regression > Simple Linear o Select the x-variable, select the y-variable, select COMPUTE.  To find r, the correlation coefficient, on the TI-84 calculator: o Enter your data, using one list for x-variable and one list for the yvariable. Remember to enter your data in order as pairs. o Push STAT > CALC then select option 8: LINREG(A+BX). o Enter the lists where you entered your data separated by a comma after the LinReg command. For example, LinReg(a + bx) L1, L2 and press ENTER.  Finding the Regression Equation Using StatCrunch o Enter the data into StatCrunch. o STAT > Regression > Simple Linear o Select the x-variable, select the y-variable, select COMPUTE. Chapter 6  To find a probability for a Normal distribution on the TI-84 calculator: o Push 2ND Dist then select option 2: normalcdf. o Enter the left boundary of your shaded area, the right boundary of your shaded area, the mean, and the standard deviation and press ENTER.  Using StatCrunch o Select STAT > Calculators > Normal. o Enter the mean and standard deviation. o Enter x ≥ 31. o Press COMPUTE.  Standard Normal Model o N(0,1) o Normal distribution with a mean=0 and a standard deviation=1  To find an x-value for a Normal distribution on the TI-84 calculator given an area: o Push 2nd DIST then select option 3: invNorm. o Enter the area to the left of the x-value of interest, the mean, and the standard deviation. o To find the 15th percentile for the seal pup lengths, o invNorm(0.15, 29.5, 1.2) = 28.3 inches. Chapter 7 

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Finding Bias and Standard Error o The bias of

is 0.

o The standard error of is o if the following conditions are met:  The sample is randomly selected from the population of interest.  If the sampling is without replacement, the population must be at least 10 times larger than the sample size.  Central Limit Theorem for Sample Proportions o If we take a random sample from a population, and if the sample size is large and the population size is much larger, then the sampling distribution of is approximately Normal with a mean of p and a standard deviation of

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o If you don’t know the value of p, you can substitute the value of Margin of Error o Tells us how far from the population value our estimate can be o Margin of error = z* SE o where z* is a number that tells how many standard errors to include in the margin of error.

Confidence Interval for a Population Proportion

o Using the TI-84 Calculator o To construct a confidence interval for a population proportion on the TI-84 calculator:  Push STAT then select TESTS.  Select option 1-PropZInt.  Enter values for x and n, enter the confidence level (C-Level), and press Calculate.  Using StatCrunch o Stat > Proportion Stats > One sample > with data o Enter # successes (x), # observations (n), select Confidence Interval and enter confidence level. o Click Compute. o L Limit = lower limit of confidence interval o U Limit = upper limit of confidence interval  Relationship between Confidence Level and Interval Width o As the level of confidence increases, the width of the confidence intervals also increases. 

 Chapter 9  Use technology to create the interval. o StatCrunch: Stats > T stats > One sample > with summary

To construct a confidence interval for a population, mean on the TI-84 calculator:  Push STAT > TESTS then select T-INTERVAL.  If you have data in a list, select DATA. Enter the name of the list where the data is stored, leave Freq: 1, select your C-level and press Calculate. o If you do not have data in a list, select STATS. Enter the sample mean, standard deviation, sample size. Select your C-level and press Calculate.  To find upper and lower limit for ___________% confidence interval using statcrunch o Type in the data o Stat o T-stats o One sample o With data o Select a column o Perform ___________ confidence interval  

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Four Steps for Hypothesis Testing o Hypothesize State your hypotheses about the population parameter.

o Prepare Choose a significance level and test statistic, check conditions and assumptions. o Compute to Compare Compute a test statistic and p-value. o Interpret Do you reject the null hypothesis or not? What does this mean?  Hypothesis Test: Claim about a Population Mean o Test Statistic for a One-Sample t-Test:

x- m 0 t= SEEST

where

SEEST =

s n

o If conditions hold, the test statistic follows a t-distribution with df = n – 1. o Two Conditions:  Random, independent sample  Large sample: The population must be Normal or the sample size must be at least 25.\  One- and Two-sided Alternative Hypotheses o Just as with hypothesis tests for proportions, hypothesis tests can be one-sided or two-sided depending on the research question. o The choice of the alternative hypothesis determines how the p-value is calculated.

o Using Technology o Both the test-statistic and p-value can be computed using technology. o StatCrunch: Stats > t Stats > One Sample > with summary  Using the TI-84 Calculator o To conduct a hypothesis test for a mean with one population on the TI-84 calculator:  Push STAT > TESTS then select the T-test option.  If your data is in a list, select DATA, enter the number in H0, the list the data is in. Leave Freq at 1 and highlight the sign in your Ha. If you have summary statistics, select STATS and enter the required statistics.  Press Calculate or Draw. The test statistic and p-value will be displayed.  Using technology to test statistics when we have data and a mean o Stats 

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T-stats One sample With data Perform hypothesis test for mu Type in H0: mu=mean and Ha: mu does not equal to mean

 Chapter 8 One-Sided vs. Two-Sided Hypotheses

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Test Statistic: Hypothesis Test of One Population Proportion

o We usually use technology to generate both the test statistic and pvalue: o StatCrunch Stat > Proportion Stat > One Sample > with summary.  Using the TI-84 Calculator o To conduct a hypothesis test for a population proportion using the TI-84 calculator:  Push STAT > TESTS then select the 1-PropZTest option.  Enter p0, the proportion in the null hypothesis.  Enter x and n (make sure to round x to a whole number, if necessary).  Select the sign that corresponds with the sign in your alternative hypothesis.  Select Calculate or Draw. The test statistic (z) and p-value (p) will be displayed.  Potential Mistakes in Hypothesis Testing o 

Confidence Level (1 – α)

Alternative Hypothesis

Significance Level (α)

90%

Two-Sided ≠

10%

95%

Two-Sided ≠

5%

99%

Two-Sided ≠

1%

Relationship between Confidence Levels and Significance Levels Hypotheses: One-Sided and Two-Sided Tests

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Changes to The Test Statistic

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Two Proportions: The Test Statistic

o We use technology to compute the test statistic and p-value. o StatCrunch: Stat > Proportion Stats > Two Sample > with summary.  Using the TI-84 Calculator o To conduct a hypothesis test for comparing proportions from two populations using the TI-84 calculator:  Push STAT > TESTS then select the 2-PropZTest option.  Enter p0, the proportion in the null hypothesis.  Enter x1, n1, x2, and n2 (make sure to round x to a whole number, if necessary).  Select the sign that corresponds with the sign in your alternative hypothesis.  Select Calculate or Draw. The test statistic (z) and p-value (p) will be displayed. ...