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Chapter 2: Entering Data
Step 1: Enter a list of data in L1 using STATS key (select “Edit”) Note: if you need to clear the data from the list first, use the arrow up to highlight L1, then press CLEAR, and ENTER. Then start entering data into the list. If one of the lists (for example L1) is missing, press STAT, then scroll down to SetUpEditor, then press ENTER twice. When you press STAT again, and then ENTER, all lists will be in place.
Chapter 3: Calculating Mean, Standard Deviation, and 5-Number Summary
Example: Suppose the sample consists of the following 9 data items: x ={5, 9, 7, 4, 6, 250, 35, 100, 84}
Step 1: Enter the list of possible x values in L1 using STATS key (select “EDIT”) Step 2: Press STAT and then right cursor to enter the CALC menu. Choose 1-Var Stats from the CALC menu and press ENTER Step 3:* Read the Calculated Values
x is the mean of the random variable SX is the sample standard deviation In this example: mean = 55.56, sample standard deviation = 81.56. You many scroll down to find the five-number summary: minX = 4, Q1 = 5.5, Med (median) = 9, Q3 = 92, maxX = 250. Note: if you need to find variation, use the fact that it is squared standard deviation: 81.55536633^2 = 6651.
*Step 3 for an upgraded TI-84: You will see a screen with three lines. Enter L1 (press 2nd, 1) into the first line. Move cursor down to the second line and press DEL to delete any entries in this line, then move down to the third line “Calculate” and press “Enter”. Read the results as stated above.
Youtube video tutorial: https://www.youtube.com/watch?v=brs_HP7R9yc
Chapter 4: Probability Theory
1. How to calculate Factorials Example: Find 5! Step 1: Enter 5 Step 2: Press MATH and then right cursor to enter the PRB (probability) menu. Note: In the upgraded TI-84, this function is PROB. Choose “!” and press ENTER twice Step 3: Read the answer: 120. 2. How to calculate Permuations and Combinations “Permutations” Example: Find 5 P 2. Step 1: Enter 5 Step 2: Press MATH and then right cursor to enter the PRB (or PROB) menu. Choose nPr (permutations function) and press ENTER Step 3: Enter 2 and press ENTER Step 4: Read the answer: 20.
“Combinations” Example: Find 5 C 2. Step 1: Enter 5 Step 2: Press MATH and then right cursor to enter the PRB (or PROB) menu. Choose nCr (combinations function) and press ENTER Step 3: Enter 2 and press ENTER Step 4: Read the answer: 10.
Youtube video tutorial: https://www.youtube.com/watch?v=zfaB6EhxY2g
Chapter 5: Discrete Probability Distributions, Binomial Distribution
How to calculate Mean and Standard Deviation: Example: A talk radio station has four telephone lines. If the host is unable to talk, the other callers are placed on hold. The probabilities that 0, 1, 2, 3, or 4 people will get through are below. Use calculator to find mean and standard deviation for the distribution.
Step 1: Enter the list of possible x values in L1 and the set of corresponding P x ( )values in L2 using STATS (select EDIT)
For this example: Enter 0, 1, 2, 3, 4 into L1, and 0.18, 0.34, 0.23, 021, 0.04 into L2. Step 2:* Press STAT again, move to CALC, and choose 1-Var Stats from the CALC menu as when finding the mean of a data set and when it appears on the screen type L1 comma L2 (2nd^ “ 1 ”, 2nd^ “ 2 ”): 1 - Var Stats L 1 , L 2 Press ENTER to calculate. Step 3: Read the Calculated Values
x is the mean of the random variable; for this example x =1.
x is the standard deviation of the random variable; for this example x = 1.
*Step 2 for an upgraded TI-84: Press STAT again, move to CALC, and choose 1-Var Stats from the CALC menu as when finding the mean of a data set. You will see a screen with three lines. Enter L1 (press 2nd, 1) into the first line. Move cursor down to the second line and enter L2 (press 2nd, 2), then move down to the third line “Calculate” and press “Enter”. Read the results as stated above.
Youtube video tutorial: https://www.youtube.com/watch?v=cvUgnTCneyg
How to find Probability for the Binomial Distribution (the binompdf command):
Example : For any hourly employees chosen at random, management of the Star, Inc. estimates a probability of 0.1 that the person will not be with the company next year. Choosing 3 hourly employees at random, what is the probability that 1 of them will leave the company this year?
Step 1: Press 2 nd, then VARS for the DISTR menu. Scroll down to binompdf and press ENTER. Step 2:* The syntax for the binomial probability density function command is binompdf(n,p,x).
- n - is the number of trials. For this example, n = 3 (the number of employees).
- p - is the “success” probability. For this example, p = 0.10 (the probability that an employee is leaving). Note that p must be in decimal form.
- x - is the number of successes. For this example, we want to find the probability that one of the 3 employees will leave the company, so x = 1. Note that x must be a whole number (0, 1, 2, 3, …). Putting it all together, type 3,0.1,1) and press ENTER.
Step 3: Your calculator will return 0.243. So, there is a 24.3% chance that one of the 3 employees will leave the company.
Step 2 for an upgraded TI-84:* You will see four lines: trials, p, x value, and Paste. Enter the number corresponding to n in the “trials” line (in our example it is 3), then the probability of success p (0.10 in our example) into the second line, and the number of successes x (1 in this case) into the third line. Scroll down to “Paste” and press ENTER. This will bring binompdf(n,p,x) to the screen. After you press ENTER, the result will show on the screen.
How to find Cumulative Binomial Probabilities (the binomcdf command): The binomcdf(n, p, x) accessed from the DISTR menu, gives the probability of at most x successes.
Example: 21% of flights from Tampa International Airport are delayed. If 20 flights are chosen at random, then we can consider each flight to be an independent trial. If we define a successful trial to be that a flight takes off on time, then the probability of at most 12 on-time flights (out of 20) from Tampa can be found on the TI-83 as follows:
binomcdf (20,0.79,12) =.
Note: the probability of success is 0.79, not 0.21, because in this problem the successful event is the flight will take off on time.
Youtube video tutorial: https://www.youtube.com/watch?v=oS4AwUim-ic
X 0 1 2 3 4
P(X) 0.18 0.34 0.23 0.21 0.
Section 6.5: Central Limit Theorem
To find probability for the sample mean: 2 nd, VARS, normalcdf (lower x value, upper x value, , standard error) ENTER.
Note: the standard error is
x
n
Example: The weights of women are normally distributed with = 143 lb, and σ = 29 lb. If 36 women are randomly
selected, find the probability that their mean weight is between 140 lb and 211 lb. 2 nd, VARS, normalcdf (140, 211, 143, (29/sqroot of 36)) ENTER Answer:.
*For an upgraded TI-84: Press 2nd^ VARS, scroll down and select “normalcdf” function, press ENTER. You will see five lines: lower, upper, Mu, sigma, and Paste. Enter the number corresponding to the lower bound (140) of the shaded area into the first line, then the number corresponding to the upper bound (211) into the second line, then 143 for Mu, and 29/sq root of 36 (the syntax is “2nd^ “ then x^2, then 36 ) for sigma. Scroll down to “Paste” and press ENTER. This will bring normalcdf(…) to the screen. After you press ENTER, the result will show on the screen.
Section 7.2 Finding Confidence Intervals for Population Proportion
Example: Engineers are interested in estimating the percentage of defective bottles manufactured by the facility. They take a simple random sample of 100 bottles and find that 8 of them are defective. Find 95% confidence interval for the percentage of defective bottles manufactured by the factory.
Solution: There are 8 defective bottles, so x=8; there are 100 bottles in the sample, so n = 100. Your calculator: STAT, TESTS , scroll down to 1 - PropZInt , enter 8 for x , 100 for n , .95 for C-Level (95% confidence), Calculate. Answer: (.02683, .13317), which is the confidence interval.
Youtube video tutorial: https://www.youtube.com/watch?v=tM6fpZfVUqY
Section 7.3 Finding Confidence Intervals for Population Mean
To find Confidence Intervals for mean when sigma is known:
Example: You want to estimate the average price of a home in Minneapolis. From past information, σ = $100,000. You take a simple
random sample of size n = 50 and compute a sample mean of x =$ 246 , 000. Find a 95% confidence interval for the population mean.
STAT , TESTS , Z Interval , from the Input select “ Stats ” (press ENTER to highlight it), enter 100000 for σ , 246000 for X , 50 for n ,
and .95 for C-Level , select CALCULATE , press ENTER Answer: (218282, 273718)
To find Confidence Intervals for mean when sigma is NOT known:
Example: You randomly select 16 restaurants and measure the temperature of the coffee sold at each. The sample mean temperature is 162^0 F with a sample standard deviation of 10^0 F. Find the 99% confidence interval for the mean temperature.
STAT , TESTS , T Interval , from the Input select “ Stats ” (press ENTER to highlight it), enter 162 for X , 10 for Sx , 16 for n , and.
for C-Level , select CALCULATE , and press ENTER Answer: (154.63, 169.37)
Youtube video tutorial: https://www.youtube.com/watch?v=H3uU-Tx2Yq
Section 8.3 Testing a Claim about a Proportion Example: The newspaper claims that 50% of Americans own a pet, but Joe thinks that it is different than that. To test this claim, he takes a simple random sample of 100 Americans and finds that 57 of them own pets. Test his claim with significance level α = 0.05.
STAT, TESTS , select 1 - PropZTest , enter .5 for p0 , 57 for x , and 100 for n , select the type of test, highlight Calculate , ENTER Result: p =. Answer using the P-value method: since p-value 0.1615 > 0.05 (significance level α) we do not reject H 0.
Youtube video tutorial: https://www.youtube.com/watch?v=7TCzhbHCFOM
Section 8.4 Testing a Claim about a Mean To find test a claim about a mean when sigma is known:
Example: A jewelry designer claims that women have wrist breadths with a mean of 5cm. A simple random sample of 40 has a mean of 5.07 cm. Assume that population standard deviation is 0.33 cm. Test the claim.
STAT, TESTS, Z-Test , select “Stats ” (press ENTER to highlight it), enter 5 for 0 , .33 for σ, 5.07 for X , 40 for n , select the test ( ≠
for this problem), highlight Calculate , ENTER.
Result on display : ≠ 5, z = 1.341572341, p = .1797348219, X = 5.07, n = 40.
Interpretation: Using p-value method, p-value = .1797 is greater than the significance level of a = 0.05, so we fail to reject H0.
To find test a claim about a mean when sigma is NOT known:
Example: A power company wants to see if the average amount of current passing through a series of connections is larger than 30 milliamperes (mA). They randomly select 35 of the connections and find a sample average current of 32mA, with a sample standard deviation of 5 mA. Run a hypothesis test with α = 0.05 to see if the population average current is more than 30 mA.
STAT, TESTS, T-Test , select “Stats ” (press ENTER to highlight it), enter 30 for 0 , 32 for X , 5 for Sx, 35 for n , select the test
( > 0 for this problem), highlight Calculate , ENTER.
Result on display : > 30, z = 2.366431913, p =. 0118994098 , X = 32, Sx = 5, n = 35.
Interpretation: Using p-value method, p-value = .0119 is less than the significance level of a = 0.05, so we reject H0.
Youtube video tutorial: https://www.youtube.com/watch?v=m69HQJSP5Nw
Chapter 10: Correlation and Regression
- Make sure you have Diagnostic On: press 2nd, 0 (to open catalog), scroll down to select DiagnosticOn, press ENTER twice.
- Enter your data into L1 and L2 lists, using the Stat, Edit functions.
- To compute the linear regression of a variable in L2 on another variable in L1:
- press STAT > CALC and choose 4:LinReg(ax+b),
- hit enter and type "2nd 1" = L1, then ",", then "2nd 2" = L2, hit enter.
The screen shows the coefficients of the regression equation a and b , and the value for r.
*Step 3 for an upgraded TI-84: Press STAT > CALC and choose 4:LinReg(ax+b), press ENTER. You will see five lines: Xlist, Ylist, FreqList, Store RegEQ, and Calculate. Enter L1 into the first line, L2 into the second line, nothing in the third and fourth lines (press Del if there is something already entered in those two lines). Scroll down to “Calculate” and press ENTER. The result will show on the screen.
Note: you can also find all this information by pressing VARS. Go to 5:Statistics and then to EQ. Choose 1:RegEQ to see the regression equation, 2:a to see the slope, 3:b to see the intercept, 7:r to see the correlation coefficient, and 8:r^2.
Scatterplots
- Press 2nd STAT PLOT and press enter. Switch plot 1 to "on". Select the type of the plot. For example, to make a scatter plot of the data in list 1 against the data in list 2, move the cursor to the scatter plot symbol and press enter. Type L1 (2nd^ 1) as Xlist and L2 (2nd^ 2) as Ylist. Finally choose the mark for your plot and press GRAPH.
- In order to make sure that your plot will fit in the screen, press “ZOOM” key (right under the screen) and select “ZoomStat”, press ENTER.
- To graph a linear regression line, press “Y=” key (right under the screen), enter the equation with coefficients a and b, and press Graph.
Youtube video tutorial: https://www.youtube.com/watch?v=7v1-2kiGAEY
