STP226 Exam 1 Study Guide

***STUDY THIS***Qs. 51, page 131, Section 3.2

***LOOK UP EMPIRICAL RULE AND MEMORIZE THESE THINGIES AND DO PRACTICE*** Since the distribution is bell-shaped, that tells us that we can use the Empirical Rule. N = 621, mean = 3234 gram, SD = 871 gram. 1 SD away from mean is the range (3234 - 871, 3234 + 871) = (2363, 4105) 2 SD away from the mean is the range (3234 - 2*871, 3234 + 2*871) = (1492, 4976) 3 SD away from the mean is the range (3234 - 3*871, 3234 + 3*871) = (621, 5847) P(x < 4105) = 50% + 34% = 84% 84% of 621 = 521.64 or 522 b). P(x > 1492 = 50% + 47.5% = 97.5% 97.5% of 621 = 605.5 or 606 c). P(3234 < x < 4976) = 47.5% 47.5% of 621 = 294.975 or 295

When a data set is skewed to the right, there are large values in the right tail. Because the median is resistant while the mean is not, the mean is generally more affected by these large values. Therefore for a data set that is skewed to the right, the _______

...mean is greater than the median. ---------------------- Remember how the distribution curve looks. Instead of this distribution curve, you might be given a bunch of histograms. You then need to draw a distribution curve over the histograms to reach the conclusion whether the data is skewed to the left or right and the relation between mean and median.

Similarly, when a data set is skewed to the left, the ______

...mean is smaller than the median. ---------------- Remember how the distribution curve looks. Instead of this distribution curve, you might be given a bunch of histograms. You then need to draw a distribution curve over the histograms to reach the conclusion whether the data is skewed to the left or right and the relation between mean and median.

Use the data to construct a scatter plot and compute the correlation coefficient.

Go to [STAT] "CALC" "8:" [ENTER] to view. to see correlation coefficient- easy just do that and enter the info from the data table and you get r (the correlation coefficient) y2-y1/x2-x1 (rise/run) = slope

relative frequencies- Qs 21 on page 63, Section 2.2.

I looked it up in book and this is easy. done! part (a), add up the relative frequencies above 240, and you will get approximately 30%. To find the answer to part (b), add up the relative frequencies for each of the given classes in the question and compare.

Continuous

It is continuous since you can use any numbers like "3 miles", "3.5 miles", "3 quarter miles", etc. to describe the distance.

Qs. 27, page 147, Section 3.3

Looked it up in book and it is easy, just practice z-score equation! Mean for ACT = 21.1 SD = 5.2 Mean for SAT Math = 514 SD for SAT Math = 117 All the distributions are bell shaped means we can apply the z-score and the Empirical Rule. Z-score is done by doing (the score-mean)/SD= z-score (a). Z-score for ACT of 27 = (27 - 21.1)/5.2 = 1.1346 (b). z-score for SAT Math of 650 is (650 - 514)/117 = 1.1623 (c). SAT since 1.16 > 1.13 (d). 0.75 = (x - 21.1)/5.2 x = 0.75*5.2 + 21.1 = 25 (e). -2 = (x - 514)/117 x = -2*117 + 514 = 280

Qs. 41 on page 224, Section 5.2

Looked it up- it is easy and you know how to do it!! To solve these types of questions, you need to apply the concepts of probability along with the concepts of addition rule, mutually exclusive events and the complement rule. (a) Add all the values for the runny nose - 6 + 12 = 18. Thus, P(children has runny nose) = 18/25 = 0.72 (b) . Add all the values for the sore throat - 6 + 4 = 10. Thus, P(children has sore throat) = 10/25 = 0.4 (c) P(runny nose or a sore throat) = P(A) + P(B) - P(A and B). The word "or" gives you the hint that you need to apply the addition rule. The table tells you that runny nose and sore throat are not mutually exclusive and thus you realize which formula to use. Let A = child has runny nose, B = child has sore throat. Then, A and B = child has both runny nose and sore throat. Thus, P(runny nose or sore throat) = P(child has runny nose) + P(child has sore throat) - P(child has both) = 18/25 + 10/25 - 6/25 = 22/25 = 0.88 (d). P(child has neither runny nose nor sore throat) = 1 - P(child has either sore throat or runny nose) = 1 - 0.88 = 0.12

The mean and median measure the center of a data set in different ways. When a data set is symmetric, the ______

Mean = Median.

Discrete

Number of Siblings: It is discrete since you need to use whole numbers to describe how many siblings a person has. You cannot say something like "I have 2.5 sisters."

Determine whether the random variable is discrete or continuous: a). The number of heads in 100 tosses of a coin b). The weight of a randomly chosen student's backpack.

The answer to (a) is discrete because you can only use whole numbers. (b). is continuous because you can use any sort of number to describe weight.

A group of elementary school children took a vocabulary test. It turned out that children with larger shoe sizes tended to get higher scores on the test, and those with smaller shoe sizes tended to get lower scores. As a result, there was a large positive correlation between vocabulary and shoe size. Does this mean that learning new words causes one's feet to grow, or that growing feet cause one's vocabulary to increase?

They are not correlated -------------------- The fact that shoe size and vocabulary are correlated does not mean that changing one variable will cause the other to change. Correlation is not the same as causation. In general, when two variables are correlated, we cannot conclude that changing the value of one variable will cause a change in the value of the other.

Suppose that three dice are rolled, the smallest possible total is 3 and the largest possible total is 18. Following are the frequencies for each possible outcome when the dice are "rolled" 1000 times. Compute P(10)

To solve these types of problems, add up all the frequencies. In this case, we are already told that the sum of frequencies = 1000. ----------- So, P(10) = Frequency of 10/Sum of frequencies = 128/1000 = 0.128

***PRACTICE THIS TYPE OF PROBLEM***The Statistical Abstract of the US reported that 66% of students who graduated from high school in 2012 enrolled in college. 30 high school students are sampled. Find (a). What is the probability that exactly 18 of them enrolled in college? (b). What is the mean number who enroll in college in a sample of 30 high school graduates? (c). What is the standard deviation of the number who enroll in college in a sample of 30 high school graduates?

calc buttons: 2nd--> VARS--> binompdf/binomcdf ---> enter in numbers Probability of student who graduated from high school and enrolled in a college = 0.66 (because 66% = 66/100 or 0.66). Let us call this the probability of success Then, the probability of failure = probability student graduate but didn't enroll in a college is 1 - 0.66 = 0.34 N = 30 So, we see that there can be only success (enroll in college) or failure (didn't enroll in college). That tells us that we need to apply the Binomial Theorem. a). P(x = 18) = = 0.11655 b). The mean of a binomial random variable = np = 30*0.66 = 19.8 c). The variance is np(1 - p) = 30*0.66*0.34 = 6.732. Thus, the standard deviation is sqrt(6.732) = 2.59461calc

What is the probability that the sampled family owns a house? What is the probability that the sampled family rents?

just divide the owned or rented # by the total number

The table shows the probability distribution for the age of a student at a certain public high school. Calculate the variance and the standard deviation of the ages.

just go to the table where you enter the values and then it shows the mean and SD. you know how to do this bb!!

Find the median, mean and mode number

median: put #s in order and it is the middle one mean: add them together and divide by the # of numbers total mode: # that appears more than once

Find the regression line of the following data-set. ---------------- Predict the selling price of a House of size 2800 sq. ft. Two houses are up for sale. One house is 1900 square feet in size and the other is 1750 square feet. ***By how much should we predict their prices to differ?*** study that part

same formula for correlation coefficient: Go to [STAT] "CALC" "8:" [ENTER] to view. -also pretty easy, just look at the graph, and create the y=bx + a and when you do the line regression thing in the calculator, it will give you all of that plus r squared. and then you can enter all the data points into the L1 and L2 in your calculator and get the correlation coefficient and then you can also plug in whatever for x once you have the y=mx +b equation. y = 0.0992x + 160.19 and R² = 0.8111 -------------- Once you have the equation, you can then answer all the other questions: The predicted selling price of a house of size 2800 sq. ft is y = 0.0992*2800 + 160.19 = 437.95 (thousand) Slope of the line is 0.0992. We know slope = Difference between two prices/difference between two sizes. Therefore 0.0992 = (price_1 - price_2)/(1900-1750) 0.0992 = (price_1 - price_2)/150 price_1 - price_2 = 0.0992*150 = 14.88 (thousand) is the value by which we should predict the prices to differ.