Unit 1
You measure age(years), weight(pounds), and breed(beagle,pug,terrior, or golden retriever) of 200 dogs. How many variables did you measure?
3
The LSRL for a set of data is ŷ=3/4x+b. You know the LSRL passes through the point (8,3). What does ȳ equal, in terms of x̄?
ȳ= 3/4x-3
b=-3
Why do we use a control group in experiments?
To control how the experiment is conducted and make sure that the result are what we expected.
You pick one marble from a bag that contains 8 marbles (2 blue, 3 red, and 3 yellow). Find p(Yellow)
3/8;0.375
A die is loaded so that the number 6 comes up three times as often as any other number. What is the probability of rolling a 4,5,6?
5/8
Which planet is closest to the sun?
Mercury
What does the correlation of -0.89 suggest about two variables.
As the explanatory(X) variable increases, the response(Y) variable decreases
The Wisconsin Forward Exam is a standarized test given to every student in the fall and spring seasons. They created a new version of the test and want to get a baseline score from a random sample of 8th graders across the state. They have a list of all 318 middle schools in Wisconsin, and they randomly select 10 middle schools. The baseline eaxm was given to every 8th grade in the middle school selected. What kind of sample is this?
A Cluster Sample
You pick one marble from a bag that contains 8 marbles (2 blue, 3 red, and 3 yellow). Find p(not blue)
6/8;0.75
Allan leads a report that says 80% of high school students has a computer at home. He believes the proportion is smaller than .8 at our school. Allan chooses a SRS of 60 students and record whether they have a computer at home. He wants to te this at a 5% significance level. In his sample, 41 of the students have a computer at home.
Is this evidence that the proportion of students who have a computer at home is less than the national proportion?
P=Proportion of students who have computer at home
Ho:P=.80 Ha: P<.80 a=0.05 n=60
Random, Independent 60<.10(all students), Normal 60(.8)>10 & 60(.2)>10
One Prop Z test
Z=-2.27 P=0.0116
Because our p-value of 0.0116 is lower than a=.05, we reject Ho. We have convincing evidence that the true proportion of students who have a computer is less than 0.8.
On a website that has brain games and cognitive tests, the distribution of reaction times for a certain clicking task follows approximately normal distribution with a mean of 284 milliseconds and a standard deviation of 50 milliseconds.
What percent of people take longer that 300 milliseconds to complete the task?
37.45%
The LSRL for a set of data is ŷ=-1.5x+5.5. The ordered pair (5,-5) is in the data set. What is the residual of this point?
-3
Proactive has developed a new treatment for acne. You think the age of the participants might influence their reaction to the new treatment, so you separate them into two groups: one group of 18-25 year olds and ine group of 26 and older year olds. Which type of design is this experiment
Randomized Block Design
A card is selected at random from a deck of 52 cards. Each deck has 4 different suits: Clubs (black), Spades (Black), Diamonds (Red), and Hearts (Red). Each suit contains the following cards: Ace, 2,3,4,5,6,7,8,9,10, Jack, Queen, and a King. Find P(number card)
36/52;0.69
Which fruit has its seeds on the outside?
Strawberry
A student obtained a z score of -1.40 on a national test for which the mean score was 500 and standard deviation was 50. The students actual test score was...
430
What animal is known to spend up to 90% of its life sleeping?
Koala
What is the only country that is also a continent?
Australia
A card is selected at random from a deck of 52 cards. Each deck has 4 different suits: Clubs (black), Spades (Black), Diamonds (Red), and Hearts (Red). Each suit contains the following cards: Ace, 2,3,4,5,6,7,8,9,10, Jack, Queen, and a King. Find P(not heart)
39/52; 0.75
A teacher claims that the average score on a final exam for her class is 75. You believe the average score is different and decide to test it. You collect a random sample of 10 students, and the sample mean score is 72 with a sample standard deviation of 8. You want to test this at a 5% significance level.
H0:μ=75 Ha:μ≠=75
Sample mean : 72
Sample standard deviation (s): 8
Sample size (n): 10
Df= 9
t=-1.19
P=.266
Because our p-value of .266 is more than a=.05, we fail to reject Ho. We don't have convincing evidence that the mean of the class is different to the sample we took.
The length of time an alkaline AA battery is usable in a CD player is described by a normal distribution with a mean of 76.3 hours and standard deviation of 2.1 hours.
A battery getting 78 hours of se would be in what percentil?
79 Percentile
The equation y=2.579+0.99xy=2.579+0.99x represents the least squares regression line that summarizes the relationship between the height (yy) in centimeters of a certain plant in respect to time (xx) in days recorded by a scientist over the past month. What does the scientist predict the height of the plant will be after 10 days?
12.479
Your football coach finds a new exercise program that will increase upper-body strength better than lifting weights. He wants to start this new program in the off season with the team. He lets his players choose which of the two treatments they will undergo for 3 weeks- exercise or weight lifting. He will use the number of push-ups a player can do at the end of the experiment as the response variable . Which principle of experimental design does his plan violate?
Randomization
What color was the original Coca-Cola drink?
Green
A cereal company claims that the distribution of marshmallow shapes in its cereal is uniform. The shapes are stars, moons, clovers, and hearts. A curious student counts the number of each shape in a random sample of 200 marshmallows and finds:
Stars-52 Moons-47 Clovers-55 Hearts-46
At the α = 0.05 significance level to test whether the distribution of marshmallow shapes is uniform.
H₀: The distribution of marshmallow shapes is uniform, so each shape has a probability of 0.25.
Ha: The distribution of marshmallow shapes is not uniform.
Random✅
All expected counts 5
Chi Squared Goodness of Fit
P=0.781
Because our p-value of 0.781 is larger than a=0.05, we fail to reject. We do not have convincing evidence to conclude that the distribution of marshmallow shapes is different from uniform.