Populations and Parameters of Interest
Mixed Review
Why do I get hungry doing these problems
Medians, Averages, and Slopes
Definitions
100
A school administration wants to know what percentage of their students who are taking Calculus 1 took the AP Calculus test before taking the class. Out of their 4 Calculus 1 classes they decide to randomly select a quarter of each class to survey. The find out that on average, 10% of them did. What is the population of interest, the parameter of interest, the sample, and the statistic?
Population: Students taking Calculus 1 at the school.
Parameter: How many students taking Calc 1 took the AP test
Sample: A quarter of randomly selected students of each of the 4 Calc 1 classes
Parameter: Average number of Calc students who took the AP test is 10%
100
Given this set of numbers: 9,1,10,13,2,4,5,10,1,3,4,4,7
What is the Q1,median, and Q2?
Q1: 2.5
Median: 4
Q2: 9.5
100
A can of a new experimental energy drink gives 57.92 grams of sugar per drink. If a small pastry gives around 2.67 grams of sugar per pastry, how many do you need to eat to get the same amount as the new energy drink?
-21.69 pastries
100
What is the formula for finding slope?
- (y2-y1)/(x2-x1)
100
What is the formula for z-score?
- z = (x - mean)/(standard deviation)
200
A manager runs a fast food shop in New York and does not like that a new fast food shop has opened across the street. After a year he reads a study that their fast food chain get an average of 50 customers every day. He believes that they are stealing his customers so he decides to run his own survey but only surveys 4 shops, the ones he can walk to or drive to but not those across the state. He gets that on average they get 23 customers and gets angry when he reads that the previous year they were getting 62. Should he get angry?
-Short answer: no, he did not conduct a random study with a large sample size
200
A class set of test scores are about normally distributed. If the mean is 82 and the standard deviation is 2, what percent of scores is between 84 and 86?
- 13.5% of all scores are between 84 and 86
200
Starbucks offers their tall cappuccino in Russia for about $12.30 while in China it costs a little over $7. What is the percent decrease in cost of a tall cappuccino?
-43.09% decrease
200
What is the average number of each pet owned?
-6.8 is the average number of each pet owned.
200
Define mean.
The average of a data set computed by adding the values and dividing by the amount of values.
300
A man who runs a casino suspects that someone is counting cards and stealing his money. He knows that on average the casinos makes 500 dollars a day per table. There are 50 tables that deal cards and decides to survey 30 of them at random towards the end of the day. He gets an average of 350 dollars. What is the parameter and sample? Are his suspicions correct?
-Parameter: Average amount of money made per table
Sample: 30 of the 50 tables
-Yes, his suspicions are correct since his sample was random and large enough.
300
In the year 2000, a student invested all his money in creating a company and thus was left with no money that year. In 2018, his company has now made 1.2 million dollars in that year alone. Write the year and amount of money he made as an ordered pair for both years, where year is the x-coordinate and money in millions made as the y-coordinate, and find the slope of these two points.
- (2000,0),(2018,1.2)
- 0.07 Million dollars made per year.
300
A large(32oz) gatorade has 45.7 grams of sugar. If a Medium gatorade is 22oz, how many grams of sugar does it have?
-31.42 grams of sugar in a medium gatorade
300
In 1990 a company made 1.2 million dollars and by 2020 they are expected to make 25 million dollars. Write down these pairs of numbers as coordinates, x in years and y in dollars per million, and find the slope.
-(1990,1.2),(2020,25)
-0.79 millions of dollars per year
300
Define parameter and its differences between sample statistic
A number describing some feature of a population. The difference between this and a sample statistic is that the parameter is unknown while the statistic is known and is used to guess what the parameter could be.
400
A man reads a study done on a local coffee place and finds out that the large coffee he always orders on average is about 23.7oz. He decides to check this is true and decides to buy 1 large coffee at the place. He takes it home and measures it and finds out that his was about 22.9oz. He then concludes that the study was done incorrectly. Is his logic correct?
-No his logic is not correct since his "sample" is one coffee. If he were to buy multiple coffees he would get an average that is close to the reported average.
400
What income is the lowest compared to the others? Highest? About how many times more is the lowest to the highest?
-less the 5000
-50,000 to 74.999
-6.36 times more
400
The average number of pizza slices Mitch eats is normally distributed. The mean amount of slices he eats is 8 with a standard deviation of 1. What is the z-score of 5?
-The z-score of 5 is -3
400
What is the difference between median and mean? How do you find each one?
-Median is the value int he middle of the data set while the mean is the average value in a data set
-Median can be found using the formula (n+1)/2 where n is the number of data points and the mean is found by adding all the data points and dividing by the number of data points
400
What is the difference between expected profit and expected winning?
-Expected profit is how much money you make in the long run
-Expected winning is how much you get back without factoring in how much you pay, if any
500
When possible, can the population of interest be taken as the sample? Ex. If the population of interest is 1 class of students can I take the entire class to be the sample?
-yes
500
80 degrees Fahrenheit is a rather hot temperature int he summer in California. Given the formula C=(5/9)(f-32) what is that degree in Celsius?
-26.67 degrees Celsius
500
A mad scientist wants to see if dumping 10 gallons of Red Bull on a Human in the US really makes them grow rings. He kidnaps 100 people randomly all over the US. He then takes them to his lair where he conducts his "study" and dumps Red Bull. He is disappointed when his study shows that no one grew wings. What is the population of interest, sample, parameter, and sample statistic in his "study"?
-Population: Humans in the US
-Sample: 100 randomly kidnapped people
-Parameter: Average number of people who grow wings when Red Bull is dumped on them
-Sample Statistic: 0 people on average grew wings when Red Bull was dumped on them
500
An amusement park charges $80 per 1 person and $300 per 5 people. If the slope of these two pairs of numbers is 55 interpret the slope in this context.
-The cost of admission changes by $55 per person.
500
How much of the data does the Interquartile range represent?
-50% of all the data or half.