Concepts 1
Concepts 2
Concepts 3
Ind v Dep 1
Ind v Dep 2
100
When would you mention P-value, hypotheses, rejecting or not rejecting regarding confidence interval estimation?
NEVAAAAAH!! P-value, hypotheses, rejecting or not rejecting are NOT RELEVANT in confidence interval estimation. They are ONLY RELEVANT in hypothesis testing
100
True or False: A confidence interval will always contain a lower and upper limit
TRUE: A confidence interval is a range of values, never just one value!! It is always a two-tailed inference centered at the point estimate.
100
What does mu represent? P?
mu represents the population mean. P represents the population proportion.
100
A zoologist wants to know if animals in captivity weigh more, on average, than animals in the wild. He goes to Stone Zoo and records the weights of several animals. He then goes on a trek in the wild to tranquilize and weigh the same types of animals that he weighed in the zoo.
DEPENDENT SAMPLING. He can match the weight of the zoo animal to the weight of that same type of animal in the wild. (Snake to snake, bear to bear etc)
100
I want to participate on a game show and win the most amount of money possible. To decide which game show I should enter, I sample 15 past contestants on The Price is Right and record their winnings. I also sample 15 past contestants on Family Feud and record their winnings.
INDEPENDENT SAMPLING. The sample sizes are different. Also there is no link from one specific amount of winning on Family Feud to another specific amount of winnings on The Price is Right.
200
What is a point estimate? What is it for one population mean, one population proportion, two population means, two population proportions?
A point estimate is the closest one value estimate of the parameter of interest. One population mean: x-bar. One population proportion: p-hat. two population means: x-bar1-x-bar2. Two population proportions: p-hat1-p-hat2.
200
What assumptions does your inference need to be under when you are dealing with one population?
1. Random sample of ___(IN CONTEXT!!!)___ 2. Probability distribution of number of __(in context)__ is approximately normal. NEVER include the words in assumptions: true, population, actual, average, or mean.
200
True or false: When making a conclusion from a statistical inference you must include that this evidence that you found or did not find, may not or may exist, respectively.
FALSE: You are performing an error analysis when you caution that the opposite of your conclusion may be true. This does not have a place in the conclusion of your inference. Only mention it if you are asked about possible error.
200
A local night club owner wants to know if men buy more drinks, on average, than women. He samples 21 men named: Jamie, Jesse, Pat, Sam, Bri, Alex, Taylor, Blair, Cameron, Casey, Corey, Devon, Dylan, Hayden, Lee, Morgan, Payton, Reese, Sydney, Jan, Jordan, and 21 women who also happen to be named: Jamie, Jesse, Pat, Sam, Bri, Alex, Taylor, Blair, Cameron, Casey, Corey, Devon, Dylan, Hayden, Lee, Morgan, Payton, Reese, Sydney, Jan, Jordan. The owner records the number of drinks each group buys.
INDEPENDENT SAMPLING. Despite the fact that the two groups happen to have the same names, they are not linked in any other way. These are two independent samples of men and women.
200
A nutritionist wants to compare the prices of Stop and Shop to the prices of Big Y grocery stores. She buys one apple, one gallon of milk, one red bell pepper, one bag of rice, one carton of orange juice, one chocolate cake, one package of sugar cookies, and a bottle of ranch salad dressing from each store. She records the prices of all items bought.
DEPENDENT SAMPLING. Each specific item's price from Stop and Shop can be paired with the matching item's price from Big Y.
300
What is the margin of error?
The part of the CI equation that comes after the +or- sign.
300
Define P-value.
The smallest probability of a type one error at which you can still reject the null hypothesis.
300
What is the difference between an interpretation and conclusion to a confidence interval
An interpretation is an abstract concept regarding any confidence interval which never involves your sample data. It only deals with level of confidence and the parameter of interest. A conclusion is a concrete answer to the question of interest using your sample confidence interval. You will decide whether there is or isn't sufficient evidence to answer your question.
300
A chef wants to buy chocolate in bulk and can only choose one variety. She can get an equally good deal on dark chocolate and white chocolate. She gives 20 customers at her restaurant a one piece of dark chocolate and she gives another 20 customers one piece of white chocolate. She asks each customer to rate their piece of chocolate on a scale from 0 to 10 with 10 being the best. She records the rankings.
INDEPENDENT SAMPLING. There is no reason to match any customer's ranking of dark chocolate to another customer's ranking of white chocolate.
300
A UMASS student wants to test the delivery speed of two local pizza parlors. From his dorm room he places 10 separate orders for delivery from Dominoes and 10 separate orders for delivery from Antonio’s. All pizzas are delivered to his dormitory. He records the time from order placement to delivery.
INDEPENDENT SAMPLING. There is no basis to link one specific delivery time of Dominoes pizza to one other specific delivery time of Antonio’s pizza.
400
In a criminal trial, an innocent person being convicted would be which type of error?
Type I error. In this case the null hypothesis is that the defendant is innocent (innocent until proven guilty). This would be the equivalent to rejecting a true null hypothesis.
400
True or false: You would always reject the null hypothesis at the .05 level of significance if you rejected it at the .075 level of significance.
FALSE: If P-value falls in between .05 and .075 then we would reject at .075 but not at .05 (If P-value = .06).
400
True or False: One can reduce the width of a confidence interval by taking a smaller sample
FALSE: By reducing 'n', you decrease the denominator in the margin of error, thereby increasing the width of the confidence interval
400
A college student wants to know which fruit has the most Vitamin C, on average. She buys a sample of 10 apples and 10 oranges from Big Y and tests and records the Vitamin C content.
INDEPENDENT SAMPLING. The samples of fruits are from the same grocery store, but there is no basis to match one apple's Vitamin C content to one orange's Vitamin C content.
400
Ten UMASS students want to test the delivery speed of two local pizza parlors. All students involved live all across campus and they each place 1 order for delivery from Dominoes and 1 order for delivery from Antonio’s to their own residences. Each student records the time from order placement to delivery.
DEPENDENT SAMPLING. You can clearly match the delivery time of Dominoes pizza to one location (one student’s residence) to the delivery time of Antonio’s pizza to that same location.
500
What are the 3 components of the Central Limit Theorem?
1. The mean of all sample means = population mean 2. The standard deviation of all sample means = the population standard deviation/ sqare root of n 3. If sample size is sufficiently large (>30) then the probability distribution is approximately normal
500
True or false: You would always expect to draw the same conclusions from a hypothesis test and a confidence interval when your level of significance is the same.
FALSE. Your CI is always a two tailed inference, but a HT could be two or one tailed. You would expect to draw the same conclusion from a CI and HT with the same significance level if the HT is a two-tailed test. Your conclusions from a CI and one-tailed HT with the same significance level could be the same or different
500
If your hypotheses are: Ho: P = .1 Ha: P not= .1 and your test statistic is 1.96, then what is your P-value?
.05. The area associated with the test statistic 1.96 is .025. HOWEVER this is a two tailed inference so you need to double the P-value. YOU DO NOT HALF THE SIGNIFICANCE LEVEL.
500
Mona wants to know who is smarter: Robin or Mikey. They took the same 5 classes last semester and compare the final grades.
DEPENDENT SAMPLING. We can match the final grade from one class that Robin took to the final grade from the same class that Mikey took. PS., then ran the test and found sufficent evidence to prove that Mike is smarter. Then they found enough evidence to suggest Robin is smarter because she knows how to spell "sufficient" and that we are never proving anything in statistical inference. We are only finding evidence to suggest certain outcomes. But in all seriousness... Igor is the smartest. No testing needed.
500
A restaurant owner wants to know if playing soft music will increase sales over playing no music. For 15 weeks in the summer she plays soft music on Tuesdays, and no music on Wednesdays in her restaurant. She records the sales for all days sampled.
INDEPENDENT SAMPLING. Although sampling for both music and no music takes place at the same restaurant, there is no basis to match one specific daily sales with music to one specific daily sales without music
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