Math Test 3

Which of the following lottery combinations (6 numbers from 1-30, no repeats allowed) is the least likely to come up as a winning ticket?

ALL ARE UNLIKELY 1, 2, 3, 4, 5, 6 11, 19, 14, 12, 17, 15 2, 10, 23, 27, 30, 11

A (BLANK) test is a statistical procedure that is used to determine whether or not there is a relationship between two categorical variables.

Chi-Square

The (BLANK) represents the average value of any measurement over the long run.

Expected Value

Another name for the alternative hypothesis is the (BLANK) hypothesis.

Research

Suppose the outcomes of births within a given family are independent of each other, and a couple has already had four boys. Which of the following best describes the probability that their next baby will be a girl?

approximately 50%

Using the criterion of 0.05, which of the following results allows a researcher to conclude that a relationship between two categorical variables is statistically significant?

p-value = 0.04

Suppose you find a statistically significant relationship between two categorical variables (with no other supporting evidence available). When can such results correctly lead you conclude a cause and effect relationship?

only when the data were from a randomized experiment

Which of the following beliefs are examples of the gambler's fallacy?

- Random events are self-correcting. (For example if you are losing, believing that your luck is about to turn around.) - The long-run frequency of an event should apply in the short term as well. (For example, "He's a 90% free-throw shooter, and he's already missed 2 out of 3 tonight. There's no way he's going to miss this next one.") - Knowledge of one event will help predict the next event even though the events are independent. (For example, you may hear someone at the craps table saying to the person rolling the dice, "You're on a roll! Don't stop now!")

Simpson's Paradox

- Simpson's paradox is a phenomenon in probability and statistics, in which a trend appears in several different groups of data but disappears or reverses when these groups are combined. - Relationship appears to be in one direction if third variable is not considered and in other direction if it is. - Can be dangerous to summarize information over groups.

Which of the following problems can arise when intuition differs from relative frequency?

- confusion of the inverse - always thinking that a coincidence has a low chance of occurring - the gambler's fallacy

Which of the following is a true probability?

1

Suppose you know that for each ticket the probability of winning a certain "instant win" lottery game is 1/100 You have purchased 99 tickets so far with no luck. What is your chance that the next ticket you buy is a winner?

1/100

A study done by the Ohio State University Medical Center examined whether or not taking an aspirin a day would help colon cancer patients reduce the chance of getting subsequent colon polyps. 635 patients with colon cancer participated; 317 of them were randomly assigned to the aspirin group, and the other 318 patients were assigned to a placebo (non-aspirin) group. 54 patients in the aspirin group developed subsequent polyps, compared to 86 patients in the non-aspirin group. Many confounding variables were controlled for in this well-designed randomized experiment. What percentage of all the patients in this study developed subsequent polyps?

140/635 = 22%

When there is a treatment or behavior for which researchers want to study risk, they often compare it to the (BLANK) risk, which is the risk without the treatment or behavior.

Baseline

If two events are mutually exclusive, they (BLANK) be independent.

Cannot

The probability of a coincidence happening may be (BLANK) you think.

Larger

The question researchers are really asking when they are looking for a relationship between two variables is whether or not that relationship is present in the...

Population

Using the relative frequency approach, we can define the probability of any specific outcome as the (BLANK) of times it occurs over the long run.

Proportion

The (BLANK) of a test for a certain disease is the proportion of people who correctly test positive when they actually have the disease.

Sensitivity

Suppose a talent contest is looking for people who can either sing or act. 900 people tried out for the first round of auditions, 300 women and 600 men. Of the men who tried out, 55% of them were allowed to go on to the next round, compared to 42% of the women. However, if you break the data down by singing versus acting auditions, the relationship changes. For acting, 20% of the women made it through compared to 15% of the men; for singing, 85% of the women made it through compared to 75% of the men. What is the statistical phenomena that occurred in this situation?

Simpson's Paradox

An interesting relationship in the population may fail to achieve (BLANK) significance if there are too (BALNK) observations.

Statistical, Few

Suppose you encounter one traffic light on your commute to work each day. You have determined that the probability that this light will be red is 1/3 Which of the following is not a correct interpretation of this probability?

The light will always be red one out of every three times that you encounter it.

Suppose there is not enough evidence to conclude that the relationship in the population is real. Which of the following is not an equivalent way of saying this?

We accept the null hypothesis

What is meant by a test result that is a false positive?

You don't have the disease, but the test results were positive

Suppose you hear a report that says the chances of developing lung cancer increase by 10 times just by living in the city versus the country. How do you interpret this?

You need to find out what the baseline risk is and what confounding variables were adjusted for before you can determine how serious this is for you.

Each row and column combination in a contingency table is called

a cell

A table that displays the number of individuals who fall into each combination of categorical variables is called (BLANK) table.

a contingency

One of the common ways the media misrepresent statistics about risk is that the reported risk is not necessarily your risk. What is the underlying problem that causes this?

confounding variables, which may differ for you and those in the study

Which of the following is an example of using the personal probability interpretation of probability?

deciding that your football team has a high chance of winning their next game

Which of the following describes an example of an expected value in a lottery situation?

the average amount of money you'll win/lose in the long run when playing the lottery

Which of the following describes the 'specificity' of a test for a certain disease?

the proportion of people who correctly test negative when they don't have the disease