This course is designed to acquaint the student with the principles of descriptive and inferential statistics. Topics will include: types of data, frequency distributions and histograms, measures of central tendency, measures of variation, probability, probability distributions including binomial, normal probability and student's t distributions, standard scores, confidence intervals, hypothesis testing, correlation, and linear regression analysis. This course is open to any student interested in general statistics and it will include applications pertaining to students majoring in athletic training, pre-nursing and business.
Ten of the 100 digital video recorders (DVRs) in an inventory are known to be defective.
What is the probability you randomly select an item that is not defective?
Assume that 1100 births are randomly selected and exactly 276 of the births are girls.
Use subjective judgment to determine whether the given outcome is unlikely.
Determine whether it is unusual in the sense that the result is far from what is typically expected.
It is unlikely because there are many other possible outcomes that have similar or higher probabilities.
An event is unlikely if its probability is very small, such as 0.05 or less. Consider the complement of the outcome and how likely it is.
It is unusual because it is not about 550 as expected.
An event has an unusually low number of outcomes of a particular type or an unusually high number of those outcomes if that number is far from what is typically expected. Consider how many girls would typically be expected in a given random selection of births.
For a certain casino slot machine, the odds in favor of a win are given as 29 to 71.
Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
You are certain to get a heart, diamond, club, or spade when selecting cards from a shuffled deck.
Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive
In a test of a gender-selection technique, results consisted of 239 baby girls and 221 baby boys.
Based on this result, what is the probability of a girl born to a couple using this technique?
Does it appear that the technique is effective in increasing the likelihood that a baby will be a girl?
In a survey, 173 respondents say that they never use a credit card, 1221 say that they use it sometimes, and 2838 say that they use it frequently.
What is the probability that a randomly selected person uses a credit card frequently?
Is it unlikely for someone to use a credit card frequently? Consider an event to be unlikely if its probability is less than or equal to 0.05.
How are all of these results affected by the fact that the responses were obtained by those who decided to respond to a survey posted on the Internet?
The probability that a randomly selected person uses a credit card frequently is 0.671.
2838 ÷ (173 + 1221 + 2838)
= 2838/4232 = 0.6706049149
No, because the probability of a randomly selected person using a credit card frequently is greater than 0.05.
Since this is a voluntary response sample, valid conclusions can only be drawn about the specific group of people who chose to participate.
A test for marijuana usage was tried on 150 subjects who did not use marijuana. The test result was wrong 4 times.
a. Based on the available results, find the probability of a wrong test result for a person who does not use marijuana.
b. Is it "unlikely" for the test to be wrong for those not using marijuana? Consider an event to be unlikely if its probability is less than or equal to 0.05.
In a survey of consumers aged 12 and older, respondents were asked how many cell phones were in use by the household. (No two respondents were from the same household.) Among the respondents, 217 answered "none," 288 said "one," 371 said "two," 152 said "three," and 93 responded with four or more. A survey respondent is selected at random.
Find the probability that his/her household has four or more cell phones in use.
Is it unlikely for a household to have four or more cell phones in use? Consider an event to be unlikely if its probability is less than or equal to 0.05.
To the right are the outcomes that are possible when a couple has three children. Refer to that list, and find the probability of each event.
a. Among three children, there are exactly 3 boys.
b. Among three children, there are exactly 0 boys.
c. Among three children, there is exactly 1 girl.
d. Among three children, there is exactly 2 girls.
a. 1/8
Out of the 8 possible outcomes, how many result in exactly 3 boys?
bbb
b. 1/8
Out of the 8 possible outcomes, how many result in exactly 0 boys (3 girls)?
ggg
c. 3/8
Out of the 8 possible outcomes, how many result in exactly 1 girl?
gbb, bgb, bbg
d. 3/8
Out of the 8 possible outcomes, how many result in exactly 2 girls (1 boy)?
ggb, gbg, bgg
If a couple were planning to have three children, the sample space summarizing the gender outcomes would be: bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg.
a. Construct a similar sample space for the possible weight outcomes (using o for overweight and u for underweight) of two children.
b. Assuming that the outcomes listed in part (a) were equally likely, find the probability of getting two overweight children.
c. Find the probability of getting exactly one overweight child and one underweight child.
Each of two parents has the genotype brown divided by red, which consists of the pair of alleles that determine hair color, and each parent contributes one of those alleles to a child. Assume that if the child has at least one brown allele, that color will dominate and the child's hair color will be brown.
a. List the different possible outcomes. Assume that these outcomes are equally likely.
b. What is the probability that a child of these parents will have the red divided by red genotype?
c. What is the probability that the child will have brown hair color?
A modified roulette wheel has 44 slots. One slot is 0, another is 00, and the others are numbered 1 through 42, respectively. You are placing a bet that the outcome is an odd number. (In roulette, 0 and 00 are neither odd nor even.)
a. What is your probability of winning?
b. What are the actual odds against winning?
c. When you bet that the outcome is an odd number, the payoff odds are 1:1. How much profit do you make if you bet $13 and win?
d. How much profit should you make on the $11 bet if you could somehow convince the casino to change its payoff odds so that they are the same as the actual odds against winning?
a. The probability of winning is 21/44.
b. The actual odds against winning are 23:21.
c. If you win, the payoff is $11.
The payoff odds against event A represent the ratio of net profit (if you win) to the amount bet.
payoff odds against A = (net profit):(amount bet) = 1:1
If the payoff odds are a:b and the bet is c, the payoff is (a*c)/b . (1*11)/1
d. $12.05
The actual odds against winning are 23:21
(23*11)/21 = 12.04761905
In a clinical trial of 2019 subjects treated with a certain drug, 24 reported headaches. In a control group of 1579 subjects given a placebo, 20 reported headaches.
Denoting the proportion of headaches in the treatment group by p_{t} and denoting the proportion of headaches in the control (placebo) group by p_{c}, the relative risk is p_{t}/p_{c}. The relative risk is a measure of the strength of the effect of the drug treatment.
Another such measure is the odds ratio, which is the ratio of the odds in favor of a headache for the treatment group to the odds in favor of a headache for the control (placebo) group, found by evaluating (see image) . The relative risk and odds ratios are commonly used in medicine and epidemiological studies.
Find the relative risk and odds ratio for the headache data.
What do the results suggest about the risk of a headache from the drug treatment
Which of the following is NOT a principle of probability?
Decide whether the following two events are disjoint.
1. Randomly selecting an animal with green eyes
2. Randomly selecting an animal with brown eyes
Determine whether the two events are disjoint for a single trial. (Hint: Consider "disjoint" to be equivalent to "separate" or "not overlapping.")
Randomly selecting a statistics student and getting someone who brings a notebook to class.
Randomly selecting a statistics student and getting someone who brings a text book to class.
Determine whether the two events are disjoint for a single trial. (Hint: Consider "disjoint" to be equivalent to "separate" or "not overlapping.")
Randomly selecting someone who plays soccer.
Randomly selecting someone taking a calculus course.
Find the indicated complement.
A certain group of women has a 0.09% rate of red/green color blindness. If a woman is randomly selected, what is the probability that she does not have red/green color blindness?
The following data lists the number of correct and wrong dosage amounts calculated by 32 physicians. In a research experiment, a group of 17 physicians was given bottles of epinephrine labeled with a concentration of "1 milligram in 1 milliliter solution," and another group of 15 physicians was given bottles labeled with a ratio of "1 milliliter of a 1:1000 solution."
If one of the physicians is randomly selected, what is the probability of getting one who calculated the dose correctly?
Is that probability as high as it should be?
The following data lists the number of correct and wrong dosage amounts calculated by 32 physicians. In a research experiment, a group of 16 physicians was given bottles of epinephrine labeled with a concentration of "1 milligram in 1 milliliter solution," and another group of 16 physicians was given bottles labeled with a ratio of "1 milliliter of a 1:1000 solution."
a. For the physicians given the bottles labeled with a concentration, find the percentage of correct dosage calculations, and then express it as a probability.
b. For the physicians given the bottles labeled with a ratio, find the percentage of correct dosage calculations, and then express it as a probability.
c. Does it appear that either group did better? What does the result suggest about drug labels?
a. The probability of a correct dosage calculation given the bottle is labeled with a concentration is 0.750.
P(correct dose calculation with a concentration label)
= 12/16
= 0.75
b. The probability of a correct dosage calculation given the bottle is labeled with a ratio is 0.313.
P(correct dose with a ratio label)
= 5/16
= 0.3125
c. It appears that the group given the labels with concentrations performed better because the probability of a correct dosage calculation for the bottles labeled with a concentration is much greater than the probability of a correct dosage calculation for the bottles labeled with a ratio.This result suggests that labels with concentrations are much better than labels with ratios.
The probability that the subject responded or is between the ages of 22 and 39 is 0.896.
---------------------------------------------------
= (75 + 257 + 247 + 138 + 140 +
204) ÷ (75 + 257 + 247 + 138 + 140 + 204 + 11 + 20 + 33 + 26
+ 35 + 57) = (1061
/ 1243)
= (20 + 33) ÷ 1243 = (53 / 1243)
= 0.8962188254
Use the following results from a test for marijuana use, which is provided by a certain drug testing company. Among 149 subjects with positive test results, there are 29 false positive results. Among 155 negative results, there are 4 false negative results.
a. How many subjects were included in the study?
b. How many subjects did not use marijuana?
c. What is the probability that a randomly selected subject did not use marijuana?
Use the following results from a test for marijuana use, which is provided by a certain drug testing company. Among 148 subjects with positive test results, there are 30 false positive results; among 154 negative results, there are 3 false negative results.
If one of the test subjects is randomly selected, find the probability that the subject tested negative or did not use marijuana. (Hint: Construct a table.)
Use the following results from a test for marijuana use, which is provided by a certain drug testing company. Among 144 subjects with positive test results, there are 25 false positive results; among 151 negative results, there are 3 false negative results.
If one of the test subjects is randomly selected, find the probability of a false positive or false negative. (Hint: Construct a table.)
What does the result suggest about the test's accuracy?
Complete the following statement.
P(A or B) indicates _______.
For the given pair of events A and B, complete parts (a) and (b) below.
A: When a page is randomly selected and ripped from a 23-page document and destroyed, it is page 7.
B: When a different page is randomly selected and ripped from the document, it is page 1.
a. Determine whether events A and B are independent or dependent. (If two events are technically dependent but can be treated as if they are independent according to the 5% guideline, consider them to be independent.)
b. Find P(A and B), the probability that events A and B both occur.
Consider a bag that contains 223 coins of which 6 are rare Indian pennies. For the given pair of events A and B, complete parts (a) and (b) below.
A: When one of the 223 coins is randomly selected, it is one of the 6 Indian pennies.
B: When another one of the 223 coins is randomly selected, it is also one of the 6 Indian pennies.
a. Determine whether events A and B are independent or dependent.
b. Find P(A and B), the probability that events A and B both occur.
With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is accepted if every item in the sample is okay. A company has just manufactured 1087 CDs, and 467 are defective.
If 3 of these CDs are randomly selected for testing, what is the probability that the entire batch will be accepted?
Does this outcome suggest that the entire batch consists of good CDs? Why or why not?
The principle of redundancy is used when system reliability is improved through redundant or backup components. A region's government requires that commercial aircraft used for flying in hazardous conditions must have two independent radios instead of one. Assume that for a typical flight, the probability of a radio failure is 0.0052.
What is the probability that a particular flight will be threatened with the failure of both radios?
Describe how the second independent radio increases safety in this case.
In a market research survey of 2354 motorists, 229 said that they made an obscene gesture in the previous month.
a. If 1 of the surveyed motorists is randomly selected, what is the probability that this motorist did not make an obscene gesture in the previous month?
b. If 50 of the surveyed motorists are randomly selected without replacement, what is the probability that none of them made an obscene gesture in the previous month? Should the 5% guideline be applied in this case? Select the correct choice below and fill in the answer box within your choice.
Refer to the figure below in which surge protectors p and q are used to protect an expensive high-definition television. If there is a surge in the voltage, the surge protector reduces it to a safe level. Assume that each surge protector has a 0.94 probability of working correctly when a voltage surge occurs.
a. If the two surge protectors are arranged in series, what is the probability that a voltage surge will not damage the television?
b. If the two surge protectors are arranged in parallel, what is the probability that a voltage surge will not damage the television?