a) Draw a tree diagram representing this situation. b) What proportion of tests given to asymptomatic people will be true positives? c) What proportion of tests given to asymptomatic people will be true negatives?
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The BinaxNOW COVID-19 antigen test is sold as an in-home test. Pollack et al. (2021) estimate that among
asymptomatic adults, the test has a 70.2% sensitivity and 99.6% specificity. Assume for this question that 8% of people
who use this test actually have the disease.
a) Draw a tree diagram representing this situation.
b) What proportion of tests given to asymptomatic people will be true positives?
c) What proportion of tests given to asymptomatic people will be true negatives?
d) What is the probability that an asymptomatic person who tests positive truly does have COVID-19?
“Fun” fact: this probability is called the positive predictive value.
e) What is the probability that an asymptomatic person who tests negative truly does not have COVID-19? This
quantity is called the negative predictive value.
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- Since an instant replay system for tennis was introduced at a major tournament, men challenged 1435 referee calls, with the result that 413 of the calls were overturned. Women challenged 748referee calls, and 222 of the calls were overturned. Use a 0.01 significance level to test the claim that men and women have equal success in challenging calls. Complete parts (a) through (c) below.A cigarette-manufacturing firm distributes two brands of cigarettes. If it is found that 56 of 200 smokers prefer brand A and 29 of 150 smokers prefer brand B, can we conclude at the .05 level of significance that brand A outsells brand B?Mars, Inc. claims that 20% of its M & M plain candies out of a sample of 100 are blue. Does your data (your individual package) agree, why or why not?
- According to the February 2008 Federal Trade Commission report on consumerfraud and identity theft, 23% of all complaints in 2007 were for identity theft. Inthat year, Arkansas had 1,601 complaints of identity theft out of 3,482 consumercomplaints ("Consumer fraud and," 2008). Does this data provide enoughevidence to show that Arkansas had a higher proportion of identity theft than23%? Test at the 5% level.A sociologist wants to investigate the question, "Is there a relationship between texting during class and grade-point-average (GPA) among high school seniors in a large district?" Which study design is most appropriate? Before the semester starts, randomly select 40 seniors from each high school who do not text during class. Assign 20 to the texting treatment group (text three or more times during every class meeting) and 20 to the control group (no texting during class). At the end of the semester, obtain each student’s GPA from the appropriate admissions and records office. Compare the GPA of students who routinely text during class to the GPA of students who do not text during class. Before the semester starts, randomly select 40 seniors from each high school who do not text during class. Assign 20 to the texting treatment group (text three or more times during every class meeting) and 20 to the control group (no texting during class). At the end of the semester,…Since an instant replay system for tennis was introduced at a major tournament, men challenged 1386 referee calls, with the result that 421 of the calls were overturned. Women challenged 745 referee calls, and 222 of the calls were overturned Use a 0.05 significance level to test the claim that men and women have equal success in challenging calls, Complete parts (a) through (e) below.
- Based on a survey of 12,344 U.S. college students and 6,729 Canadian college students, Kuo, Adlaf, Lee, Gliksman, Demers, and Wechsler (2002) report that alcohol use is more common among Canadian than U.S. students, but heavy drinking (five or more drinks in a row for males, four or more for females) is significantly higher among U.S. students than Canadian students. Is this an example of a survey research design?Suppose you are asked to sample 100 students at the University to get their opinions about a requirement that all students get Covid-19 vaccine before resuming inperson classes in the Fall 2021.a) Describe how you could go about getting a stratified sample. b) Describe how you could go about getting a voluntary response samplea random sample of 60 and in terms of age groups was stratified as follows: 35 are youth (below 35yrs) ,15 are medium aged adults between 35-65yrs and 10 are elderly (above 65yrs).Your research outcome is to determine their attitude regarding compulsory putting on of masks wherever in public during lifting up of COVID -19 Lockdown. You carry out a survey to determine the above outcome and come up with the following observations. Those with positive attitude are 34 detailed as follows: Youth 20, medium adults 9 and elderly 5. Those with negative attitude were stratified as follows:15 youth,6 medium adults and 5 elderly. (i) Sketch a 3 by 2 contingency summary of this data (ii) State the hypothesis of this data, giving your α-level and degree of freedom Critical t-value from the chi-square distribution is 5.991
- a random sample of 60 and in terms of age groups was stratified as follows: 35 are youth (below 35yrs) ,15 are medium aged adults between 35-65yrs and 10 are elderly (above 65yrs).Your research outcome is to determine their attitude regarding compulsory putting on of masks wherever in public during lifting up of COVID -19 Lockdown. You carry out a survey to determine the above outcome and come up with the following observations. Those with positive attitude are 34 detailed as follows: Youth 20, medium adults 9 and elderly 5. Those with negative attitude were stratified as follows:15 youth,6 medium adults and 5 elderly. (i) Sketch a 3 by 2 contingency summary of this data (ii) State the hypothesis of this data, giving your α-level and degree of freedomThe accompanying data came from a study of collusion in bidding within the construction industry (“Detection of Collusive Behavior." J. of Construction Engr. and Mgmnt. 2012:1251- 1258)a. What proportion of the contracts involved at most five bidders? At least five bidders? b. What proportion of the contracts involved between five and 10 bidders, inclusive? Strictly between five and 10 bidders? c. Construct a histogram and comment on interesting features.A study of the characteristics of subcarriers—telecommunication signals carried on top of one another—for underwater acoustic communications was conducted. A sub-carrier can be classified as either a data subcarrier (used for data transmissions), a pilot subcarrier (used for channel estimation and synchronization), or a null subcarrier (used for direct current and guard banks transmitting no signal). In a sample of 1,024 subcarrier signals transmitted off the coast of Martha’s Vineyard, 672 were determined to be data subcarriers, 256 pilot subcarriers, and 96 null subcarriers. Suppose a communications engineer who works near Martha’s Vineyard believes that fewer than 70% of all subcarrier signals transmitted in the area are data subcarriers. Is there evidence to support this belief? Test using a significance level of .05. Write all steps.