3. Home Covid-19 tests have the advantage of being fast and cheap, but they are not always perfect.Sometimes people who have Covid will test negative, and people who do not have Covid will testpositive. In January of 2021, the CDC posted a paper entitled “Evaluation of Abbott BinaxNOWrapid antigen test for SARS-CoV-2 infection at two community-based testing sites-Pima County,Arizona, November 3-17, 2020" in which the authors tested participants using BinaxNOW home tests,and then again using PCR, which returns a much more accurate result. For the purposes of thishomework, we will consider the PCR result the ground truth (i.e. if a PCR result is negative, we canassume the person does not have a Covid-19 infection). Below is the data from their study:Positive BinaxNOW home testNegative BinaxNOW home testTotalPositive PCR(has Covid-19)157142299Negative PCR(does not have Covid-19)43,1163,120NOWThe following questions are about the performance of thepopulation of individuals at community-based testing sites in Pima County:a) What is the false positive rate of the home test?b) What is the positive predictive value of the home test?c) What is the false negative rate of the home test?d) What is the negative predictive value of the home test?testTotal1613,2583,419this particulare) Suppose you take a BinaxNOW home test, and it comes back negative. Which of the four valuesabove is the most relevant for your situation, and why?

Answered: a) What is the false positive rate of…

a) What is the false positive rate of the home test? b) What is the positive predictive value of the home test? c) What is the false negative rate of the home test?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 31E

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19. A local brewery produces three premium lagers named Half Pint, XXX, and Dark Knight. Of its premium lagers, the brewery bottles 40% Half Pint, 40% XXX, and 20% Dark Knight. In a marketing test of a sample of 80 consumers, 26 preferred the Half Pint lager, 42 preferred the XXX lager, and 12 preferred the Dark Night lager. Using a chi-square goodness-of-fit test, test whether the production of the premium lagers matches these consumer preferences using a .05 level of significance. 19a. Step 2: Compute the df and locate the critical values. df = _______ Critical value = ________
19. A local brewery produces three premium lagers named Half Pint, XXX, and Dark Knight. Of its premium lagers, the brewery bottles 40% Half Pint, 40% XXX, and 20% Dark Knight. In a marketing test of a sample of 80 consumers, 26 preferred the Half Pint lager, 42 preferred the XXX lager, and 12 preferred the Dark Night lager. Using a chi-square goodness-of-fit test, test whether the production of the premium lagers matches these consumer preferences using a .05 level of significance. 19. Step 1: Which of the following is the correct set of hypotheses?A. H0: The preferences will not match production (40% Half Pint, 40% XXX, 20% Dark Knight); and H1: The preferences will match production B. H0: \mu_{1}μ1 = \mu_{2}μ2 = \mu_{3}μ3; and H1: At least one of the categories will be different than the others C. H0: The preferences will match production (40% Half Pint, 40% XXX, 20% Dark Knight); and H1: The preferences will not match production 19b. Step 2: Compute the df and locate the…
19. A local brewery produces three premium lagers named Half Pint, XXX, and Dark Knight. Of its premium lagers, the brewery bottles 40% Half Pint, 40% XXX, and 20% Dark Knight. In a marketing test of a sample of 80 consumers, 26 preferred the Half Pint lager, 42 preferred the XXX lager, and 12 preferred the Dark Night lager. Using a chi-square goodness-of-fit test, test whether the production of the premium lagers matches these consumer preferences using a .05 level of significance. 19. Step 3: Compute the test statistic -- Chi-square χ2 = (use 2 decimal places) _____________ Step 4: Decision and Conclusions 19. Step 4: Decision: A. Reject H0 B. Retain H0 19. Step 5: Conclusion: Did the production of the premium lagers match consumer preferences? A. Yes. The observed frequencies did not differ from the expected frequencies. B. No. The observed frequencies differed from the expected frequencies.
19. A local brewery produces three premium lagers named Half Pint, XXX, and Dark Knight. Of its premium lagers, the brewery bottles 40% Half Pint, 40% XXX, and 20% Dark Knight. In a marketing test of a sample of 80 consumers, 26 preferred the Half Pint lager, 42 preferred the XXX lager, and 12 preferred the Dark Night lager. Using a chi-square goodness-of-fit test, test whether the production of the premium lagers matches these consumer preferences using a .05 level of significance.
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A researcher was interested in studying if there is a significant relationship between the severity of COVID 19 and blood types of individuals. 2400 individuals were studied and the results are shown below. blood types condition O A B AB Total critical 64 44 20 8 136 severe 175 129 50 15 369 moderate 211 528 151 125 1015 mild 200 400 140 140 880 total 650 1101 361 288 2400 a. State both the null and alternative hypotheses. b. Provide the decision rule for making this decision. Use an alpha level of 5%. c. Show all of the work necessary to calculate the appropriate statistic. d. What conclusion are you allowed to draw? e. Would your conclusion change at the 10% level of significance? [2 marks]
A researcher was interested in studying if there is a significant relationship between the severity of COVID 19 and blood types of individuals. 2400 individuals were studied and the results are shown below. Condition Blood Type O A B AB Total Critical 64 44 20 8 136 Severe 175 129 50 15 369 Moderate 211 528 151 125 1015 Mild 200 400 140 140 880 Total 650 1101 361 288 2400 a. State both the null and alternative hypotheses. b. Provide the decision rule for making this decision. Use an alpha level of 5%. c. Show all of the work necessary to calculate the appropriate statistic. d. What conclusion are you allowed to draw? e. Would your conclusion change at the 10% level of significance?
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