Florida State College What Is the Conclusion of Your Hypothesis Test Questions

3.4 Post-Class Biostats Problems
Please solve the following practice problems using one sample hypothesis test.
1. To investigate the prevalence rate of Hypertension of a certain population, we drew a
random sample of 75 people from that population and among them 10 people had
hypertension. For the following hypotheses, what would be your conclusion based on the
information provided and why? X=10, n=75, p-hat=x/n=10/75
H0: P = 0.2 (Null)
H1: P < 0.2 (Alternative) a. What is the appropriate test statistic? 𝑋̅ −𝜇 i. 𝑧 = 𝑠/ 𝑛 √ ii. 𝑧 = 𝑋̅1 −𝑋̅2 1 1 + 𝑛1 𝑛2 𝑆𝑝 √ iii. 𝑧 = iv. 𝑧 = 𝑝̂−𝑝0 𝑝 (1−𝑝0 ) √ 0 𝑛 𝑝̂1 −𝑝̂2 𝑥 +𝑥 , where 𝑝̂ = 𝑛1 +𝑛2 ̂ (1−𝑝 ̂) 𝑝 √ 𝑛1 +𝑛2 1 2 b. What is the decision rule value if the level of significance is .05—Reject H0 if z ≤ ______ c. What is the value of your test statistic (z)? (round to 2 decimal places) d. What is the conclusion of your hypothesis test? 2. Eighty undergraduate students were randomly selected from a university and their systolic blood pressure was tested. The sample mean and standard deviation were 117.3 mmHg and 13.8 mmHg respectively. Supposing that you are asked to test hypotheses: H0: µ = 120 H1: µ < 120 a. What is the appropriate test statistic? 𝑋̅ −𝜇 i. 𝑧 = 𝑠/ 𝑛 √ ii. 𝑧 = 𝑋̅1 −𝑋̅2 1 1 + 𝑛1 𝑛2 𝑆𝑝 √ iii. 𝑧 = iv. 𝑧 = 𝑝̂−𝑝0 𝑝 (1−𝑝0 ) 𝑛 √ 0 𝑝̂1 −𝑝̂2 𝑥 +𝑥 , where 𝑝̂ = 𝑛1 +𝑛2 ̂ (1−𝑝 ̂) 𝑝 √ 𝑛1 +𝑛2 1 2 b. What is the decision rule value if the level of significance is .05—Reject H0 if z ≤ ______ c. What is the value of your test statistic (z)? (round to 2 decimal places) d. What is the conclusion of your hypothesis test? 3. The mean lifetime for cardiac stents is 8.7 years. A medical device company has implemented some improvements in the manufacturing process and hypothesizes that the lifetime is now longer. A study of 100 new devices reveals a mean lifetime of 9.3 years with a standard deviation of 3.8 years. Is there statistical evidence of a prolonged lifetime of the stents? a. What is the appropriate test statistic? 𝑋̅ −𝜇 i. 𝑧 = 𝑠/ 𝑛 √ ii. 𝑧 = 𝑋̅1 −𝑋̅2 1 1 + 𝑛1 𝑛2 𝑆𝑝 √ iii. 𝑧 = iv. 𝑧 = 𝑝̂−𝑝0 𝑝 (1−𝑝0 ) √ 0 𝑛 𝑝̂1 −𝑝̂2 𝑥 +𝑥 , where 𝑝̂ = 𝑛1 +𝑛2 ̂ (1−𝑝 ̂) 𝑝 √ 𝑛1 +𝑛2 1 2 b. What is the decision rule value if the level of significance is .05—Reject H0 if z ≥ ______ c. What is the value of your test statistic (z)? (round to 2 decimal places) d. What is the conclusion of your hypothesis test?