# 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?
πΜ
βπ
i. π§ = π / π
β
ii. π§ =
πΜ
1 βπΜ
2
1
1
+
π1 π2
ππ β
iii. π§ =
iv. π§ =
πΜβπ0
π (1βπ0 )
β 0
π
πΜ1 βπΜ2
π₯ +π₯
, where πΜ = π1 +π2
Μ (1βπ
Μ)
π
β
π1 +π2
1
2
b. What is the decision rule value if the level of significance is .05βReject H0 if z β€
______
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: Β΅ = 120
H1: Β΅ < 120
a. What is the appropriate test statistic?
πΜ
βπ
i. π§ = π / π
β
ii. π§ =
πΜ
1 βπΜ
2
1
1
+
π1 π2
ππ β
iii. π§ =
iv. π§ =
πΜβπ0
π (1βπ0 )
π
β 0
πΜ1 βπΜ2
π₯ +π₯
, where πΜ = π1 +π2
Μ (1βπ
Μ)
π
β
π1 +π2
1
2
b. What is the decision rule value if the level of significance is .05βReject H0 if z β€
______
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?
πΜ
βπ
i. π§ = π / π
β
ii. π§ =
πΜ
1 βπΜ
2
1
1
+
π1 π2
ππ β
iii. π§ =
iv. π§ =
πΜβπ0
π (1βπ0 )
β 0
π
πΜ1 βπΜ2
π₯ +π₯
, where πΜ = π1 +π2
Μ (1βπ
Μ)
π
β
π1 +π2
1
2
b. What is the decision rule value if the level of significance is .05βReject H0 if z β₯
______
c. What is the value of your test statistic (z)? (round to 2 decimal places)
d. What is the conclusion of your hypothesis test?

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