The Hemoglobin A1c (HbA1c) level is a continuous variable that measures the amount of blood glucose attached to hemoglobin. Normal levels range from 4-5.6. The (HbA1c) level is used to diagnose Type 2 Diabetes.
A research team is investigating whether the current HbA1c levels in men living in San Diego has changed from 2000. The population mean HbA1c in 2000 was μ2000 = 5.0. A random sample of men (N=81) measured in 2021 had sample mean 𝒙̅= 5.2 and sample standard deviation s= 0.75.
Use the One Sample t Test (α=0.05 and 0.001) to determine if there is a significant change in this population.
(a) State the null and alternative hypothesis in terms of means
H0 :
HA :
(b) Calculate the tstat for the One Sample t Test.
(c) Answer the following question in the space provided. Use the provide tables.
1)Degrees of Freedom (d.f.)
2)t value α =.05
3)t value α = .001
4)Standard Error of the Mean
5)P value for tstat (give the most precise value or range based on the provided table)
(d) State the results of your One Sample T Test and justify your answer using the values you found in parts (b) and (c).
α-level
Result/Conclusion of Analysis
α =.05
α = .001
e. Find the 95% C.I. for the 2021 population mean (μ2021) from the 2021 sample data. (10 pts)
f. Based on the 95% C.I. explain how you would decide to reject or not reject the null hypothesis. (10 pts)
g. Would the 90% C.I. be wider or narrower than the 95% C.I.? Circle the correct answer. (2pts)
WIDER /NARROWER