2. The Hemoglobin A1c (HbA1c) level is a continuous variable that measures the amount of blood glucose attached to hemog

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2. The Hemoglobin A1c (HbA1c) level is a continuous variable
that measures the amount of
blood glucose attached to hemoglobin. The (HbA1c) level is used to
diagnose Type 2 Diabetes.
Normal levels range from 4-5.6.
(a) Suppose we HbA1c in a healthy population is normally
distributed with population mean =
4.8 and population standard deviation = 0.5 . What proportion of
the population has HbA1c
levels between 4.3 and 5.3 ?


(b) If repeated random samples of N=100 were selected from this
population, what
proportion of these samples would have means between 4.3 and
5.3?


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. Population
standard deviation is not knowns. 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.
(c) State the null and alternative hypothesis in terms of means
(d) Calculate the tstat for the One Sample t Test.
(e)Answer the following question in the space provided. Use the
provide tables. (6 pts)
Degrees of Freedom (d.f.)
(f) State the results of your One Sample t Test and justify your
answer using the values you
found in parts c-f.
(g) Find the 95% C.I. for the 2021 population mean (μ2021) from
the 2021 sample data.



(h) Based on the 95% C.I. explain how you would decide to reject or
not reject the null
hypothesis.


(i) Is the 90% C.I. be wider or narrower than the 95% C.I.? Circle
the correct answer.
WIDER NARROWER