1) NHI-reported mean total cholesterol level in 2020 for all adults is 203 and the standard deviation
is 28.7. Suppose a new drug is proposed to lower total cholesterol. A study is designed to
evaluate the drug's efficacy in lowering cholesterol. Fifteen patients were enrolled in the study
and asked to take the new drug for 6 weeks. At the end of 6 weeks, each patient's total
cholesterol level is measured and the sample statistics are as follows: n =15 and x̄ =195.9. Is
there statistical evidence of a reduction in mean total cholesterol in patients after using the new
drug for 6 weeks? Use α = 0.05. (10 marks)
tsat = t=(s/√n)xˉ−μ0
t=195.9−203/(28.7/√15)
=-0.9581
Degree of freedom = n-1 = 15-1=14
Critical value for T= 1.76
ANS – tsat is less than critical value for t
NO evidence of the reduction in mean total cholesterol in patients after using the new drug
under a level of significance of 0.05
In a cover story, Amandala published information about sleep habits of Belizeans. The article
noted that sleep deprivation causes a number of problems, including highway deaths. Fifty-one
percent of adult drivers admit to driving while drowsy. A researcher hypothesized that this issue
was an even bigger problem for night shift workers. A sample of 400 night shift workers
identified 240 who admitted to driving while drowsy. Test the researcher’s claim at 0.01 level of
significance.
P = 0.51
n-400
x-240
p = number of night shift workers admitting to driving while drowsy / Total number of night shift
workers
= 240/400= 0.6
Standard error
Standard Error= square root p(1-p)/n = square root 0.51(1-0.51)/400 = 0.0498
Test statistic – z = 0.6-0.51/0.0498 = 1.8036
1.8036 lesss than 2.33
Reject the null hypothesis not evidence to support the reserecher