Analysis of Gamma Interferon in Chronic Granulomatous Disease (CGD)

STATISTICS 2, 2018 1
STA2300 DATA ANALYSIS S2, 2018
[Name of Student]
[Institutional Affiliation]
[Date of Submission]
Assignment 3

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Question One
This sample data set has been adapted from a subset of data collected from a study of Gamma
Interferon in Chronic Granulomatous Disease (CGD).
You should use SPSS to calculate the sample statistics you will need to do this question, but for
the confidence interval in part (a) and test statistic in part (d) you are required to do the rest of
the calculations by hand, using a calculator.
(a) Using SPSS find the estimate of the Mean of population and SD of Diastolic BP of the
patients at beginning of the study (DBP_1). Find a 99% confidence interval for the
mean population Diastolic BP of the population of patients at the beginning of the study
by hand (show all working).
SPSS output of estimate of population mean and SD of Diastolic BP of the patients at the
beginning of the study (DBP_1).
Descriptive Statistics
N Mean Std. Deviation
DBP_1 170 84.69 13.019
Valid N (listwise) 170
Table 1: Estimate of population mean and SD of Diastolic BP of Patients at the beginning of
the study (DBP_1)
We then determine/construct the 99% confidence interval for the mean population Diastolic BP
of the population of patients at the beginning of the study (one-sample mean);
ӯ = 84.69
n = 170
s = 13.019
df (degrees of freedom)= n-1 = 169
Then t *(99%) = 2.576 from the given study table.
Both ӯ and S were obtained using SPSS as shown in the table 1 above (As stated in the
question).

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Thus the 99% confidence interval is constructed and obtained by;
95% CI = ӯ ± t*× s
√ n
= 84.69 ± 2.576 × 13.019
√ 170
= 84.69 ± 2.5722
Hence the 1% level of significance (99% confidence interval) for the mean population Diastolic
BP of the population of patients at the beginning of the study is 82.1178 to 87.2622
(b) Check the appropriate conditions and assumptions needed for the validity of the
confidence interval or hypothesis test for the population mean Diastolic BP of the
patients at the beginning of the study. Include graphical illustration in support of your
answer.
Checking the conditions and assumptions for the validity of the confidence interval or
hypothesis test for the population mean Diastolic BP of the patients at the beginning of the
study;
 Independence assumption; It is reasonable to assume that the population of Diastolic BP
patients is independent since we have a random sample.
 Random Sampling; we assume that we have a random sample as stated in the dataset (It
was a random sample from the normal distribution).
 Independency; It is assumed that the mean Diastolic BP of the patients at the beginning
of the study are independent of the Diastolic patients at the end of the study.
 Nearly condition of the normality; it is assumed that the distribution of the Diastolic BP
of the patients for the groups is normal. Also, the size of the sample n is relative bigger
for the theory of the central limit to be applied and the sampling distributions of the
sample mean will each be the normal model. The histogram below show that both the
groups have approximately symmetrical distribution.

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Figure 1: Histogram showing the distribution of the Diastolic BP patients at the beginning of
the study.
(c) A doctor suspect that the average Diastolic BP of the population of patients is more than
82 mm Hg. State appropriate hypotheses (define any symbols used) to perform a
hypothesis test to see if there is evidence to support the suspicion, based on the data in
DBP_1 (regardless of whether the conditions in part (b) are satisfied or not).
Stating the hypotheses to be tested as;
Ho: ӯ = 82 mm Hg
H1: ӯ > 82 mm Hg
Where ӯ is the average Diastolic BP of the population of the patients
(d) Using descriptive statistics of DBP_1 produced by SPSS, determine the appropriate
value of the test statistic for testing the hypotheses in part (c) by hand.
Since this was a an independent sample t test and thus we calculate the test statistic;