-0.021 0.029 -0.009 -0.002 0.002 -0.006 0.006 -0.064 0.023 0.031
Table 1: A sample of FIR
Your friend seek help from you to use your knowledge from TSTA602
to assist Bank X to do the following data analysis. Please write a
report to answer all the following questions.
(a). calculate (mannually) the sample mean, and sample
standard de- viation for the sample in Table 1.
(b). if we draw samples of sizes 10 many times and form a
distribution of sample mean, state the distribution of the sample
mean and provide the reason for your conclusion; calculate the mean
of the sample means and its standard deviation.
(c). based on (b), find the probability that the sample
mean is smaller than 0.02. Please keep two decimal places in the
calculation of standardization.
(d). if the sample mean from (a) is your observed value,
calculate the 95% confidence interval for the sample mean.
(e). An outlier is a data point outside the interval [Q1
− 1.5IQR, Q3 + 1.5IQR], where Q1 and Q3 ko are first and third
quartile respectively, and IQR
1
is the interquartile range. Explain whether there is
any outlier appears in the sample in Table 1? You can calculate Q1
and Q3, and IQR using R (in Rstudio).
(f). Use R (in Rstudio) to generate 1,000,000 samples of
size 10 from N(0.032, 0.0016) (please set the seed equals to 602),
compute the sample mean for each of these samples, draw a histgram
(set the frequency parameter to FALSE) for these sample means and
add a density curve to the histgram. Please provide the histgram
with the density curve here and attach your R code as appendix.
a.
Sample standard deviation:
b.
According to central limit theorem, distribution of sample mean follows normal distribution with mean and standard deviation .
Hence mean of sampling distribution of sample mean is = - 0.0011 and standard deviation is .
c.
The probability that the sample mean is smaller than 0.02,
d.
95% confidence interval for sample mean:
Degrees of freedom = n - 1 = 10 - 1 = 9
Cut off for 95% confidence interval = t0.05/2, 9 = 2.262
Thus confidence interval is,
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