Download the file data.csv (comma separated text file) and read the data into R

Question

Download the file data.csv (comma separated text file) and read the data into R using the function read.csv0. Your data answer the following questions. Do not assume that the variances are equal. Denote the mean body temperature of females and males by F and A4, respectively. (a) Find the p-value for the test Ho : F = M versus HA : F M. (b) Are the body temperatures for men and women significantly different? Use significance level 0.06. no er set consists of 100 measurements in Celsius of body temperatures from women and men. Use the function t.test0 to (c) Denote the sample mean of the females by iF and the sample mean of the males by iM. Then iF = and XM = 36.732 (d) The 94% two-sided confidence interval for the difference F-41 ranges from Please answer all parts of the question. 36.874 to Check

Explanation / Answer

MALE DATA

FEMALE DATA

TRADITIONAL METHOD
given that,
mean(x)=36.732
standard deviation , s.d1=0.3891
number(n1)=46
y(mean)=36.8739
standard deviation, s.d2 =0.4215
number(n2)=54
I.
stanadard error = sqrt(s.d1^2/n1)+(s.d2^2/n2)
where,
sd1, sd2 = standard deviation of both
n1, n2 = sample size
stanadard error = sqrt((0.151/46)+(0.178/54))
= 0.081
II.
margin of error = t a/2 * (stanadard error)
where,
t a/2 = t -table value
level of significance, = 0.06
from standard normal table, two tailed and
value of |t | with min (n1-1, n2-1) i.e 45 d.f is 1.929
margin of error = 1.929 * 0.081
= 0.156
III.
CI = (x1-x2) ± margin of error
confidence interval = [ (36.732-36.8739) ± 0.156 ]
= [-0.298 , 0.015]
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DIRECT METHOD
given that,
mean(x)=36.732
standard deviation , s.d1=0.3891
sample size, n1=46
y(mean)=36.8739
standard deviation, s.d2 =0.4215
sample size,n2 =54
CI = x1 - x2 ± t a/2 * Sqrt ( sd1 ^2 / n1 + sd2 ^2 /n2 )
where,
x1,x2 = mean of populations
sd1,sd2 = standard deviations
n1,n2 = size of both
a = 1 - (confidence Level/100)
ta/2 = t-table value
CI = confidence interval
CI = [( 36.732-36.8739) ± t a/2 * sqrt((0.151/46)+(0.178/54)]
= [ (-0.142) ± t a/2 * 0.081]
= [-0.298 , 0.015]
-----------------------------------------------------------------------------------------------
interpretations:
1. we are 94% sure that the interval [-0.298 , 0.015] contains the true population proportion
2. If a large number of samples are collected, and a confidence interval is created
for each sample, 94% of these intervals will contains the true population proportion

# 1 count 46 mean 36.7320 sample variance 0.1514 sample standard deviation 0.3891 minimum 35.94 maximum 37.5 range 1.56

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