Question

Download the file data.csv (comma separated text file) and read the data into R using the function read.csv(). Your data set consists of 100 measurements in Celsius of body temperatures from women and men. Use the function t.test() to answer the following questions. Do not assume that the variances are equal.

Denote the mean body temperature of females and males by μFμF and μMμMrespectively.

(a) Find the p-value for the test H0:μF=μMH0:μF=μM versus HA:μF≠μM.HA:μF≠μM. Answer

(b) Are the body temperatures for men and women significantly different? Use significance level α=0.1.α=0.1.Answeryesno

(c) Denote the sample mean of the females by x¯Fx¯F and the sample mean of the males by x¯M.x¯M. Then x¯F=x¯F= Answer and x¯M=x¯M= Answer .

(d) The 90% two-sided confidence interval for the difference μF−μMμF−μM ranges from Answer to Answer .

35.94," M"
36.06," M"
36.17," M"
36.17," M"
36.17," M"
36.22," M"
36.28," M"
36.33," M"
36.33," M"
36.44," M"
36.44," M"
36.5," M"
36.56," M"
36.56," M"
36.56," M"
36.56," M"
36.61," M"
36.61," M"
36.67," M"
36.67," M"
36.67," M"
36.67," M"
36.67," M"
36.72," M"
36.72," M"
36.78," M"
36.78," M"
36.78," M"
36.78," M"
36.83," M"
36.83," M"
36.89," M"
36.89," M"
36.89," M"
36.89," M"
36.94," M"
37," M"
37," M"
37," M"
37," M"
37.06," M"
37.06," M"
37.11," M"
37.11," M"
37.11," M"
37.17," M"
37.22," M"
37.22," M"
37.22," M"
37.39," M"
37.44," M"
37.5," M"
35.78," F"
36," F"
36.22," F"
36.22," F"
36.5," F"
36.5," F"
36.56," F"
36.61," F"
36.67," F"
36.67," F"
36.67," F"
36.78," F"
36.78," F"
36.78," F"
36.78," F"
36.78," F"
36.83," F"
36.83," F"
36.89," F"
36.89," F"
36.89," F"
36.89," F"
36.89," F"
36.94," F"
37," F"
37," F"
37," F"
37.06," F"
37.06," F"
37.06," F"
37.06," F"
37.06," F"
37.11," F"
37.11," F"
37.11," F"
37.11," F"
37.11," F"
37.17," F"
37.22," F"
37.22," F"
37.28," F"
37.28," F"
37.33," F"
37.33," F"
37.39," F"
37.72," F"
37.78," F"
38.22," F"

Answer 1

a)

R Output:-

p-value = 0.02038

b) Since p-value is greater than 0.01 we accept H₀ and conclude that the body temperatures of men and women are not significantly different.

c) Mean of females,x^-F = 36.94

Mean of males,x^-M = 36.75

d) The 90% Confidence interval is (0.0553,0.3183).