A randem sample of n 15 heat pumps of a certain type yielded the fellowing obser

Question

A randem sample of n 15 heat pumps of a certain type yielded the fellowing observaticns on lifetime (in years) 2.0 1.1 6.0 18 5.2 0.4 1.0 5.3 15.6 0.8 4.8 0.9 12.4 5.3 0.6 (a) Assume that the lifetime distribution is exponential and use an argument parallel to that of this example to obtain a 95% CI for expected true average) lifetime. (Round your answers to two decimal places.) years b) How should the interval of part (a) be altered to achieve a confidence level of 99%? A 99% confidence level requires using a new value of to capture an area of 0.1 in each tail of the chi-squared distribution. A 99% confidence level requires using a new value of n to capture an area of 0.005 in each tail of the chi-squared distribution. ·A 99% confidence level requires using critical va ues that capture an area of 0.005 in each tail of the chi-squared distribution. A 99% confidence level requires using critical values that capture an area of 0.1 in each tail of the chi-squarec distribution. (c) what is a 95% CI for the standard deviation of the lifetime distribution? [Hint: what is te standard ceviation of an exponential random variable?) Round your answers to two decimal paces.) )ye

Explanation / Answer

Given that,
mean(x)=2.94
standard deviation , 1 =2.6
number(n1)=916
y(mean)=3.03
standard deviation, 2 =2.57
number(n2)=753
null, Ho: u1 = u2
alternate, H1: 1 != u2
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic (z) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
zo=2.94-3.03/sqrt((6.76/916)+(6.6049/753))
zo =-0.71
| zo | =0.71
critical value
the value of |z | at los 0.05% is 1.96
we got |zo | =0.708 & | z | =1.96
make decision
hence value of | zo | < | z | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -0.71 ) = 0.47884
hence value of p0.05 < 0.47884,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: 1 != u2
test statistic: -0.71
critical value: -1.96 , 1.96
decision: do not reject Ho
p-value: 0.47884

we dont have evidence that population means differ for men and women

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