Question 4 Not complete Marked out of 4.00 What is the life span of a lab mouse?

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Question 4 Not complete Marked out of 4.00 What is the life span of a lab mouse? You measured the following life spans (in days) for a certain standard inbred laboratory strain. 958, 724, 704, 919 You may assume for the following questions that the distribution of life span is normal. Flag question (a) Calculate the sample mean . T (b) Calculate the sample standard deviation 8, 8 = (c) Calculate the critical value t* for a 99 percent two-sided confidence interval.t (d) Calculate the margin of error m for a two-sided confidence interval. m (e) The lower bound of the two-sided confidence interval is and the upper bound of the two-sided confidence interval is (1) Calculate the critical valuet*for the 99 percent lower-bound confidence interval. t* (g) Calculate the lower bound of the 99 percent lower-bound confidence interval. We can be 99 percent confident that the mean life span of the lab mouse is more than days (h) Calculate the upper bound of the 99 percent upper-bound confidence interval. We can be 99 percent confident that the mean life span of the lab mouse is less than days Please note that you must decide which of the three confidence intervals you wish to calculate before you look at the data. In particular, the confidence intervals in (g) and (h) are not simultaneously valid.

Explanation / Answer

a) Sample mean = Xbar= sum(Xi)/n = (958+724+704+919)/4

Xbar= 826.25

b) Sample S.D. = Sqrt((Xi-Xbar)^2/n)

Sample S.D= 130.8444

c) critical value for 99% two sided confidence interval

alpha =level of significance

  t*= tn-1, alpha/2 = t3, 0.005 = 5.841

d) Margin of Error

E= ( t3, 0.005 * S.D) / sqrt(n)

E= 5.841*130.8444/2

E= margin of error = 382.13

e) Lower bound for two sided confidence interval = Xbar- ( S.D. *  t3, 0.005/Sqrt(n))

= 826.25 - ( 130.8444*5.841/2)

= 444.1189

Upper bound for two sided confidence interval = Xbar + ( S.D. *  t3, 0.005/Sqrt(n))

= 826.25 + ( 130.8444*5.841/2)

= 1208.3810

f) critical value for 99% lower bound confidence interval

alpha =level of significance =0.01

  t*= tn-1, alpha = t3, 0.01 =4.541

g) Lower bound of 99% lower bound confidence interval = Xbar- (S.D *t3, 0.01/2)

   = 826.25-(130.8444* 4.541/2)

   = 529.16

99 percent confident that the mean life span of the lab mouse is more than 529 days.

h) Upper bound of 99% lower bound confidence interval = Xbar + (S.D *t3, 0.01/2)

   = 826.25-(130.8444* 4.541/2)

   =1123.3332

99 percent confident that the mean life span of the lab mouse is less than 1123 days.

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