Question

141, secton 71. Spring 2020 | WebAssign of tree-ring dating gave the following years A.D. for an archaeological excavation site. Assume that the population of an approximately normal distribution 1,250 1,271 1,236 1,194 1,268 1,316 1,275 1,317 1,275 calculator with mean and standard deviation keys to find the sample mean year x and sample standard deviation s. nd your answers to the nearest whole number.) A.D. Jyr finding an 90% confidence interval, what is the critical value for confidence level? (Give your answer to three decimal is the maximal margin of error when finding a 90% confidence interval for the mean of all tree-ring dates from this aeological site? (Round your answer to the nearest whole number.) a 90% confidence interval for the mean of all tree-ring dates from this archaeological site. (Round your answers to the est whole number.) limit r limit A.D. elp? Read It Watch It

Answer 1

Here, we have given that,

Xi
1250
1271
1236
1194
1268
1316
1275
1317
1275

(A)

n= Number of observation =9

= sample mean =
1250 + ... + 1276
= 1267

S= sample standard deviation= =38

V n-1

(B)

Now, we want to find the 90% confidence interval for population mean

Formula is as follows,

Τ – Ε <μ τ +Ε

Where

E=Margin of error =

S t(critical) * - in)

Now first we find the margin of error,

Degrees of freedom = n-1 = 9-1=8

c=confidence level =0.90

=level of significance=1-c=1-0.90=0.10

and we know that confidence interval is always two tailed

t-critical = 1.860 ( using t table )

(C)

Now, we get the margin of error

E = t(critical) * Vin)

=

38 1.860 * (9)

=23.63

We get the 90% confidence interval for the population mean

Τ – Ε <μ τ +Ε

1267 – 23.63 <μ< 1267 + 23.63

1243 <μ<1291

We get the 90 % confidence interval for population mean

Lower limit= 1243

Upper limit= 1291

Interpretation:

90% confidence interval we can say that we are 90% confidant that the population mean will fall within this interval.