Question

The method of tree ring dating gave the following years A.D. for
an archaeological excavation site. Assume that the population of
*x* values has an approximately normal distribution.

1229 | 1264 | 1292 | 1222 | 1268 | 1316 | 1275 | 1317 | 1275 |

(a) Use a calculator with mean and standard deviation keys to
find the sample mean year *x* and sample standard deviation
*s*. (Round your answers to the nearest whole number.)

x = |
A.D. |

s = |
yr |

(b) Find a 90% confidence interval for the mean of all tree ring
dates from this archaeological site. (Round your answers to the
nearest whole number.)

lower limit | A.D. |

upper limit | A.D. |

Answer #1

Solution:

Part a

Sample mean = Xbar = 1273

Sample standard deviation = S = 33

(by using calculator or excel)

Part b

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data,

We have

Xbar = 1273.111111

S = 33.16038466

n = 9

df = n – 1 = 8

Confidence level = 90%

Critical t value = 1.8595

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 1273.111111 ± 1.8595*33.16038466/sqrt(9)

Confidence interval = 1273.111111 ± 1.8595*11.05346155

Confidence interval = 1273.111111 ± 20.5544

Lower limit = 1273.111111 - 20.5544 = 1252.56

Upper limit = 1273.111111 + 20.5544 = 1293.67

Lower limit = 1253 A.D.

Upper limit = 1294 A.D.

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