Question

Inorganic phosphorous is a naturally occurring element in all plants and animals, with concentrations increasing progressively up the food chain (fruit < vegetables < cereals < nuts < corpse). Geochemical surveys take soil samples to determine phosphorous content (in ppm, parts per million). A high phosphorous content may or may not indicate an ancient burial site, food storage site, or even a garbage dump. The Hill of Tara is a very important archaeological site in Ireland. It is by legend the seat of Ireland's ancient high kings†. Independent random samples from two regions in Tara gave the following phosphorous measurements (ppm). Assume the population distributions of phosphorous are mound-shaped and symmetric for these two regions.

Region I: x_{1};
n_{1} = 12 |
|||||

540 | 810 | 790 | 790 | 340 | 800 |

890 | 860 | 820 | 640 | 970 | 720 |

Region II: x_{2};
n_{2} = 16 |
|||||||

750 | 870 | 700 | 810 | 965 | 350 | 895 | 850 |

635 | 955 | 710 | 890 | 520 | 650 | 280 | 993 |

(a) Use a calculator with mean and standard deviation keys to
calculate *x*_{1}, *s*_{1},
*x*_{2}, and *s*_{2}. (Round your
answers to one decimal place.)

x_{1} |
= ppm |

s_{1} |
= ppm |

x_{2} |
= ppm |

s_{2} |
= ppm |

(b) Let *μ*_{1} be the population mean for
*x*_{1} and let *μ*_{2} be the
population mean for *x*_{2}. Find an 85% confidence
interval for *μ*_{1} − *μ*_{2}.
(Round your answers to one decimal place.)

lower limit | ppm |

upper limit | ppm |

(c) Explain what the confidence interval means in the context of
this problem. Does the interval consist of numbers that are all
positive? all negative? of different signs? At the 85% level of
confidence, is one region more interesting than the other from a
geochemical perspective?

Because the interval contains both positive and negative numbers, we can not say that one region is more interesting than the other.

Because the interval contains only positive numbers, we can say that region I is more interesting than region II.

Because the interval contains only negative numbers, we can say that region II is more interesting than region I.

We can not make any conclusions using this confidence interval.

(d) Which distribution (standard normal or Student's *t*)
did you use? Why?

Standard normal was used because *σ*_{1} and
*σ*_{2} are unknown.

Standard normal was used because *σ*_{1} and
*σ*_{2} are known.

Student's *t* was used because *σ*_{1} and
*σ*_{2} are known.

Student's *t* was used because *σ*_{1} and
*σ*_{2} are unknown.

Answer #1

(A) Using TI 84 calculator

enter the first data set in L1 and second data set in L2

press stat then calc then 2var stat

select L1 and L2 as data sets

we get

x1= 747.5, s1 = 170.4, n1 = 12

x2 = 738.9, s2 = 190.2, n2 = 16

(B) using TI 84 calculator

press stat then tests then 2-sampTinterval

enter the data

x1= 747.5, s1 = 170.4, n1 = 12

x2 = 738.9, s2 = 190.2, n2 = 16

Pooled: No

c-level = 0.85

press calculate

we get

(-93.0, 110.2)

(C) Because the interval contains both positive and negative numbers, we can not say that one region is more interesting than the other.

(D) We have used student's t distribution because we have unknown population standard deviations.

option D

Inorganic phosphorous is a naturally occurring element in all
plants and animals, with concentrations increasing progressively up
the food chain (fruit < vegetables < cereals < nuts <
corpse). Geochemical surveys take soil samples to determine
phosphorous content (in ppm, parts per million). A high phosphorous
content may or may not indicate an ancient burial site, food
storage site, or even a garbage dump. The Hill of Tara is a very
important archaeological site in Ireland. It is by legend...

Inorganic phosphorous is a naturally occurring element in all
plants and animals, with concentrations increasing progressively up
the food chain (fruit < vegetables < cereals < nuts <
corpse). Geochemical surveys take soil samples to determine
phosphorous content (in ppm, parts per million). A high phosphorous
content may or may not indicate an ancient burial site, food
storage site, or even a garbage dump. The Hill of Tara is a very
important archaeological site in Ireland. It is by legend...

Inorganic phosphorous is a naturally occurring element in all
plants and animals, with concentrations increasing progressively up
the food chain (fruit < vegetables < cereals < nuts <
corpse). Geochemical surveys take soil samples to determine
phosphorous content (in ppm, parts per million). A high phosphorous
content may or may not indicate an ancient burial site, food
storage site, or even a garbage dump. The Hill of Tara is a very
important archaeological site in Ireland. It is by legend...

A.) Inorganic phosphorous is a naturally occurring element in
all plants and animals, with concentrations increasing
progressively up the food chain (fruit < vegetables < cereals
< nuts < corpse). Geochemical surveys take soil samples to
determine phosphorous content (in ppm, parts per million). A high
phosphorous content may or may not indicate an ancient burial site,
food storage site, or even a garbage dump. The Hill of Tara is a
very important archaeological site in Ireland. It is by...

Independent random samples of professional football and
basketball players gave the following information. Assume that the
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Weights (in lb) of pro football players:
x1; n1 = 21
248
262
255
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276
240
265
257
252
282
256
250
264
270
275
245
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253
265
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220
210
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Independent random samples of professional football and
basketball players gave the following information. Assume that the
weight distributions are mound-shaped and symmetric.
Weights (in lb) of pro football players:
x1; n1 = 21
245
262
254
251
244
276
240
265
257
252
282
256
250
264
270
275
245
275
253
265
271
Weights (in lb) of pro basketball players:
x2; n2 = 19
202
200
220
210
192
215
223
216
228
207
225
208
195
191
207...

Independent random samples of professional football and
basketball players gave the following information. Assume that the
weight distributions are mound-shaped and symmetric.
Weights (in lb) of pro football players:
x1; n1 = 21
245
263
256
251
244
276
240
265
257
252
282
256
250
264
270
275
245
275
253
265
271
Weights (in lb) of pro basketball players:
x2; n2 = 19
202
200
220
210
193
215
223
216
228
207
225
208
195
191
207...

Independent random samples of professional football and
basketball players gave the following information. Assume that the
weight distributions are mound-shaped and symmetric.
Weights (in lb) of pro football players:
x1; n1 = 21
248
263
256
251
244
276
240
265
257
252
282
256
250
264
270
275
245
275
253
265
271
Weights (in lb) of pro basketball players:
x2; n2 = 19
204
200
220
210
192
215
223
216
228
207
225
208
195
191
207...

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