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: x1; n1 = 12 540 810 790 790 340 800 890 860 820 640 970 720 Region II: x2; n2 = 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 x1, s1, x2, and s2. (Round your answers to one decimal place.) x1 = ppm s1 = ppm x2 = ppm s2 = ppm(b) Let μ1 be the population mean for x1 and let μ2 be the population mean for x2. Find an 85% confidence interval for μ1 − μ2.

Question
Asked Nov 4, 2019

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: x1; n1 = 12
540
810
790
790
340
800
890
860
820
640
970
720
Region II: x2; n2 = 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 x1, s1, x2, and s2. (Round your answers to one decimal place.)
x1
=

ppm
s1
=

ppm
x2
=

ppm
s2
=

ppm

(b) Let μ1 be the population mean for x1 and let μ2 be the population mean for x2. Find an 85% confidence interval for μ1 − μ2.

check_circleExpert Solution
Step 1

From the given information,

As given that population is normally distributed for both regions.

a)

Thus, required descriptive statistics can be calculated as;

Region 1) and region 2) with required descriptive statistics are as follows:

(data - mean)
data
data-mean
540
-207.5
43056.25
810
62.5
3906.25
790
42.5
1806.25
42,5
790
1806.25
340
-407.5
166056.25
800
52.5
2756.25
20306.25
890
142.5
12656.25
860
112.5
820
72.5
5256.25
-107.5
640
11556.25
970
222.5
49506.25
720
-27.5
756.25
help_outline

Image Transcriptionclose

(data - mean) data data-mean 540 -207.5 43056.25 810 62.5 3906.25 790 42.5 1806.25 42,5 790 1806.25 340 -407.5 166056.25 800 52.5 2756.25 20306.25 890 142.5 12656.25 860 112.5 820 72.5 5256.25 -107.5 640 11556.25 970 222.5 49506.25 720 -27.5 756.25

fullscreen
Step 2
Σ
п
540 810
.+ +720
12
= 747.5
12
(x-F)
Σ(-3)
n-1
319425
12-1
170.4
help_outline

Image Transcriptionclose

Σ п 540 810 .+ +720 12 = 747.5 12 (x-F) Σ(-3) n-1 319425 12-1 170.4

fullscreen
Step 3

Similarly,

For reg...

ΣΣ
750+870+....
+993
16
738.9
1
Σα-3)
n-1
675090.9375
16-1
=212.1
help_outline

Image Transcriptionclose

ΣΣ 750+870+.... +993 16 738.9 1 Σα-3) n-1 675090.9375 16-1 =212.1

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour*

See Solution
*Response times may vary by subject and question
Tagged in

Math

Statistics

Hypothesis Testing

Related Statistics Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: Big babies: The National Health Statistics Reports described a study in which a sample of 355 one-ye...

A: a) From the given information, the claim of the problem is testing whether the mean weight of one-ye...

question_answer

Q: For this problem, carry at least four digits after the decimal in your calculations. Answers may var...

A: (a) Computation of point estimate for p:Let p be the proportion of all permanent dwellings on the en...

question_answer

Q: A Harriss poll taken surveyed 2016 adults and found that 423 of them had one or more tattoos. can yo...

A: The hypotheses for the test is given below.Null hypothesis:H0: p = 0.25Alternative hypothesis:H1: p ...

question_answer

Q: An investigator wants to estimate the impact of smoking on the incidence of prostate cancer. The inc...

A: Note: Hi there! Thanks for posting the question. It is not clear from your question that what to cal...

question_answer

Q: Suppose that the duration of a particular type of criminal trial is known to be normally distributed...

A: a)It is given that criminal trial is known to be normally distributed with a mean of 20 days and a s...

question_answer

Q: According to securelist, 71.8% of all email sent is spam. A system manager at a large corporation be...

A: a)The hypotheses for the test is given below.

question_answer

Q: Please show TI 84 steps

A: Click to see the answer

question_answer

Q: Please show ti 84 steps

A: Given information:Here, the mean change in score corresponding to Math is x-bar=18; standard deviati...

question_answer

Q: Will you show me step by step how to solve this?

A: Here two z values are required to be calculated.Given:P(|Z|&gt;zo) = 0.056It could be simplified as: