Question

The Human Toxome Project (HTP) is working to understand the scope of industrial pollution in thehuman body. Industrial chemicals may enter the body through pollution or as ingredients inconsumer products. In October 2008, the scientists at HTP tested cord blood samples for 20newborn infants in the United States. The cord blood of the "In utero/newborn" group wastested for 140 industrial compounds, pollutants, and other chemicals, including chemicals linkedto brain and nervous system toxicity, immune system toxicity, and reproductive toxicity, andfertility problems. There are health concerns about the effects of some chemicals on the brainand nervous system.  Here is the data:

79, 145,147,160, 116, 100, 159, 151, 156, 126, 137, 83, 156, 94, 121, 144, 123, 114, 139, 99

At the 5% level of significance, do newborn infants have less than 140 compounds in their cord blood?

This problem is a one-mean t-test because:

Question 1 options:

	There is a population standard deviation that is known.
	The sample standard deviation is known but no population standard deviation is known.
	There is a level of significance that is known.

Question 2 (1 point)

What is the population mean?

Question 2 options:

	140 compounds
	150 compounds
	127 compounds

Question 3 (1 point)

What is the sample mean?

Question 3 options:

	150 compounds
	127 compounds
	140 compounds

Question 4 (1 point)

What is the sample standard deviation?

Question 4 options:

	26 compounds
	20 compounds
	127 compounds

Question 5 (1 point)

What is the level of significance?

Question 5 options:

	0.05
	0.01
	0.50

Question 6 (1 point)

What is the sample size?

Question 6 options:

	10
	15
	20

Question 7 (1 point)

Choose the correct null hypothesis (Ho):

Question 7 options:

	Ho: µ ≥ 140 compounds
	Ho: µ ≤ 140 compounds
	Ho: µ = 140 compounds

Question 8 (1 point)

Choose the correct alternative hypothesis (Ha):

Question 8 options:

	Ha: µ < 140 compounds
	Ha: µ > 140 compounds
	Ha: µ ≠ 140 compounds

Question 9 (1 point)

What is the T- test statistics?

Question 9 options:

	0
	2.16
	-2.16

Question 10 (1 point)

What is the p-value?

Question 10 options:

	.022
	.22
	.0022

Question 11 (1 point)

What is the conclusion when you compare the p-value and the level of significance (alpha)?

Question 11 options:

	Reject the null since the p-value is equal to the level of significance.
	Reject the null since the p-value is less than the level of significance.
	Fail to Reject the null since the p-value is greater than the level of significance.

Question 12 (1 point)

What is the conclusion based on the original claim?

Question 12 options:

	At the 5% level of significance, newborn infants do not have less than 140 compounds in their cord blood.
	At the 5% level of significance, newborn infants have less than 140 compounds in their cord blood.

Answer 1

Question 1

This problem is a one-mean t-test because:

The sample standard deviation is known but no population standard deviation is known

Question 2

What is the population mean?

140 compounds

Question 3

What is the sample mean

Given,

$\overline{x}=\frac{\Sigma x}{n}$

n : sample size = 20

	x:Number of compunds
	79
	145
	147
	160
	116
	100
	159
	151
	156
	126
	137
	83
	156
	94
	121
	144
	123
	114
	139
	99
Total	$\Sigma x$=2549
Mean: $\overline{x}$ =2549/20	127.45

Ans :

127 compounds

Question 4

What is the sample standard deviation?

S Σ(x – )2 TV η -1 = 1

	x:Number of compunds	(x-$\overline{x}$)	(x-$\overline{x}$)2
	79	-48.45	2347.4025
	145	17.55	308.0025
	147	19.55	382.2025
	160	32.55	1059.5025
	116	-11.45	131.1025
	100	-27.45	753.5025
	159	31.55	995.4025
	151	23.55	554.6025
	156	28.55	815.1025
	126	-1.45	2.1025
	137	9.55	91.2025
	83	-44.45	1975.8025
	156	28.55	815.1025
	94	-33.45	1118.9025
	121	-6.45	41.6025
	144	16.55	273.9025
	123	-4.45	19.8025
	114	-13.45	180.9025
	139	11.55	133.4025
	99	-28.45	809.4025
Total	2549		Σ(x – ΤΣ =12808.95
Mean	127.45

Σ(A - Z)2 η 1 12808.95 -0 90 1 O-V = 25.9645

Ans : 26

What is the level of significance?

Ans: 0.05

Question 6 (1 point)

What is the sample size?

Ans : 20

Question 7

Choose the correct null hypothesis (Ho):

Ho: $\mu$ = 140 compounds

Question 8

Choose the correct alternative hypothesis (Ha):

H_a : $\mu$ < 140 compounds

Question 9 (1 point)

What is the T- test statistics

T-HO (127.45 – 140) Test Statistic : Istat = s/n = 25.9645/20 -12.55 - 5.8058 25.9645/20 = 5.8058 = -2.1616

Ans:

-2.16

Question 10 (1 point)

What is the p-value?

for left tailed test:

P - Value = P(t <tstat) = P(t < -2.1616)

for 19 degrees of freedom,  P(t<-2.1616)=0.0218

p-value = 0.0218

p-value = 0.022

Question 11 (1 point)

What is the conclusion when you compare the p-value and the level of significance (alpha)?

Reject the null since the p-value is less than the level of significance.

Question 12 (1 point)

What is the conclusion based on the original claim?

At the 5% level of significance, newborn infants have less than 140 compounds in their cord blood.