Arsenic is a compound naturally occurring in very low concentrations. Arsenic bl
ID: 3155359 • Letter: A
Question
Arsenic is a compound naturally occurring in very low concentrations. Arsenic blood concentrations in healthy individuals are Normally distributed with mean = 3.2 micrograms per deciliter (g/dl) and standard deviation = 1.5 g/dl. Some areas are known to have naturally elevated concentrations of arsenic in the ground and water supplies. We take two SRSs of 25 adults residing in two different high-arsenic areas. The data from the first sample give x = 3.35 and that the data from the second sample give x = 3.75 g/dl.
1) What is the P-value for the 1st study?
2. True or False: True False Enter the number of the term that corresponds to each choice:
This outcome is statistically significant at the = 0.05 level.
This outcome is statistically significant at the = 0.01 level.
3.What is the p value for the second experiment True or False:
4. True False Enter the number of the term that corresponds to each choice:
.This outcome is statistically significant at the = 0.05 level.
This outcome is statistically significant at the = 0.01 level.
5.Explain briefly why these P-values tell us that one outcome is strong evidence against the null hypothesis and that the other outcome is not.
A)x = 3.35 is statistically significant, giving little reason to doubt H0, whereas x = 3.75 is not statistically significant, suggesting that we should doubt that H0 is true.
B)The P-value of x = 3.75 is rare enough that we would reject H0 at = 5%, whereas the P-value of x = 3.35 is statistically insignificant at 5% and 1%, providing no evidence that we should doubt that H0 is true.
C)Both outcomes are statistically insignificant at = 1%, however the P-value for x = 3.75 is larger suggesting that we should doubt that H0 is true.
D)x = 3.35 would rarely occur when H0 is true, suggesting that we should doubt that H0 is true, whereas x = 3.75 gives little reason to doubt H0.
Explanation / Answer
1.
Formulating the null and alternative hypotheses,
Ho: u <= 3.2
Ha: u > 3.2
As we can see, this is a right tailed test.
Getting the test statistic, as
X = sample mean = 3.35
uo = hypothesized mean = 3.2
n = sample size = 25
s = standard deviation = 1.5
Thus, z = (X - uo) * sqrt(n) / s = 0.5
Also, the p value is
p = 0.308537539 [ANSWER, P VALUE]
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2.
As P > 0.05 and P > 0.01, it is not significant in either level, so
This outcome is statistically significant at the = 0.05 level. [FALSE]
This outcome is statistically significant at the = 0.01 level. [FALSE]
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3.
Formulating the null and alternative hypotheses,
Ho: u <= 3.2
Ha: u > 3.2
As we can see, this is a right tailed test.
Getting the test statistic, as
X = sample mean = 3.75
uo = hypothesized mean = 3.2
n = sample size = 25
s = standard deviation = 1.5
Thus, z = (X - uo) * sqrt(n) / s = 1.833333333
Also, the p value is
p = 0.033376508 [ANSWER, P VALUE]
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4.
P < 0.05, but P > 0.01. Hence,
.This outcome is statistically significant at the = 0.05 level. [TRUE]
This outcome is statistically significant at the = 0.01 level. [FALSE]
****************************
5.
OPTION B: B)The P-value of x = 3.75 is rare enough that we would reject H0 at = 5%, whereas the P-value of x = 3.35 is statistically insignificant at 5% and 1%, providing no evidence that we should doubt that H0 is true.
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