School

Southern New Hampshire University **We aren't endorsed by this school

Course

IHP 315

Subject

Statistics

Date

Aug 9, 2023

Pages

3

Uploaded by ElderScience10712 on coursehero.com

IHP 525 Quiz Two
1.
A telephone survey uses a random digit dialing machine to call subjects. The random
digit dialing machine is expected to reach a live person 15% of the time.
a.
True or False:
Each call is an independent random event.
In two attempts, what is the probability of achieving......
True, each of the calls is a random event
.
b.
exactly two successful calls? (success = reach a live person)
n=2
p=0.15
p(x=2) = (2/2) x (0.15
2) x (0.85
0) = 0.0225
ᶺ
ᶺ
0.0225 = 2.25%
c.
one success and one failure (in any order)?
P(x=1) = (2/1) x (0.85
1) = 0.255
ᶺ
P(x=1) = (0.15 x 0.85) + (0.85 x 0/15) = 0.1275 + 0.1275 = 0.255 = 25.5%
2.
The prevalence of a trait is 76.8%.
In a simple random sample of
n
= 50, how many
individuals are expected to exhibit this characteristic and what is the corresponding
standard deviation of this estimate?
P = 76.8% = 0.768
Q = 1 - p = 1 - 0.768 = 0.232
N = 50 n x p = 50 x 0.768 = 38.4
Sd = square root n x p x q = square root of 50 x 0.768 x 0.232 = square root .
9088 = 2.9847 = 2.985
3.
Linda hears a story on National Public Radio stating that one in six eggs in the United
States are contaminated with
Salmonella
. If
Salmonella
contamination occurs
independently within and between egg cartons and Linda makes a three-egg omelet, what
is the probability that her omelet will contain at least one
Salmonella
contaminated egg?
P = 1/6 = 0.1666
Q = 1 - p
Q = 1 - 0.1666 = 0.8334
P (x ≥ 1) = 1- p (x = 0) = 1 - (.833)3
= 1 - .578
= 0.422
= 42.2%

4.
Suppose that heights of 10-year-old boys vary according to a normal distribution with µ =
138 cm and σ = 7 cm.
What proportion of 10-year-old boys is less than 140 cm in
height?
Z - score =
µ = 138
o = 7 cm
z = (x - µ) / o
Z = (140-138)/7
Z = 2/7
Z = 0.2857
P (Z<0.2857) = 0.612 = 61.2%
5.
A survey selects a simple random sample of
n
= 500 people from a town of 55,000. The
sample shows a mean of 2.3 health problems per person. Based on this information, say
whether each of the following statements is
true
or
false
. Explain your reasoning in each
instance. No calculations necessary.
a.
It is reasonable to assume that the number of health problems per person will vary
according to a normal distribution.
False, because the variable does not follow the normal distribution when the
mean of sampling distribution does.
b.
It is reasonable to assume that the sampling distribution of the mean will vary
according to a normal distribution.
True, because the sample size is large to where it can produce a normal
distribution.

6.
A simple random sample of 18 male students at a university has an average height of 70
inches. The average height of men in the general population is 69 inches. Assume that
male height is approximately normally distributed with σ = 2.8 inches. Conduct a two-
sided hypothesis test to determine whether the male students have heights that are
significantly different than expected. Show all hypothesis testing steps.
Hypothesis:
Ho: µ = 69 versus Ha: µ ≠ 69
Test Statistic:
Zstat = 1.52
P = Pr(z≥1.52) = 0.0643
µ = 60
o = 2.8
n = 18
x = 70
one sided
two sided
o/square root of n
p = 2(0.643)
2.8/square root of 18 = 2.8/4.24 = 0.66
p = 0.1286
Z stat = (x - µ)/o
= (70-69)/ 2.8
= 1/0.66
= 1.515 = 1.52
It is considered nonsignificant by usual conventions.
7.
True or false? The
p
-value refers to the probability of getting the observed result or
something more extreme assuming the null hypothesis
True, because the P-value explains the rejection area for the null hypothesis.

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