Question

- Assume that the population of human body temperatures has a mean of 98.6 degrees F, as is commonly believed. Also assume that the population has a standard deviation of 0.62 degrees F.

- If a sample size of n=106 is randomly selected, find the probability of getting a mean of 98.2 degrees F or lower. (Verify that the central limit theorem applies if you are using it.)

- A study was done with this sample size of 106 randomly selected adults and they obtained 98.2 degrees F as the mean body temperature of the sample. Using part (a), how can we interpret this result?

Answer #1

(a) Assume that the population of human body temperatures has a
mean of 98∘F as is commonly believed. Also assume that
the population standard deviation is 0.62∘F. If a sample of 100
people are randomly selected, find the probability of getting a
sample mean of 98.2∘F or higher? (3pts)
(b) The state of New South Wales has an unemployment rate of 5%.
The state conducts monthly surveys in order to track the
unemployment rate. In a recent month, a random sample...

2. The human body temperature has an average of 98.6° F and
standard deviation of 0.62° F. [10pts] a. State the Central Limit
Theorem. b. Find the probability that 1 randomly selected person
has less than 98.2° F. c. If 106 people are randomly selected, find
the probability that the average temperature for the sample is
98.2° F or lower. d. Given the results, what can you conclude about
this event?

10. A sample of 106 body temperatures with a mean of 98.2 F and
a standard deviation of 0.62 F is given. At a 0.05 significance
level, test the claim that the mean body temperature of the
population is equal to 98.6 F. Assume normality.
a)
b)
c)
d)
e)

A sample of 100 body temperatures has a mean of 98.6
oF. Assume that population standard deviation σ is known
to be 0.5 oF. Use a 0.05 significance level to test the
claim that the mean body temperature of the population is equal to
98.5 oF, as is commonly believed. What is the value of
test statistic for this testing?
2.0
–2.0
1.0
3.0

The body temperatures of adults are normally distributed with a
mean of 98.6 degrees Fahrenheit and a standard deviation of 1.2
degrees Fahrenheit. If 31 adults are randomly selected, find the
probability that their mean body temperature is greater than 99.3
degrees Fahrenheit.

6. A sample of 200 body temperatures of adults has a mean
temperature of 98.10◦F. Suppose the population standard deviation
is 0.62◦F. Use a 0.05 significance level to test the claim that the
mean body temperature of all adults is equal to 98.6◦F as is
commonly believed. Fill in the following information as you test
the above claim: State the claim symbolically and the opposite of
the claim.
H0 :
H1 :
Teststatistic:
P-value:
Conclusion:

Suppose that human body temperature are normally distributed
with a mean of 98.2 degrees F and a standard deviation of 0.62
degrees F.
1. Physicians want to select the lowest body temperature
considered to be a fever and decide that only 5% of the population
should exceed the temperature. What values should they use for this
temperature?
2. Suppose that one individual is selected at random. Find the
probability that their temperature will exceed 100 degrees F.
3. Suppose that...

A random sample of 130 human body temperatures, provided in the
Journal of Statistical Education, has a mean of 98.25◦ F and a
standard deviation of 0.73◦ F. A researcher named Violet believes
that the commonly reported mean body temperature of 98.6◦ F is
incorrect. In this problem, you will conduct a hypothesis t-test to
test Violet’s claim and determine if the given data indicates that
the average human body temperature is diﬀerent from 98.6◦ F.
(a) Verify that the...

John wishes to study the mean human body temperature. John
organizes a simple random sample which allows him to measure the
human body temperature of 45 people at school. His calculations
show that his sample has a mean human body temperature of 98.40°F
and a standard deviation of 0.62°F. Prior studies indicate that
human body temperatures are normally distributed with a standard
deviation of 0.50°F. Use the p-value method and a 2% significance
level to test the claim that the...

It’s commonly known that the average human body temperature is
98.6 degrees F, right? A group of scientists used smartphones to
measure the body temperature of many people using their wearables
(Apple Watches, Fitbits, etc) and compared the average body
temperature of their sample to the expected population mean of
98.6.
a) Define the null and make a decision about it by doing the
following: Using words and specific values (not something
like “μ1 = μ2”), report the specific null...

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