Question

(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 of 500 people showed that 20 were unemployed.

- If the true unemployment rate is 5%, describe the sampling distribution of the sample proportion of unemployed people? (1 pt)
- Find the probability that the sample unemployment rate is at most 4%. (2 pts)
- Assume the population proportion p is unknown. Based on the most recent sample, find the probability that the sample proportion will lie within 0.005 of the true proportion pof people who are unemployed. (4 pts)

Answer #1

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...

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)

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...

Assume that human body temperatures are normally distributed
with a mean of 98.18 degrees Upper F and a standard deviation of
0.62 degrees Upper F. a. A hospital uses 100.6 degrees Upper F as
the lowest temperature considered to be a fever. What percentage of
normal and healthy persons would be considered to have a fever?
Does this percentage suggest that a cutoff of 100.6 degrees Upper F
is appropriate? b. Physicians want to select a minimum temperature
for requiring...

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:

Assume the population of fully loaded delux SUVs has a mean cost
of $62,000 with a standard deviation of $5,100. We dont know the
exact distribution of the costs, just the population mean and
standard deviation.
A. We plan to take a ranodm sample of fully loaded deluxe SUVs
and calculate the mean cost for analysis. Approximately, how big
should our sample be so we dont care about the exact distribution
of cost.
We take a random sample of 100...

BIOS 376 Homework 7
1. A professor claims that the mean IQ for college students is
92. He collects a random sample of 85 college students to test this
claim and the mean IQ from the sample is 84.
(a) What are the null and alternative hypotheses to test the
initial claim? (1 pt)
(b) Using R, compute the test statistic. Assume the population
standard deviation of IQ scores for college students is 17.6
points. (1 pt)
(c) Using R,...

In Problems 1 - 3, assume that the population
of x values has an
approximately normal distribution. Answers may vary slightly due to
rounding to TWO decimals:
(a) What is the level of significance? State the null
and alternate hypothesis. (b) What sample distribution will use?
Write the formula for test statistic and find the value? (c) Find
the P-Value of the test statistic. (d) Sketch the graph of sampling
distribution and show the area corresponding to P-Value. (e) Based...

In Problems 1 - 3, assume that the population of x values has an
approximately normal distribution. Answers may vary slightly due to
rounding to TWO decimals: (a) What is the level of significance?
State the null and alternate hypothesis. (b) What sample
distribution will use? Write the formula for test statistic and
find the value? (c) Find the P-Value of the test statistic. (d)
Sketch the graph of sampling distribution and show the area
corresponding to P-Value. (e) Based...

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