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WGU Academy Statistics Module 11 Clearly Explained and answered Questions
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WGU Academy Statistics Module 11 Clearly Explained and answered Questions A certain prescription allergy medicine is supposed to contain an average of 245 parts per million (ppm) of a certain chemical. If the concentration is higher than 245 ppm, the drug will likely cause unpleasant side effects....

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  • August 22, 2024
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  • 2024/2025
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WGU Academy Statistics Module 11
Clearly Explained and answered
Questions
A certain prescription allergy medicine is supposed to contain an average of 245 parts
per million (ppm) of a certain chemical. If the concentration is higher than 245 ppm, the
drug will likely cause unpleasant side effects. If the concentration is below 245 ppm, the




A
drug may be ineffective. The manufacturer wants to check whether the mean
concentration in a large shipment is the required 245 ppm or not. To this end, a random




VI
sample of 64 portions from the large shipment is tested. The testing reveals that the
sample mean concentration is 250 ppm with a sample standard deviation of 12 ppm.
Let's analyze this example according to the four steps of hypotheses testing we outlined




TU
on the previous page:
1.Stating the claims:
Claim 1: The mean concentration in the shipment is the required 245 ppm.
Claim 2: The mean concentration in the shipment is not the required 245 ppm.
IS
Note that again, claim 1 basically says: "There is nothing unusual about this shipment.
The mean concentration is the required 245 ppm." This claim is challenged by the
manufacturer, who wants to check whether that is, indeed, the case or not.
OM

2.Choosing a sample and collecting data:
A sample of n = 64 portions is chosen. Af


For many years, "working full-time" has meant 40 hours per week. Nowadays it seems
NA


that corporate employers expect their employees to work more than this amount. A
researcher decides to investigate this hypothesis.
Claim 1: The average time full-time corporate employees work per week is 40 hours.
Claim 2: The average time full-time corporate employees work per week is more than
JP




40 hours.
To substantiate his claim, the researcher randomly selects 250 corporate employees
and finds that they work an average of 47 hours per week with a standard deviation of
3.2 hours.

In order to assess the evidence, we need to ask:

how likely it is in a sample of 250 we will find that the mean number of hours per week
corporate employees work is as high as 47.

,how likely it is that the true mean number of hours per week corporate employees work
is 40.


how likely it is that the true mean number of hours per week corporate employees work
is more than 40.




A
how likely it is that in a sample of 250 we will find that the mean number of hours per
week corporate employees work is as high as 47 if the true mean is 40.




VI
how likely it is that in a sample of 250 we will find that the mean number of hours per
week corporate employees work is as high as 47 if the true mean is 40.
-Indeed, in hypothesis testing, in order to assess the evidence, we need to find how




TU
likely is it to get data like those observed assuming that claim 1 is true.


According to the Centers for Disease Control and Prevention (CDC), roughly 21.5% of
IS
all high-school seniors in the United States have used marijuana. (Comments: The data
were collected in 2002. The figure represents those who smoked during the month prior
to the survey, so the actual figure might be higher.) A sociologist suspects that the rate
OM

among African-American high school seniors is lower, and wants to check that. In this
case, then,
Claim 1: The rate of African-American high-school seniors who have used marijuana is
21.5% (same as the overall rate of seniors).
Claim 2: The rate of African-American high-school seniors who have used marijuana is
NA


lower than 21.5%.
To check his claim, the sociologist chooses a random sample of 375 African-American
high school seniors, and finds that 16.5% of them have used marijuana.

In order to assess this evidence, we need to find:
JP




how likely it is that the true rate (i.e., the rate among all African-American high-school
seniors) is 21.5%.


how likely it is that the true rate is lower than 21.5%.

, how likely it is that in a sample of 375 we'll find that as low as 16.5% have used
marijuana.


how likely it is that in a sample of 375 we'll find t
how likely it is that in a sample of 375 we'll find that as low as 16.5% have used
marijuana, when the true rate is actually 21.5%.
-Indeed, in hypothesis testing, in order to assess the evidence, we need to find how
likely it is to get data like those observed assuming that claim 1 is true.




A
The most commonly accepted tradition is that college students will study two hours




VI
outside of class for every hour in class. This means 30 hours/week for a full-time
student taking 15 units (hours of class). An educator suspects that this figure is different
now than in the past.




TU
Claim 1: The average time full-time college students study outside of class per week is
30 hours.
Claim 2: The average time full-time college students study outside of class per week is
not 30 hours.
IS
To substantiate her claim, the educator randomly selects 1,500 college students and
finds that they study an average of 27 hours per week with a standard deviation of 1.7
hours.
OM

In order to assess the evidence, we need to determine:

how likely it is to observe a mean number of hours of studying outside of class per week
that is different from 30 hours per week.
NA



how likely it is in a random sample of 1,500 students to observe that the average
number of hours spent per week studying outside of class an average of a little as 27
hours or as many as 33 hours per week outside of class.
JP




how likely it is in a random sample of 1,500 students to observe that the mean amount
of hours of studying outside of class per wee
how likely it is in a random sample of 1,500 students to observe students studying an
average of a little as 27 hours or as many as 33 hours per week outside of class, if the
mean number is actually 30 hours per week.

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