Question

**SITUATION HYPOTHESIS TESTING TOOL:**

I work at a radio station that also has an app, where you can upgrade to a premium product. The premium app makes it possible to swipe away more songs you don’t like. The data will be relating to the age of the costumers buying premium packages. (The age is very important for our radio station, as we are targeting a very young audience).

Null Hypothesis & Alternate Hypothesis:

H_{0} : μ = 20

H_{1}: μ ≠ 20

Type 1 error could be that we conclude that the age is greater than 20, when it is actually not.

Type 2 error could be that we conclude that the age is greater than 20, when it actually is.

Imagine the p-value is 0.01, I would conclude that there is
substantial evidence against H_{0} and that it can be
rejected. The result is very efficient and my assumption about the
audience is not true.

Imagine the p-value is 0.20, I would conclude that H_{0}
is ok but still not super sure. With the p-value of 0.01, the
probability was only 1 % and therefore made it very unlikely but
with a p-value of 0.20, there is 20% probability. The H_{0}
is ok to be rejected by mistake with a 20 % probability. The result
is not very efficient.

**Feedback:**

If young audience is important, your hypothesis should be
\mu>=20 \mu<20. If the test result is to reject the null,
then you know you do have a young audience. Your interpretations of
type 1 and II errors are not consistent with your hypotheses. And
they are opposite with the above hypotheses - **how can I
change it?**

**Questions**

Reformulate your hypothesis test from above incorporate a 2-sample hypothesis test. What would be your data? What is your null hypothesis? What is your alternate hypothesis? What would be your Type 1 and Type 2 errors relative to your decision? Suppose you have a p-value of 0.01, what does this mean relative to your problem and decision? Suppose the p-value is 0.20, what does this mean relative to your problem and decision?

If you reformulated your design for 3 or more samples, what would be the implications of interaction? When would you use Tukey-Kramer test?

Answer #1

**Solution**
**:**

**Given that**

In your environment (business or personal), please describe a
quantitative hypothesis test related to a decision. What would be
your data? What would be your null hypothesis? What would be your
alternate hypothesis? What would be your Type 1 and Type 2 errors
relative to your decision? Suppose you have a p-value of 0.01, what
does this mean relative to your problem and decision? Suppose the
p-value is 0.20, what does this mean relative to your problem and
decision?

PLEASE SHOW WORK
Suppose that in a two-tailed hypothesis test you
calculated a Z statistic of -1.75. What is your p-value? And how
would you conclude if α = 5%?
P-value = 0.0401. H0 should be rejected at the 5% level
P-value = 0.0802. H0 should be rejected at the 5% level
P-value = 0.0802. H0 should not be rejected at the 5% level
P-value = 0.0402. H0 should be rejected at the 5% level
None of the above...

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24
16
22
14
12
13
17
22
15
19
23
13
11
18
The sample mean is
x ≈ 17.1.
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1. Describe in full sentences the hypothesis testing steps &
provide an example to solve by using hypothesis testing.
2. What does Type I and Type II errors mean?
3. The cost of a Starbucks Grande Caffe Latte varies from city
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standard deviation of $0.28.
A research was done to test the claim that the mean cost of a
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1. The P-value of a test of the null hypothesis is
a. the probability the null hypothesis is true.
b. the probability the null hypothesis is false.
c. the probability, assuming the null hypothesis is false, that
the test statistic will take a value at least as extreme as that
actually observed.
d. the probability, assuming the null hypothesis is true, that
the test statistic will take a value at least as extreme as that
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I Greatly appreciate it! I just can't figure these out ):
1)Suppose that you are testing whether a coin is fair. The
hypotheses for this test are
H0: p = 0.5
and
H1: p ≠ 0.5.
Which of the following would be a type I error?
Concluding that the coin is fair when in reality the coin is
fair.
Concluding that the coin is not fair when in reality the coin is
not fair.
Concluding that the coin is fair...

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Mr. Acosta, a sociologist, is doing a study to see if there is a
relationship between the age of a young adult (18 to 35 years old)
and the type of movie preferred. A random sample of 93 adults
revealed the following data. Test whether age and type of movie
preferred are independent at the 0.05 level.
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yr
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yr
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9
7
30
Comedy...

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