Solution
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To determine how long 70 cm is, we need to understand the context of the question. The term "long" can refer to the measurement of length or distance. Since we are given a measurement in centimeters (cm), we are dealing with a unit of length. Centimeters are a standard unit of length in the metric system.
To determine how long 70 cm is, we need to understand the context of the question. The term "long" can refer to the measurement of length or distance. Since we are given a measurement in centimeters (cm), we are dealing with a unit of length. Centimeters are a standard unit of length in the metric system.
If we want to express the length of 70 cm in different units, we can convert centimeters to other units such as meters, inches, or feet. Here are the steps for a few common conversions:
1. Converting centimeters to meters:
The metric system is based on powers of ten, which makes conversions straightforward. There are 100 centimeters in a meter. To convert centimeters to meters, we divide the number of centimeters by 100.
Therefore, 70 cm is equal to 0.7 meters.
2. Converting centimeters to inches:
To convert centimeters to inches, we use the conversion factor that 1 inch is approximately equal to 2.54 centimeters. Therefore, to convert centimeters to inches, we divide the number of centimeters by 2.54.
So, 70 cm is approximately equal to 27.56 inches.
3. Converting centimeters to feet:
Since there are 12 inches in a foot, we can first convert centimeters to inches and then convert inches to feet. Using the conversion from the previous step, we have:
Thus, 70 cm is approximately equal to 2.30 feet.
In summary, 70 cm is a specific length measurement in the metric system, and it can be converted to other units of length such as meters, inches, or feet using the appropriate conversion factors.
If we want to express the length of 70 cm in different units, we can convert centimeters to other units such as meters, inches, or feet. Here are the steps for a few common conversions:
1. Converting centimeters to meters:
The metric system is based on powers of ten, which makes conversions straightforward. There are 100 centimeters in a meter. To convert centimeters to meters, we divide the number of centimeters by 100.
Therefore, 70 cm is equal to 0.7 meters.
2. Converting centimeters to inches:
To convert centimeters to inches, we use the conversion factor that 1 inch is approximately equal to 2.54 centimeters. Therefore, to convert centimeters to inches, we divide the number of centimeters by 2.54.
So, 70 cm is approximately equal to 27.56 inches.
3. Converting centimeters to feet:
Since there are 12 inches in a foot, we can first convert centimeters to inches and then convert inches to feet. Using the conversion from the previous step, we have:
Thus, 70 cm is approximately equal to 2.30 feet.
In summary, 70 cm is a specific length measurement in the metric system, and it can be converted to other units of length such as meters, inches, or feet using the appropriate conversion factors.
Exercise 4-Part a- What are the study hypotheses and level of significance at 10%?
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Exercise 4-Part a- What are the study hypotheses and level of significance at 10%?
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A study in Europe established that men are 8 centimeters taller than women on average.
We wish to investigate whether the gender gap in height is bigger in the USA,
40 men and 40 women were randomly sampled.
Assume that the standard deviation of heights is
6 centimeters among women and 12 centimeters among men.
Part A, what are the study hypotheses and what is
the decision criterion at a 10 percent level of significance?
We've got a variable and the variable here is height in centimeters.
We're looking at 2 groups, men and women.
Let's call the average height among men Mu_1 and the average height among women Mu_2.
We're told that we've got a random sample of 40 men and 40 women.
We're given also information about the standard deviations,
standard deviation of 12 among men and 6 among women.
Now what are hypotheses?
We've got a null hypothesis,
it would be that the gap between the height is the same in the US as it is in Europe.
They told us in that first sentence that the gap in Europe
was that men are taller than women by 8 centimeters.
So that's our null hypothesis that Mu_1 minus Mu_2 equals 8.
Our alternative hypothesis when we are testing is that the difference between men
and women in the USA is greater than 8.
We want to know if it ends up being bigger gap in the USA.
But to think this through,
I'm going to draw a standard normal curve as we often do.
What this problem is saying is that we've got a 10 percent level of significance.
That means that we are really interested in knowing what the z value is
that would generate 10 percent of area under the curve over here,
as I've drawn in the diagram.
This is something that you could find on a table or using your calculator.
I always go for the calculator,
this is a kind of situation where we ask the calculator to give us the z value,
we give it the area.
What number am I going to put in here?
I'm going to put in 0.9,
why 0.9, because I'm giving the calculator the area up until that point.
If I've got 0.10 to the right,
then I've got 0.9 to the left,
that's what I need to put into the calculator.
It's now going to give me the z value that I'm interested in.
There it is, about 1.28, let's say.
Let me mark that in the graph.
So if my Z statistic comes out to be bigger than 1.28,
I'm going to reject my null hypothesis.
Now, in this problem we can't compute the Z statistic because
we haven't been given the averages in the 2 samples.
But what we can do is translate
this cut-off point in terms of our hypothesis and here let's do that together.
We can say that we will reject the null hypothesis if we end
up getting a difference x_1 bar minus x_2 bar,
if it ends up being greater than or equal to
1.28 standard
deviations
above 8.
Where am I getting all this from?
8 is our assumed difference between x_1 and x_2 bar.
If we end up getting something that's 1.28 standard deviations above 8,
we're going to reject the null hypothesis.
Now let's translate all these words into values.
What does this mean?
This means we need that the standard deviation
of the difference between 2 samples and we've got that formula right here.
So that comes out to 2.1213.
Now what I can do,
I can translate the sentence that I've written here in red.
Let me change colors.
I can say we will reject the null hypothesis if
x_1 bar minus x_2 bar is greater than or equal to 1.28 standard deviations,
which is what we just found,
1.28 standard deviations above 8.
All I did was take that sentence and now put it into a numerical expression.
If you go ahead and do that computation out,
you will get as follows.
If the difference between the sample averages comes out to be at least 10.72,
then we will reject the null hypothesis.
That's it. We are done for part A,
keep watching for part B.
This video discusses the gender gap in height between men and women in the USA. It examines the study hypotheses and decision criterion at a 10 percent level of significance. The hypotheses are that the gap between the height of men and women in the USA is the same as in Europe (8 cm) and that the difference between men and women in the USA is greater than 8 cm. The decision criterion is that the difference between the sample averages must be at least 10.72 cm in order to reject the null hypothesis.
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