Description
Given Triangle ABC with a = 9, m<A =80 degrees , and m<B=35 degrees , find c. Round the sine value to the nearest thousandth and answer to the nearest hundredth.
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Explanation & Answer
8.28
c = sin C/sin A * a = sin 65 /sin 80 * 9 =0.9063/0.9848*9= 8.28
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μD = μ1 - μ2 : Mean of the
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Some features of this activity may not work well on a cell phone
or tablet. We highly recommend that you complete this activity on a
computer.Here are the directions, grading rubric, and definition of
high-quality feedback for the Learn by Doing
discussion board exercises.A list of StatCrunch directions is provided at the bottom of
this page.ContextGosset's Seed Plot DataWilliam S. Gosset was employed by the Guinness brewing company
of Dublin. Sample sizes available for experimentation in brewing
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statistician Karl Pearson (1857-1936) and was told that there were
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follows.
Plot
Regular seed
Kiln-dried Seed
1
1903
2009
2
1935
1915
3
1910
2011
4
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2463
5
2108
2180
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1925
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pairs), we are testing the difference in yield.
Plot
Regular seed
Kiln-dried Seed
Difference
1
1903
2009
–106
2
1935
1915
20
3
1910
2011
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4
2496
2463
33
5
2108
2180
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6
1961
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7
2060
2122
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8
1444
1482
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9
1612
1542
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1316
1443
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1535
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using the T-test?
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Sample 2. (directions)
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H0 : μD = 0
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Mean
Std. Err.
DF
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P-value
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10
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to conduct a matched pairs T-test for a population mean using ...
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Learn by DoingMatched Pairs: In this lab you will learn how
to conduct a matched pairs T-test for a population mean using
StatCrunch. We will work with a data set that has historical
importance in the development of the T-test.Paired T hypothesis test:
μD = μ1 - μ2 : Mean of the
difference between Regular seed and Kiln-dried seed
H0 : μD = 0
HA : μD > 0
Hypothesis test results:
Difference
Mean
Std. Err.
DF
T-Stat
P-value
Regular seed - Kiln-dried seed
-33.727273
19.951346
10
-1.6904761
0.9391
Some features of this activity may not work well on a cell phone
or tablet. We highly recommend that you complete this activity on a
computer.Here are the directions, grading rubric, and definition of
high-quality feedback for the Learn by Doing
discussion board exercises.A list of StatCrunch directions is provided at the bottom of
this page.ContextGosset's Seed Plot DataWilliam S. Gosset was employed by the Guinness brewing company
of Dublin. Sample sizes available for experimentation in brewing
were necessarily small. At that time, Gosset contacted a famous
statistician Karl Pearson (1857-1936) and was told that there were
no techniques for developing probability models for small data
sets. Gosset studied under Pearson, and the outcome of his study
was perhaps the most famous paper in statistical literature, "The
Probable Error of a Mean" (1908), which introduced the
T-distribution.Since Gosset was employed by Guinness, any work he produced
would be owned by Guinness, so he published under a pseudonym,
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Student's T-distribution.To illustrate his analysis, Gosset used the results of seeding
11 different plots of land with two different types of seed:
regular and kiln-dried. He wanted to determine if drying seeds
before planting increased plant yield. Since different plots of
soil may be naturally more fertile, this confounding variable was
eliminated by using the matched pairs design and planting both
types of seed in all 11 plots.The resulting data (corn yield in pounds per acre) are as
follows.
Plot
Regular seed
Kiln-dried Seed
1
1903
2009
2
1935
1915
3
1910
2011
4
2496
2463
5
2108
2180
6
1961
1925
7
2060
2122
8
1444
1482
9
1612
1542
10
1316
1443
11
1511
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yields more corn than regular seed.Because of the nature of the experimental design (matched
pairs), we are testing the difference in yield.
Plot
Regular seed
Kiln-dried Seed
Difference
1
1903
2009
–106
2
1935
1915
20
3
1910
2011
–101
4
2496
2463
33
5
2108
2180
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6
1961
1925
36
7
2060
2122
–62
8
1444
1482
–38
9
1612
1542
70
10
1316
1443
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11
1511
1535
–24
Note that the differences were calculated:
regular −
kiln-dried.VariablesRegular seed: regular seeds that were traditionally
used for planting
kiln-dried: seed that were kiln-dried before plantingDataDownload the seed (Links to an external site.) data
file, and then upload the file into StatCrunch.PromptState the hypotheses and define the parameter.Checking conditions: Since Gosset invented the T-distribution,
we will assume that his sample meets the conditions and proceed
with the T-test. Regardless, answer these questions to demonstrate
your understanding of the conditions for use of the T-model.
But first you will need to review the dotplots for the data (opens
in a new tab).
Which graph is used to check conditions? Why?What do we look for in the graph to verify that conditions are
met?What else do we need to know about the sample of seeds before
using the T-test?
Use StatCrunch to find the T-score and the P-value. Hint: as
you work through the StatCrunch directions, keep in mind that we
want to calculate the differences as
regular −
kiln-dried . So you will choose
Regular seed for Sample 1 and kiln-dried seed for
Sample 2. (directions)
Copy and paste the information in the StatCrunch output window into
your initial post.State a conclusion based on the context of this scenario.EXAMPLE TO RIGHT ANSWER1. Ho: μ=0Ha: μ>0The average difference is -33.732. a) We use the graph of the differences because that is what
we are analyzing.b) We look to see if the graph is normally distributed, not
skewed, and doesn't have outliers.c) We don't know if the data is randomly selected.3.Paired T hypothesis test:
μD = μ1 - μ2 : Mean of the
difference between Regular seed and Kiln-dried seed
H0 : μD = 0
HA : μD > 0
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Difference
Mean
Std. Err.
DF
T-Stat
P-value
Regular seed - Kiln-dried seed
-33.727273
19.951346
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-1.6904761
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psychologist studied self-esteem scores and found the sample data set
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5. Part A**What
raw score cuts off the bottom 10.03% of this distribution? Or to phrase
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DRAW AND SHADE IN THE MIDDLE 34% TO VISUALIZE! Remember.....the middle
34% means that 17% is BELOW the mean and 17% is ABOVE the mean......) Steps: What are the z-scores that mark the middle 34% of this distribution? The z-score below the mean is Blank 8 The z-score above the mean is Blank 9 What is the raw score below the mean? Blank 10
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