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y-2 < -5
adding 2 on both side
y-2+2 < -5+2
y < -3
and
y-2 > 5
adding 2 on both side
y-2+2 > 5+2
y > 7
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MCAD Hypothesis Test for a Difference in Two Population Means Worksheet
Learn by DoingIn this activity you will learn to use StatCrunch to perform a two-sample t-test.Some features of this activ ...
MCAD Hypothesis Test for a Difference in Two Population Means Worksheet
Learn by DoingIn this activity you will learn to use StatCrunch to perform a two-sample t-test.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 and grading rubric for the discussion board exercises. A list of StatCrunch directions is provided at the bottom of this page.ContextDo undergraduates sleep less than graduate students?A student conducted a study of sleep habits at a large state
university. His hypothesis is that undergraduates will party more and
sleep less than graduate students. He surveyed random samples of 75
undergraduate students and 50 graduate students. Subjects reported the
hours they sleep in a typical night.For this hypothesis test, he defined the population means as follows:
μ
1
is the mean number of hours undergraduate students sleep in a typical night.
μ
2
is the mean number of hours graduate students sleep in a typical night.VariablesHours: typical number of hours a student sleeps each night Program: undergraduate or graduate Program is the explanatory variable, and the data is categorical. Hours is the response variable, and the data is quantitative.DataTwo sample T hypothesis test:μ1 : Mean of undergraduateμ2 : Mean of graduateμ1 - μ2 : Difference between two meansH0 : μ1 - μ2 = 0HA : μ1 - μ2 < 0(without pooled variances)Hypothesis test results:
DifferenceSample Diff.Std. Err.DFT-StatP-value
μ1 - μ2-0.233333330.18963708106.32776-1.23042040.1106
PromptState the null and alternative hypotheses. Include a clear description of the populations and the variable.Explain why we can safely use the two-sample T-test in this case.Use StatCrunch to carry out the test. Copy and paste the content of in the StatCrunch output window (text and the table) in your initial post. State a conclusion in the context of this problem.ANSWER(S): (hint)Since we want to check whether the data supports the claim that
undergraduate students sleep less, on average, than graduate students,
we are testing:
H
0
:
μ
1
−
μ
2
=
0
H
a
:
μ
1
−
μ
2
<
0
We can safely use the two-sample T-test in this case since:
Both samples are random, and therefore independent.The sample sizes (75 and 50) are quite large, and therefore we can
proceed regardless of whether the populations are normal or not.
T = -1.23; P-value = 0.111Here is the StatCrunch output depicting these values.Two sample T hypothesis test:
μ
1
: Mean of undergraduate
μ
2
: Mean of graduate
H
0
:
μ
1
−
μ
2
=
0
H
a
:
μ
1
−
μ
2
<
0
(without pooled variances)
Hypothesis test results:
Difference
Sample Diff.
Sd. Err.
DF
T-Stat
P-Value
μ1 - μ2
-0.23333333
0.18963708
106.32776
-1.2304204
0.1106
The P-value (0.111) is greater than 0.05. This indicates that
the observed data is not unusual if undergraduate and graduate students,
on average, have the same mean for sleep hours. Therefore, the data do
not provide evidence to reject
H
0
. So we cannot conclude that undergraduate students sleep less, on average, than graduate students.
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Most Popular Content
MCAD Hypothesis Test for a Difference in Two Population Means Worksheet
Learn by DoingIn this activity you will learn to use StatCrunch to perform a two-sample t-test.Some features of this activ ...
MCAD Hypothesis Test for a Difference in Two Population Means Worksheet
Learn by DoingIn this activity you will learn to use StatCrunch to perform a two-sample t-test.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 and grading rubric for the discussion board exercises. A list of StatCrunch directions is provided at the bottom of this page.ContextDo undergraduates sleep less than graduate students?A student conducted a study of sleep habits at a large state
university. His hypothesis is that undergraduates will party more and
sleep less than graduate students. He surveyed random samples of 75
undergraduate students and 50 graduate students. Subjects reported the
hours they sleep in a typical night.For this hypothesis test, he defined the population means as follows:
μ
1
is the mean number of hours undergraduate students sleep in a typical night.
μ
2
is the mean number of hours graduate students sleep in a typical night.VariablesHours: typical number of hours a student sleeps each night Program: undergraduate or graduate Program is the explanatory variable, and the data is categorical. Hours is the response variable, and the data is quantitative.DataTwo sample T hypothesis test:μ1 : Mean of undergraduateμ2 : Mean of graduateμ1 - μ2 : Difference between two meansH0 : μ1 - μ2 = 0HA : μ1 - μ2 < 0(without pooled variances)Hypothesis test results:
DifferenceSample Diff.Std. Err.DFT-StatP-value
μ1 - μ2-0.233333330.18963708106.32776-1.23042040.1106
PromptState the null and alternative hypotheses. Include a clear description of the populations and the variable.Explain why we can safely use the two-sample T-test in this case.Use StatCrunch to carry out the test. Copy and paste the content of in the StatCrunch output window (text and the table) in your initial post. State a conclusion in the context of this problem.ANSWER(S): (hint)Since we want to check whether the data supports the claim that
undergraduate students sleep less, on average, than graduate students,
we are testing:
H
0
:
μ
1
−
μ
2
=
0
H
a
:
μ
1
−
μ
2
<
0
We can safely use the two-sample T-test in this case since:
Both samples are random, and therefore independent.The sample sizes (75 and 50) are quite large, and therefore we can
proceed regardless of whether the populations are normal or not.
T = -1.23; P-value = 0.111Here is the StatCrunch output depicting these values.Two sample T hypothesis test:
μ
1
: Mean of undergraduate
μ
2
: Mean of graduate
H
0
:
μ
1
−
μ
2
=
0
H
a
:
μ
1
−
μ
2
<
0
(without pooled variances)
Hypothesis test results:
Difference
Sample Diff.
Sd. Err.
DF
T-Stat
P-Value
μ1 - μ2
-0.23333333
0.18963708
106.32776
-1.2304204
0.1106
The P-value (0.111) is greater than 0.05. This indicates that
the observed data is not unusual if undergraduate and graduate students,
on average, have the same mean for sleep hours. Therefore, the data do
not provide evidence to reject
H
0
. So we cannot conclude that undergraduate students sleep less, on average, than graduate students.
polynomial of degree at least 3 where all the zeros are positive whole numbers
Imagine you are writing exam questions for an algebra course. You want to write questions that include finding the zeros o ...
polynomial of degree at least 3 where all the zeros are positive whole numbers
Imagine you are writing exam questions for an algebra course. You want to write questions that include finding the zeros of polynomials. To balance the difficulty level of the test’s questions, you decide to include two different types of questions, as described here:Question #1: A polynomial of degree at least 3 where all the zeros are positive whole numbersQuestion #2: A polynomial of degree at least 3 where one or more of the roots are fractionsFind two polynomials for the two described questions. Explain how you know each question satisfies the requirements stated. What approach did you use to find these polynomials?
Grand Canyon University Statistic Type to Analyze Data Discussion
Respond these two questions 1- To determine whether a new sleeping pill has an effect that varies with dosage, a researche ...
Grand Canyon University Statistic Type to Analyze Data Discussion
Respond these two questions 1- To determine whether a new sleeping pill has an effect that varies with dosage, a researcher randomly assigns adult insomniacs, in equal numbers, to receive either 4 or 8 grams of the sleeping pill. The amount of sleeping time is measured for each subject during an 8-hour period after the administration of the dosage. What type of design is this, and what type of statistic is needed to analyze the data?2 - Dr. Bill Board designs a 2 X 2 between-subjects factorial design, where Factor A is word frequency (low or high) and Factor B is category cues (no cues or cues). Assume that the data are interval. What type of statistic is needed to analyze the data?
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