The American Trends Panel (ATP) is a national, probability-based online panel of adults living in households in the United States. The following data come from Wave 64 of the panel, which was conducted from March 19, 2020 to March 24, 2020. The Wave 64 survey focused on how Americans felt about and experienced the coronavirus pandemic at that time. The following table shows summary data for the Mental Health Index (MHI) scores for respondents, organized by political party identification. A higher score indicates that a respondent experienced more mental health issues in the past 7 days, including anxiety, hopelessness, and trouble sleeping. Mental Health Index (MHI) Scores Democrats Independents Republicans Other Political Affiliation Мean 9.67 8.83 8.07 9.06 Standard Error 0.05 0.06 0.06 0.10 Median 9 8 7 8 Mode 5 5 Standard Deviation 3.32 3.18 2.94 3.44 Sample Variance 11.02 10.13 8.62 11.85 Kurtosis -0.16 0.37 1.13 0.13 Skewness 0.65 0.90 1.21 0.88 Range 15 15 15 15 Minimum 5 5 Maximum 20 20 20 20 Sum 39279 29508 22797 9853 Count 4062 3340 2825 1087
The American Trends Panel (ATP) is a national, probability-based online panel of adults living in households in the United States. The following data come from Wave 64 of the panel, which was conducted from March 19, 2020 to March 24, 2020. The Wave 64 survey focused on how Americans felt about and experienced the coronavirus pandemic at that time. The following table shows summary data for the Mental Health Index (MHI) scores for respondents, organized by political party identification. A higher score indicates that a respondent experienced more mental health issues in the past 7 days, including anxiety, hopelessness, and trouble sleeping. Mental Health Index (MHI) Scores Democrats Independents Republicans Other Political Affiliation Мean 9.67 8.83 8.07 9.06 Standard Error 0.05 0.06 0.06 0.10 Median 9 8 7 8 Mode 5 5 Standard Deviation 3.32 3.18 2.94 3.44 Sample Variance 11.02 10.13 8.62 11.85 Kurtosis -0.16 0.37 1.13 0.13 Skewness 0.65 0.90 1.21 0.88 Range 15 15 15 15 Minimum 5 5 Maximum 20 20 20 20 Sum 39279 29508 22797 9853 Count 4062 3340 2825 1087
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
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Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
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Transcribed Image Text:The American Trends Panel (ATP) is a national, probability-based online panel of adults living in households in the United States. The following data come from Wave 64
of the panel, which was conducted from March 19, 2020 to March 24, 2020. The Wave 64 survey focused on how Americans felt about and experienced the coronavirus
pandemic at that time.
The following table shows summary data for the Mental Health Index (MHI) scores for respondents, organized by political party identification. A higher score indicates
that a respondent experienced more mental health issues in the past 7 days, including anxiety, hopelessness, and trouble sleeping.
Mental Health Index (MHI)
Democrats Independents Republicans
Other Political
Scores
Affiliation
Мean
9.67
8.83
8.07
9.06
Standard Error
0.05
0.06
0.06
0.10
Median
9
8
8
Mode
5
5
Standard Deviation
3.32
3.18
2.94
3.44
Sample Variance
11.02
10.13
8.62
11.85
Kurtosis
-0.16
0.37
1.13
0.13
Skewness
0.65
0.90
1.21
0.88
Range
15
15
15
15
Minimum
5
5
Maximum
20
20
20
20
Sum
39279
29508
22797
9853
Count
4062
3340
2825
1087
Transcribed Image Text:Round answers to two (2) decimal places. Whole numbers do not need to be reported with decimal places (eg. report as X, not X.00).
1. Among Republicans, the range for mental health scores was from
(lower limit) to
(upper limit).
2. The number of respondents who identified as Republican was
3. The most common score among respondents identified as Republicans was
4. Half of the Republicans sampled had a mental health score at or below
5.
(True/False). The distribution of mental health scores for Republicans is not normal.
6. In the general population, Republicans are estimated to have an average mental health index score of
during this time period, with
a 95% margin of error of
7. Respondents with MHI scores of 12 or higher are known to be at very high risk for mental health complications. Among Republicans, approximately
percent are at very high risk for mental health complications.
8. An MHI score above 7 is considered indicative of life conditions that are at least moderately stressful. Among Republicans, approximately
percent are experiencing life conditions that are at least moderately stressful.
9. We can be 99% confident that the true population mean MHI score for Republicans during this time period is between
(lower limit)
to
(upper limit).
10. Imagine that a public health organization would like to deploy a support program to populations where at least 50% of the population experiences life
conditions that are more than moderately stressful (defined as a mean MHI score of 8 or higher). Should this program be deployed to Republicans?
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