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SECONDARY
STATISTICS AND PROBABILITY
HIGH SCHOOL STATISTICS
Secondary
Calculus and Analysis
Algebra
Geometry
Statistics and Probability
High school statistics
Normal distributions
Study design
Data distributions
Two-way tables
Scatterplots
High school probability
Math Word Problem
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High school statistics Answers
Normal distributions
asked 2021-03-11
Consider two independent populations that are normally distributions. A simple random sample of
\(\displaystyle{n}_{{1}}={41}\)
from the first population showed
\(\displaystyle\overline{{x}}_{{11}}={33}\)
, and a simple random of size
\(\displaystyle{n}_{{2}}={48}\)
from the second population showed
\(\displaystyle\overline{{x}}_{{2}}={32}\)
Suppose
\(\displaystyle{s}_{{1}}={9}{s}_{{1}}={9}{\quad\text{and}\quad}{s}_{{2}}={10}{s}_{{2}}={10}\)
, find a 98% confidence interval for
\(\displaystyle\mu_{{1}}−\mu_{{2}}\mu_{{1}}-\mu_{{2}}\)
. (Round answers to two decimal places.)
margin of error-?
lower limit-?
upper limit-?
Data distributions
asked 2021-03-11
What is the difference between a normal profile of a random variable and normal pdf of a random variable.
Study design
asked 2021-03-11
To find:Whether the experiment is an observational or a designed experiment.
Study design
asked 2021-03-09
A proposed study design is to leave 100 questionnaires by the checkout line in a student cafeteria. The questionnaire can be picked up by any student and returned to the cashier. Explain why this volunteer sample is a poor study design.
Two-way tables
asked 2021-03-08
Using data from the 2000 census, a random sample of 348 U.S. residents aged 18 and older was selected. The two-way table summarizes the relationship between marital status and housing status for these residents.
\(\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{l}{\left|{c}\right|}{c}{\mid}{c}\right\rbrace}&{M}{a}{r}{r}{i}{e}{d}&{N}{o}{t}{m}{a}{r}{r}{i}{e}{d}&{T}{o}{t}{a}{l}\backslash{h}{l}\in{e}{O}{w}{n}&{172}&{82}&{254}\backslash{h}{l}\in{e}{R}{e}{n}{t}&{40}&{54}&{94}\backslash{h}{l}\in{e}{T}{o}{t}{a}{l}&{212}&{136}&{348}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\)
Scatterplots
asked 2021-03-08
A nutritionist collects the weight of college students in the first semester, then again in the second semester. What is the best way to visually present this data?
a) Line Graphs
b) Scatterplots
c) Bar Graphs
d) Pie Charts
Normal distributions
asked 2021-03-08
Explain some of the important characteristics of a normal distribution.
Data distributions
asked 2021-03-07
We have a set of n-elements (A), and a set of m-elements (B).
\(\displaystyle{n}\ge{0}\)
\(\displaystyle{m}\ge{0}\)
Find how many relations there're from A to B.
Scatterplots
asked 2021-03-06
Make a scatterplot for the data.
Height and Weight of Females
Height (in.): 58, 60, 62, 64, 65, 66, 68, 70, 72
Weight (lb): 115, 120, 125, 133, 136, 115, 146, 153, 159
Normal distributions
asked 2021-03-06
A normal distribution has
\(\mu = 30\)
and
\(\sigma = 5\)
.
(c)Find the raw score corresponding to
\(z =-2\)
.
Scatterplots
asked 2021-03-05
Match the values of r with the accompanying scatterplots 0.723,-0.353,0.353,0.998 and -0.998
scatterplots 1,2,3,4,5
Two-way tables
asked 2021-03-05
1950 randomly selected adults were asked if they think they are financially better off than their parents. The following table gives the two-way classification of the responses based on the education levels of the persons included in the survey and whether they are financially better off, the same as, or worse off than their parents
\(\begin{array}{|c|c|c|}\hline &\text{Less Than High School}&\text{High School}&\text{More Than High School}\\\hline \text{Better off} &140&440&430\\ \hline \text{Same as}&60&230&110\\ \hline \text{Worse off}&180&280&80\\ \hline\end{array}\\\)
Suppose one adult is selected at random from these 1950 adults. Find the following probablity.
Round your answer to three decimal places.
\(P(\text{more than high school or worse off})=?\)
Scatterplots
asked 2021-03-04
Sketch a scatterplot where the association is linear, but the correlation is close to [r = 0].
Normal distributions
asked 2021-03-04
Consider the marks of all 1st-year students on a statistics test. If the marks have a normal distribution with a mean of 72 and a standard deviation of 9, then the probability that a random sample of 10 students from this group have a sample mean between 71 and 73 is?
Two-way tables
asked 2021-03-04
How are the smoking habits of students related to their parents' smoking? Here is a two-way table from a survey of student s in eight Arizona high schools:
\(\begin{array}{c|c}&\text{Student smokes}&\text{Student does not smoke}&\text{Total}\\\hline\text{Both parents smoke}&400&1380&400+1380=1780\\\hline\text{One parent smokes}&416&1823&416+1823=2239\\\hline\text{Neither parent smokes}&188&1168&188+1168=1356\\\hline\text{Total}&400+416+188=1004&1380+1823+1168=4371&1004+4371=5375\end{array}\)
(a) Write the null and alternative hypotheses for the question of interest.
(b) Find the expected cell counts. Write a sentence that explains in simple language what "expected counts" are.
(c) Find the chi-square statistic, its degrees of freedom, and the P-value.
(d) What is your conclusion about significance?
Two-way tables
asked 2021-03-02
When performing a
\(\displaystyleχ^{{2}}\)
test of independent in a contingency table with r rows and c columns, determine the upper-tail critical value of the test statistic in each of the following circumstances:
a. α=0.05, r=4 rows, c=5 columns
b. α=0.01, r=4 rows, c=5 columns
c. α=0.01, r=4 rows, c=6 columns
d. α=0.01, r=3 rows, c=6 columns
e. α=0.01, r=6 rows, c=3 columns
Normal distributions
asked 2021-03-02
\(\displaystyle{\left(\mu{1}-\mu{2}\right)}\)
For two normal distributions
Obtain the appropriate point estimator
Study design
asked 2021-03-02
In the 1970s a study was conducted in Philadelphia in which 500 cases were randomly assigned to treatments for the common cold: 250 subjects received the medication and 250 received a placebo. A total of 383 patients improved within 24 hours. Of those who received the medication 241 improved within 24 hours and of those who received the placebo 142 improved within 24 hours. A test of significance was conducted on the following hypotheses.
\(\displaystyle{H}_{{o}}\)
: The rates for the two treatments are equal.
\(\displaystyle{H}_{{a}}\)
: The treatment of medication has a higher improvement rate.
This test resulted in a p-value of 0.0761.
a.) Interpret what this p-value measures in the context of this study.
b.) Based on this p-value and study design, what conclusion should be drawn in the context of this study? Use a significance level of
\(\displaystyle\alpha={0.05}\)
.
c.) Based on your conclusion in part (b), which type of error, Type I or Type II, could have been made? What is one potential consequence of this error?
Study design
asked 2021-03-02
The Centers for Disease Control reported the percentage of people 18 years of age and older who smoke (CDC website, December 14, 2014). Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of the proportion who smoke of .30.
a. How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of .02? Use 95% confidence.
Scatterplots
asked 2021-03-02
Unusual points Each of the four scatterplots that follow shows a cluster of points and one “stray” point. For each, answer these questions:
1) In what way is the point unusual? Does it have high leverage, a large residual, or both?
2) Do you think that point is an influential point?
3) If that point were removed, would the correlation be- come stronger or weaker? Explain.
4) If that point were removed, would the slope of the re- gression line increase or decrease? Explain
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