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37 . You had an unusually long wait time, which is bad: 82 percent of patients had a shorter wait time than you, and only 18 percent had a longer wait time.

2.4: box plots

38 . 5

39 . 3

40 . 7

41 . The median is 86, as represented by the vertical line in the box.

42 . The first quartile is 80, and the third quartile is 92, as represented by the left and right boundaries of the box.

43 . IQR = 92 – 80 = 12

44 . Range = 100 – 75 = 25

2.5: measures of the center of the data

45 . Half the runners who finished the marathon ran a time faster than 3:35:04, and half ran a time slower than 3:35:04. Your time is faster than the median time, so you did better than more than half of the runners in this race.

46 . 61.5, or $61,500

47 . 49.25 or $49,250

48 . The median, because the mean is distorted by the high value of one house.

2.6: skewness and the mean, median, and mode

49 . c

50 . a

51 . They will all be fairly close to each other.

2.7: measures of the spread of the data

52 . Mean: 15
Standard deviation: 4.3
μ = 10 + 11 + 15 + 15 + 17 + 22 6 = 15
s = ( x x ¯ ) 2 n 1 = 94 5 = 4.3

53 . 15 + (2)(4.3) = 23.6

54 . 13.7 is one standard deviation below the mean of this data, because 15 – 4.3 = 10.7

55 . z = 95 85 5 = 2.0
Susan’s z -score was 2.0, meaning she scored two standard deviations above the class mean for the final exam.

3.1: terminology

56 . P ( B ) = 25 90 = 0.28

57 . Drawing a red marble is more likely.
P ( R ) = 50 80 = 0.62
P ( Y ) = 15 80 = 0.19

58 . P ( F AND S )

59 . P ( E | M )

3.2: independent and mutually exclusive events

60 . P ( A AND B ) = (0.3)(0.5) = 0.15

61 . P ( C OR D ) = 0.18 + 0.03 = 0.21

3.3: two basic rules of probability

62 . No, they cannot be mutually exclusive, because they add up to more than 300. Therefore, some students must fit into two or more categories (e.g., both going to college and working full time).

63 . P ( A and B ) = ( P ( B | A ))( P ( A )) = (0.85)(0.70) = 0.595

64 . No. If they were independent, P ( B ) would be the same as P ( B | A ). We know this is not the case, because P ( B ) = 0.70 and P ( B | A ) = 0.85.

3.4: contingency tables

65 .

Honor roll No honor roll Total
Study at least 15 hours/week 482 200 682
Study less than 15 hours/week 125 193 318
Total 607 393 1,000

66 . P (honor roll|study at least 15 hours word per week) =  482 1000 = 0.482

67 . P ( studies less than 15 hours word per week) = 125 + 193 1000 = 0.318

68 . Let P ( S ) = study at least 15 hours per week
Let P ( H ) = makes the honor roll
From the table, P ( S ) = 0.682, P ( H ) = 0.607, and P ( S AND H ) =0.482.
If P ( S ) and P ( H ) were independent, then P ( S AND H ) would equal ( P ( S ))( P ( H )).
However, ( P ( S ))( P ( H )) = (0.682)(0.607) = 0.414, while P ( S AND H ) = 0.482.
Therefore, P ( S ) and P ( H ) are not independent.

3.5: tree and venn diagrams

69 .

This is a Venn diagram with two circles. One circle is labeled Soccer and the other is labeled Tennis. The circles do not overlap.

70 .

This is a Venn diagram with two circles. One circle is labeled Soccer and the other is labeled Tennis. The circles overlap.

Practice test 2

4.1: probability distribution function (pdf) for a discrete random variable

Use the following information to answer the next five exercises. You conduct a survey among a random sample of students at a particular university. The data collected includes their major, the number of classes they took the previous semester, and amount of money they spent on books purchased for classes in the previous semester.

1. If X = student’s major, then what is the domain of X ?

Questions & Answers

If X is a Uniform random variable in [ -2, 2 ], find the pdf of Y X  and E Y[ ].
Kezang Reply
I want to know statistics
Okosa Reply
why is data so important in statistics
Trixie Reply
want summary statistic on gender, age group, weight, and weight loss
are you asking question or looking for Solution
solution pls
1st convert gender and group to factor than use summary function It will give mean median and mode with other details
its a bit complicated could u bring it to my level of under standing
u know the question was put in a tabular form where we were to find the variable type, summary statistics and graph type of the given variables that's the gender,age group, weight and weight loss
if you see, gender and group are not numerical due to which they will not give you correct statistics
how you denote gender m or f
or t
ok tnk u
these are not numerical so you have to convert they as f=1; m=2; t=3 same thing you have to do with group or any variable which is character else you should drop them
from your calculation
oh OK tnk u
so pls why is data important in statistics
not only data correct data is imp
statistics works on data only
without data you can not summarize, can not predict future, can not establish relationship between two and more variables, can not prepare reports and make decisions on it
so I'll give example. suppose you want to open a restaurant and you have to choose one best location out of 5. then how you will decide which location is best for you
awww thank you pls
pls I want a brief note on observation, survey and experimentation way of obtaining data
please Tell me difference parameters and non parameter
can you tell me about the scopes of statistics?
plzzz answer me anyone .
Methods of Collecting Data Observation Observational studies allow researchers to document behavior in a natural setting and witness events that could not be produced in a lab.
Key Points Observation differs from most other forms of data collection in that the researcher does not manipulate variables or directly question participants. The advantages of observation include observing natural behavior, refining hypotheses, and allowing for observation of behavior that canno
 be produced in an artificial environment for ethical or practical reasons. The disadvantages of observation are that these studies do not produce quantitative data, do not allow for cause and effect statements, may be very time consuming, and can be prone to researcher bias.
Key Terms observational research: Research focusing on the observation of behavior outside of a laboratory setting. external validity: In research, whether or not study findings can be generalized to real world scenarios.
Surveys and Interviews Surveys are a low-cost option for gathering a large amount of data, but they are also susceptible to reporting bias.
Key Points The survey method of data collection is likely the most common of the four major research methods. The benefits of this method include low cost, large sample size, and efficiency.
The major problem with this method is accuracy: since surveys depend on subjects’ motivation, honesty, memory, and ability to respond, they are very susceptible to bias. A researcher must have a strong understanding of how to properly frame survey questions in order to gather reliable and relevant
Key Terms reliability: The degree to which a measure is likely to yield consistent results each time it is used. validity: The degree to which a measure is actually assessing the concept it was designed to measure. survey: A method for collecting qualitative and quantitative information about ind
individuals in a population.
Interviews Interviews are a type of qualitative data in which the researcher asks questions to elicit facts or statements from the interviewee. Interviews used for research can take several forms:
Informal Interview: A more conversational type of interview, no questions are asked and the interviewee is allowed to talk freely. General interview guide approach: Ensures that the same general areas of information are collected from each interviewee. Provides more focus than the conversational ap
approach, but still allows a degree of freedom and adaptability in getting the information from the interviewee. Standardized, open-ended interview: The same open-ended questions are asked to all interviewees. This approach facilitates faster interviews that can be more easily analyzed and compared
Closed, fixed-response interview (Structured): All interviewees are asked the same questions and asked to choose answers from among the same set of alternatives.
experiments An experiment involves the creation of a contrived situation in order that the researcher can manipulate one or more variables whilst controlling all of the others and measuring the resultant effects.
Boyd and Westfall1 have defined experimentation as: "...that research process in which one or more variables are manipulated under conditions which permit the collection of data which show the effects, if any, in unconfused fashion."
Experiments can be conducted either in the field or in a laboratory setting. When operating within a laboratory environment, the researcher has direct control over most, if not all, of the variables that could impact upon the outcome of the experiment
When experiments are conducted within a natural setting then they are termed field experiments. The variety test carried out by United Fruits on their Gros Michel and Valery bananas is an example of a field experiment.
parameter Parameters are factors or limits which affect the way that something can be done or made
Minhal didny get your question, can you please elaborate more
pls can u use mean n mode at the statistical summary pls
yes, statistical summary itself gives all value
but u didn't tell me the advantage and disadvantage of the experimental method
but you didn't tell me the advantage and disadvantage of experimental method
by using a sampling distribution? how to estimate the population mean using a ramdom variable n?
Jade Reply
The “average increase” for all NASDAQ stocks is the:
da Reply
any video any proof...what is point of estimation in statistics
Younis Reply
Define the meaning of statistics
Robert Reply
roductory Statistics is intended for the one-semester introduction to statistics course for students who are not mathematics or engineering majors. It focuses on the interpretation of statistical results, especially in real world settings, and assumes that students have an understanding of intermedi
statistics is science collection of method planning experiment then organizing summarizing presenting analyzing and drawing conclusion.
uses and miss uses of statistics
Identify the population, sample, parameter, statistic, variable, and data for this example. population sample parameter statistic variable data
kinds of probability samples and there advantage
Hajira Reply
are you going to explain it.
Sampling takes on two forms in statistics: probability sampling and non-probability sampling: Probability sampling uses random sampling techniques to create a sample. Non-probability samplingtechniques use non-random processes like researcher judgment or convenience sampling.
Advantages Cluster sampling: convenience and ease of use. Simple random sampling: creates samples that are highly representative of the population. Stratified random sampling: creates strata or layers that are highly representative of strata or layers in the population. Systematic sampling: creates
any example plz?
Plz write the uses and miss uses of statistical theory
what is the difference between weighted simple price index (WSPI ) & Laspeyre's Price Index ( LPI )
Basil Reply
What are the 5 steps of hypothesis testing?
Sixolisiwe Reply
5 steps of hypothesis testing
Make guesses (e.g., customers will leave if we raise our rates) State the null H0 and alternative H1 hypotheses (e.g., H0: there is no correlation) and alpha Select the sampling distribution and specify the test statistic Compute the test statistic Make a decision and interpret the results
.Five Steps in Hypothesis Testing: 1_Specify the Null Hypothesis. 2_Specify the Alternative Hypothesis. 3_Set the Significance Level (a) 4_Calculate the Test Statistic and Corresponding P-Value. 5_Drawing a Conclusion.
.Econometric Results uses Multiple Regression for the basis of looking at number of casual factors (independent χ Variables) such as Employment, being Female etc., to test for any relationship with the dependent γ Variable Wages, in order to find any evidence to support the Alternative Hypothesis(Ha
.Alternative Hypothesis (H1 or Ha) of Wage Differentials or in the extreme case, if the strength of relationship is strong enough between the dependent γ Variable, and multiple χ Variables, suggesting evidence for the Null Hypothesis ( Ho) that Wage Discrimination may exist.
.The Significance Level which is also the Critical Value gives the maximum allowable probability of making a Type I error – the Significance Level value of which is decided upon before the data sample is collected and analysed, as a guide to avoid or control making a Type I error.
Type I Error occurs when the Null Hypothesis (Ho) is not accepted when in reality the Null Hypothesis is true. A Type II Error however, occurs when one fails to reject the Null Hypothesis when in reality, the Null Hypothesis (Ho) is not true.
.The #P-Value measures the likelihood of getting the sample results if the Null Hypothesis were true, and could be defined as the smallest level of significance (observed level of significance) at which the Null Hypothesis will be rejected, assuming the Null Hypothesis (Ho) is true.
.In most cases, the research attempt is to find support for the Alternative Hypothesis (Ha or H1). Thus, the smaller the P-Value, the more the (the father out the #Test-Statistics is on the Standard Normal Distribution Diagram, and the more confident the researcher can be about rejecting the Null H
.#Test-Statistics is on the Standard Normal Distribution Diagram, and the more confident the researcher can be about rejecting the Null Hypothesis (Ho) in support for the Alternative Hypothesis (H1 / Ha).
.The #P-Value is less than the Critical Values (Significance Level) of 1% (0.01), 5% (0.05), and 10% (0.10) given in Table (1) in the Appendix, means the Null Hypothesis (Ho) that there is Wage Discrimination is not reflective of the population or equal to the Mean of the Population
.Mean of the Population(data sample of Sample Mean distribution of the Population ) which confirms that the Researcher Rejects the Null Hypothesis (Ho) and Accepts the (Alternative Hypothesis).
.See ISBN 1537512757 ; link : https://smile.amazon.co.uk/Winston-Chellie-Economics-TheBachelor-questions/dp/1537512757/ref=mp_s_a_1_1?keywords=Rachel+Adeniji&qid=1572318698&sr=8-1
see publication ' Winston and Chellie by Rachel Adeniji '
correction, dependent x variables such as Employment, being Female; dependent y variable Wages
correction, Wage Differentials such as Employment, Region affecting Wages; Wage Discrimination such as being Female or Ethnicity affecting Wages
correction_, linear regression/equation is computed as y=mx + c or y=m • x1+x2+x3+c where independent x variables eg Employment x1, Female x2 , Ethnicity x3, and dependent y variable Wages
how do you draw a line of best fit?
Josh Reply
informal explanation:lets suppose you have 10 points and you want a line to best fit on all of them. all you need to keep in mind that the distance and error should be minimum and you will get the best fit line.
how was the data collected to draw the graph
draw a straight line through the points on the graph that are most clustered with other data / points
suppose that 30% of the employees in a large factory of smokers what is the probability that there will be exactly two smokers in a randomly-chosen five-person workgroup
rayhaanah Reply
binomialPdf(5, .3, 2) .3087
are the fraction integers
Amir Reply
The ratio of male to female nurses is 2:3 or 2/3. There are 40 nurses in the ward. For every 5 nurses, how many male and female nurses are there? How many groups can be divided into shifts. Pls show the solution and explain.
DokBads Reply
in a group of 5, the probability tbat exactly 3 of the nurses are male is .6630 or 66% calculation P(X=0)+(...)+P(X=3)=.6630
i dont think u got a correct answer. you are computing for the probability not the ratio and proportion
(2+5)/40*2 = male , (2+5)/40*3 = female
40/(2+3)*2 = male , 40/(2+3)*3=female, ....sorry correction
thank you so much for the help
if x is a continuous random variable and` c` is a constant then p(x=c)
Neha Reply
the length of human pregnancies from conception to birth approximates a normal distribution with a mean of 266days and a standard deviation of 16days.(i) what length of time marks the shortest 10%of all pregnancies ?
27.6390625 days
how can I solve a Hypothetic problem that provide sample data such as 45,3_,45,28,17 ect...what is the first step
find the mean and standard deviation first
how can I get line of best fit?

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Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
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