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69 . The mean of a normally-distributed population is 50, and the standard deviation is four. If you draw 100 samples of size 40 from this population, describe what you would expect to see in terms of the sampling distribution of the sample mean.

70 . X is a random variable with a mean of 25 and a standard deviation of two. Write the distribution for the sample mean of samples of size 100 drawn from this population.

71 . Your friend is doing an experiment drawing samples of size 50 from a population with a mean of 117 and a standard deviation of 16. This sample size is large enough to allow use of the central limit theorem, so he says the standard deviation of the sampling distribution of sample means will also be 16. Explain why this is wrong, and calculate the correct value.

72 . You are reading a research article that refers to “the standard error of the mean.” What does this mean, and how is it calculated?

Use the following information to answer the next six exercises. You repeatedly draw samples of n = 100 from a population with a mean of 75 and a standard deviation of 4.5.

73 . What is the expected distribution of the sample means?

74 . One of your friends tries to convince you that the standard error of the mean should be 4.5. Explain what error your friend made.

75 . What is the z -score for a sample mean of 76?

76 . What is the z -score for a sample mean of 74.7?

77 . What sample mean corresponds to a z -score of 1.5?

78 . If you decrease the sample size to 50, will the standard error of the mean be smaller or larger? What would be its value?

Use the following information to answer the next two questions. We use the empirical rule to analyze data for samples of size 60 drawn from a population with a mean of 70 and a standard deviation of 9.

79 . What range of values would you expect to include 68 percent of the sample means?

80 . If you increased the sample size to 100, what range would you expect to contain 68 percent of the sample means, applying the empirical rule?

7.2: the central limit theorem for sums

81 . How does the central limit theorem apply to sums of random variables?

82 . Explain how the rules applying the central limit theorem to sample means, and to sums of a random variable, are similar.

83 . If you repeatedly draw samples of size 50 from a population with a mean of 80 and a standard deviation of four, and calculate the sum of each sample, what is the expected distribution of these sums?

Use the following information to answer the next four exercises. You draw one sample of size 40 from a population with a mean of 125 and a standard deviation of seven.

84 . Compute the sum. What is the probability that the sum for your sample will be less than 5,000?

85 . If you drew samples of this size repeatedly, computing the sum each time, what range of values would you expect to contain 95 percent of the sample sums?

86 . What value is one standard deviation below the mean?

87 . What value corresponds to a z -score of 2.2?

7.3: using the central limit theorem

88 . What does the law of large numbers say about the relationship between the sample mean and the population mean?

Questions & Answers

Frequency find questions
Rimsha Reply
What is nominal variable
olusola Reply
Write short notes on, nominal variable, ordinal variable, internal variable, ratio variable.
olusola
P( /x-50/ less than or equal to 5 ) where mean =52 and Variance =25
Jay Reply
how I get the mcq
Mukesh Reply
please what is data mining
Josephine Reply
the exploration and analysis of large data to discover meaningful patterns and rules
Hussein
how do we calculate the median
All Reply
f(x)=cx(1-x)^4 as x range 4rm 0<=x<=1. Can someone pls help me find d constant C. By integration only..
Akeem Reply
uses of statistics in Local Government
Saleema Reply
Hi
Tamuno
hello
Saleema
state road transport corporation
Atul
District statistical officer
Atul
statistical services
Atul
Please is this part of the IMT program
Tamuno
testing of drugs
Shambhavi
hii 2
Qamar-ul-
How about population census
Tamuno
Hello every one
Okoi
sample survey is done by local government in each and every field.
syeda
statistics is used in almost every government organisations such as health department, economic department, census, weather forecasting fields
raghavendra
that's true
syeda
statistics is one of the tool that represents the falling and rising of any cases in one sheet either that is in population census whether forecast as well as economic growth
Aadil
statistic is a technique, and statistics is a subject
syeda
what is business statistics
PM Reply
Probability tells you the likelihood of an event happening. ... The higher the probability, the more likely it is to happen. Probability is a number or fraction between 0 and 1. A probability of 1 means something will always happen, and a probability of 0 means something will never happen...
La Reply
Saying it's a number between zero and one means it is a fraction so you could remove "or fraction" from you definition.
Carlos
wouldn't be correct to remove fractions, saying a number is justified as probabilities can also be decimals between 0 and 1.
Denzel
Saying "a number" will include it being a decimal which are themselves fractions in another form.
Carlos
I will simply say a probability is a number in the range zero to one, inclusive.
Carlos
f#$
Carlos
How to delete an entry? This last one was a pocket print.
Carlos
what is probability
sky-D Reply
chance of occurrence
Sikander
what is data
Muhd Reply
raw facts and figures
Sikander
information of any kind
Tahir
What is Statistic
ibrahim Reply
what statistical analysis can i run on growth and yield of spinach.
guillio
format of the frequency distribution table
henry
what is pearson correlation coefficient indicates?
Eticha
Statistic is the mean of the sample.
Raman
can anyone determine the value of c and the covariance and correlation for the joint probability density function Fxy(x,y)=c over the range 0<x<5,0<y,and x-1<y<x-1.
Nuhu
what actually is the definition of range
Chinedu Reply
I need social statistics materials
Chinedu
the range of a set of data is the difference between the largest and smallest values
La
I need more explanation about cluster sampling
Hafsat
write the set of old number that are greater than or equal to minutes 7 butl less than 5 in both of the set notation
Jerry Reply

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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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