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Confidence interval (women's heights)

Class Time:

Names:

    Student learning outcomes

  • The student will calculate a 90% confidence interval using the given data.
  • The student will determine the relationship between the confidence level and the percentage of constructed intervals that contain the population mean.

Given:

Heights of 100 women (in inches)
59.4 71.6 69.3 65.0 62.9 66.5 61.7 55.2
67.5 67.2 63.8 62.9 63.0 63.9 68.7 65.5
61.9 69.6 58.7 63.4 61.8 60.6 69.8 60.0
64.9 66.1 66.8 60.6 65.6 63.8 61.3 59.2
64.1 59.3 64.9 62.4 63.5 60.9 63.3 66.3
61.5 64.3 62.9 60.6 63.8 58.8 64.9 65.7
62.5 70.9 62.9 63.1 62.2 58.7 64.7 66.0
60.5 64.7 65.4 60.2 65.0 64.1 61.1 65.3
64.6 59.2 61.4 62.0 63.5 61.4 65.5 62.3
65.5 64.7 58.8 66.1 64.9 66.9 57.9 69.8
58.5 63.4 69.2 65.9 62.2 60.0 58.1 62.5
62.4 59.1 66.4 61.2 60.4 58.7 66.7 67.5
63.2 56.6 67.7 62.5
  1. [link] lists the heights of 100 women. Use a random number generator to select ten data values randomly.
  2. Calculate the sample mean and the sample standard deviation. Assume that the population standard deviation is known to be 3.3 inches. With these values, construct a 90% confidence interval for your sample of ten values. Write the confidence interval you obtained in the first space of [link] .
  3. Now write your confidence interval on the board. As others in the class write their confidence intervals on the board, copy them into [link] .
    90% confidence intervals
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________

    Discussion questions

  1. The actual population mean for the 100 heights given [link] is μ = 63.4. Using the class listing of confidence intervals, count how many of them contain the population mean μ ; i.e., for how many intervals does the value of μ lie between the endpoints of the confidence interval?
  2. Divide this number by the total number of confidence intervals generated by the class to determine the percent of confidence intervals that contains the mean μ . Write this percent here: _____________.
  3. Is the percent of confidence intervals that contain the population mean μ close to 90%?
  4. Suppose we had generated 100 confidence intervals. What do you think would happen to the percent of confidence intervals that contained the population mean?
  5. When we construct a 90% confidence interval, we say that we are 90% confident that the true population mean lies within the confidence interval. Using complete sentences, explain what we mean by this phrase.
  6. Some students think that a 90% confidence interval contains 90% of the data. Use the list of data given (the heights of women) and count how many of the data values lie within the confidence interval that you generated based on that data. How many of the 100 data values lie within your confidence interval? What percent is this? Is this percent close to 90%?
  7. Explain why it does not make sense to count data values that lie in a confidence interval. Think about the random variable that is being used in the problem.
  8. Suppose you obtained the heights of ten women and calculated a confidence interval from this information. Without knowing the population mean μ , would you have any way of knowing for certain if your interval actually contained the value of μ ? Explain.

Questions & Answers

hindi notes please😫🙏🙏💓
Uttam Reply
hindi notes please😫🙏🙏💓
Uttam
How can I calculate the Class Mark, Relative frequency and the cumulative frequency on a frequency table?
IJOGI Reply
what is the important in business planning and economics
mahelt Reply
explain the limitation and scope of statistics
mahelt
statistics is limited to use where data can be measured quantitatively. statistics scope is wider such as in economic planning, medical science etc.
Gurpreet
can you send me mcq type questions
Tanuj Reply
Yas
Umar
which books are best to learn applied statistics for data science/ML
Gurpreet
A population consists of five numbers 2,3,6,8,11.consists all possible samples of size two which can be drawn with replacement from this population. calculate the S.E of sample means
Karunesh Reply
A particular train reaches the destination in time in 75 per cent of the times.A person travels 5 times in that train.Find probability that he will reach the destination in time, for all the 5 times.
Anish Reply
0.237
Amresh
explain that this answer-0.237
umesh
p(x=5)= 5C0 p^5 q^0 solve this
Amresh
please sir.
umesh
ok
umesh
5C0=1 p^5= (3/4)^5 q^0=(1/4)^0
Amresh
Hint(0.75 in time and 0.25 not in time)
kamugi
what is standard deviation?
Jawed Reply
It is the measure of the variation of certain values from the Mean (Center) of a frequency distribution of sample values for a particular Variable.
Dominic
what is the number of x
Godgift Reply
10
Elicia
Javed Arif
Jawed
how will you know if a group of data set is a sample or population
Kingsley Reply
population is the whole set and the sample is the subset of population.
umair
if the data set is drawn out of a larger set it is a sample and if it is itself the whole complete set it can be treated as population.
Bhavika
hello everyone if I have the data set which contains measurements of each part during 10 years, may I say that it's the population or it's still a sample because it doesn't contain my measurements in the future? thanks
Alexander
Pls I hv a problem on t test is there anyone who can help?
Peggy
What's your problem Peggy Abang
Dominic
Bhavika is right
Dominic
what is the problem peggy?
Bhavika
hi
Sandeep
Hello
adeagbo
hi
Bhavika
hii Bhavika
Dar
Hi eny population has a special definition. if that data set had all of characteristics of definition, that is population. otherwise that is a sample
Hoshyar
three coins are tossed. find the probability of no head
Kanwal Reply
three coins are tossed consecutively or what ?
umair
p(getting no head)=1/8
umair
or .125 is the probability of getting no head when 3 coins are tossed
umair
🤣🤣🤣
Simone
what is two tailed test
Umar Reply
if the diameter will be greater than 3 cm then the bullet will not fit in the barrel of the gun so you are bothered for both the sides.
umair
in this test you are worried on both the ends
umair
lets say you are designing a bullet for thw gun od diameter equals 3cm.if the diameter of the bullet is less than 3 cm then you wont be able to shoot it
umair
In order to apply weddles rule for numerical integration what is minimum number of ordinates
Anjali Reply
excuse me?
Gabriel
why?
Tade
didn't understand the question though.
Gabriel
which question? ?
Tade
We have rules of numerical integration like Trapezoidal rule, Simpson's 1/3 and 3/8 rules, Boole's rule and Weddle rule for n =1,2,3,4 and 6 but for n=5?
John
Someone should help me please, how can I calculate the Class Mark, Relative frequency and the cumulative frequency on a frequency table?
IJOGI
geometric mean of two numbers 4 and 16 is:
iphone Reply
10
umair
really
iphone
quartile deviation of 8 8 8 is:
iphone
sorry 8 is the geometric mean of 4,16
umair
quartile deviation of 8 8 8 is
iphone
can you please expalin the whole question ?
umair
mcq
iphone
h
iphone
can you please post the picture of that ?
umair
how
iphone
hello
John
10 now
John
how to find out the value
srijth Reply
can you be more specific ?
umair
yes
KrishnaReddy
what is the difference between inferential and descriptive statistics
Eze Reply
descriptive statistics gives you the result on the the data like you can calculate various things like variance,mean,median etc. however, inferential stats is involved in prediction of future trends using the previous stored data.
umair
if you need more help i am up for the help.
umair
Thanks a lot
Anjali
Inferential Statistics involves drawing conclusions on a population based on analysis of a sample. Descriptive statistics summarises or describes your current data as numerical calculations or graphs.
fred
my pleasure😊. Helping others offers me satisfaction 😊
umair
inferential statistics the results of the statistical analysis of the sample data of the population are used for generalization or decision making about the population why descriptive statistics, the analyzed data are presented without generalization or decision making about the population.
IJOGI

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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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