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
[link] lists the heights of 100 women. Use a random number generator to select ten data values randomly.
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] .
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
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Discussion questions
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?
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: _____________.
Is the percent of confidence intervals that contain the population mean
μ close to 90%?
Suppose we had generated 100 confidence intervals. What do you think would happen to the percent of confidence intervals that contained the population mean?
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.
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%?
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.
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
what is confidence interval estimate and its formula in getting it
There are two coins on a table. When both are flipped, one coin land on heads eith probability 0.5 while the other lands on head with probability 0.6. A coin is randomly selected from the table and flipped.
(a) what is probability it lands on heads?
(b) given that it lands on tail, what is the Condi
outlier is an observation point that is distant from other observations.
Gidigah
what is its effect on mode?
Usama
Outlier have little effect on the mode of a given set of data.
Gidigah
How can you identify a possible outlier(s) in a data set.
Daniel
The best visualisation method to identify the outlier is box and wisker method or boxplot diagram. The points which are located outside the max edge of wisker(both side) are considered as outlier.
Akash
@Daniel Adunkwah - Usually you can identify an outlier visually. They lie outside the observed pattern of the other data points, thus they're called outliers.
Ron
what is completeness?
Muhammad
I am new to this. I am trying to learn.
Dom
I am also new Dom, welcome!
Nthabi
thanks
Dom
please my friend i want same general points about statistics. say same thing
sorry question a bit unclear...do you mean how do you analyze quantitative data? If yes, it depends on the specific question(s) you set in the beginning as well as on the data you collected. So the method of data analysis will be dependent on the data collecter and questions asked.
Bheka
how to solve for degree of freedom
saliou
Quantitative data is the data in numeric form. For eg: Income of persons asked is 10,000. This data is quantitative data on the other hand data collected for either make or female is qualitative data.
Rohan
*male
Rohan
Degree of freedom is the unconditionality. For example if you have total number of observations n, and you have to calculate variance, obviously you will need mean for that. Here mean is a condition, without which you cannot calculate variance. Therefore degree of freedom for variance will be n-1.
Rohan
data that is best presented in categories like haircolor, food taste (good, bad, fair, terrible) constitutes qualitative data
Bheka
vegetation types (grasslands, forests etc) qualitative data
Bheka
I don't understand how you solved it can you teach me
how we make a classes of this(170.3,173.9,171.3,182.3,177.3,178.3,174.175.3)
Sarbaz
6.5
phoenix
11
Shakir
7.5
Ron
why is always lower class bundry used
Caleb
Assume you are in a class where quizzes are 20% of your grade, homework is 20%, exam _1 is 15%,exam _2 is 15%, and the final exam is 20%.Suppose you are in the fifth week and you just found out that you scored a 58/63 on the fist exam. You also know that you received 6/9,8/10,9/9 on the first