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.
A hypothesis in a scientific context, is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon. In a scientific experiment or study, the hypothesis is a brief summation of the researcher's prediction of the study's findings.
Hamzah
Which may be supported or not by the outcome. Hypothesis testing is the core of the scientific method.
Hamzah
statistics means interpretation analysis and representation of numerical data
Ramzan
To check the statment or assumption about population parameter is xalled hypothesis
Ali
hypothesis is simply an assumption
Patrick
what is the d.f we know that how to find but basically my question is what is the d.f? any concept please
Degrees of freedom aren’t easy to explain. They come up in many different contexts in statistics—some advanced and complicated. In mathematics, they're technically defined as the dimension of the domain of a random vector.
Hamzah
d.f >> Degrees of freedom aren’t easy to explain. They come up in many different contexts in statistics—some advanced and complicated. In mathematics, they're technically defined as the dimension of the domain of a random vector.
Hamzah
But we won't get into that. Because degrees of freedom are generally not something you needto understand to perform a statistical analysis—unless you’re a research statistician, or someone studying statistical theory.
Hamzah
And yet, enquiring minds want to know. So for the adventurous and the curious, here are some examples that provide a basic gist of their meaning in statistics.
Hamzah
The Freedom to Vary
First, forget about statistics. Imagine you’re a fun-loving person who loves to wear hats. You couldn't care less what a degree of freedom is. You believe that variety is the spice of life
Unfortunately, you have constraints. You have only 7 hats. Yet you want to wear a different
Hamzah
hat every day of the week.
On the first day, you can wear any of the 7 hats. On the second day, you can choose from the 6 remaining hats, on day 3 you can choose from 5 hats, and so on.
Hamzah
When day 6 rolls around, you still have a choice between 2 hats that you haven’t worn yet that week. But after you choose your hat for day 6, you have no choice for the hat that you wear on Day 7. You must wear the one remaining hat. You had 7-1 = 6 days of “hat” freedom—in which the hat you wore
Hamzah
That’s kind of the idea behind degrees of freedom in statistics. Degrees of freedom are often broadly defined as the number of "observations" (pieces of information) in the data that are free to vary when estimating statistical parameters.
binomial distribution and poisson both are used to estimate the number of successes probable against the. probable failures.
the difference is only that BINOMIAL dist. is for discrete data while POISSON is used for continuous data.
Salman
What do you need to understand?
Angela
The binomial distribution is frequently used to model the number of successes in a sample of size n drawn with replacement from a population of size N. If the sampling is carried out without replacement, the draws are not independent and so the resulting distribution is a hypergeometric distribution
Hamzah
poisson distribution is also for discrete data set. The difference is when the probability of occurring an event is very little and the sample size is extra large then we use poisson distribution.
Neil
Neil
yes you got it and very interested answer you gave
1 tail if greater than pr less than.2 tail if not equal.
Jojo
in such a case there is no sufficient information provided to develop an alternative hypothesis and we can decide between only two states i.e either the statement is EQUAL TO or NOT EQUAL TO under given conditions
Salman
for 1tail there must be certain criteria like the greater than or less than or some probability value that must be achieved to accept or reject the original hypothesis.
Salman
for example if we have null hypothesis
Ho:u=25
Ha:u#25(not equal to 25) it would be two tail
if we say
Ho:u=25
Ha:u>or
Ha:u<25 it would be consider as one tail
I hope you will be understand
#Coleen
Shabir
yes its true. now you have another problem. so share.
Different data sets will have different means and standard deviations, so values from one set cannot always be compared directly with those from another. The z-score standardizes normally distributed data sets, allowing for a proper comparison and a consistent definition of percentiles across data s
summation of values of x1 x2 x3 ,,,,xn divided by total number n
if it is with frequency its like this
summation of values of x1f1+x2f2+x3f3+xnfk divided by summation of frequencies like f1+f2+f3+fk
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