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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

how do you find z if you only know the area of .0808
Cady Reply
How to take a random sample of 30 observations
Hamna Reply
you can use the random function to generate 30 numbers or observation
smita
How we can calculate chi-square if observed x٫y٫z/frequency 40,30,20 Total/90
Insha Reply
calculate chi-square if observed x,y,z frequency 40,30,20total 90
Insha
find t value,if boysN1, ،32,M1,87.43 S1square,39.40.GirlsN2,34,M2,82.58S2square,40.80 Determine whether the results are significant or insignificant
Insha
The heights of a random sample of 100 entering HRM Freshman of a certain college is 157 cm with a standard deviation of 8cm. test the data against the claim that the overall height of all entering HRM students is 160 cm. previous studies showed that
Crispen Reply
complete the question.. as data given N = 100,mean= 157 cm, std dev = 8 cm..
smita
Z=x-mu/ std dev
smita
find the mean of 25,26,23,25,45,45,58,58,50,25
Asmat Reply
add all n divide by 10 i.e 38
smita
38
hhaa
amit
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Jamshaid Reply
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Syed Reply
A manufacturer estimate 3% of his output is defective. Find the probability that in a sample of 10 items (a) less than two will be defective (b) more than two will be defective.
ISAIAH Reply
A manufacturer estimates that 3% of his output of a small item is defective. Find the probabilities that in a sample of 10 items (a) less than two and (b) more than two items will be defective.
ISAIAH
use binomial distribution with parameter n=10, p= 0.03, q=0.97
Shivprasad
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Tushar Reply
A researcher observed that four out of every ten of their products are normally defective. A total of 360 samples of the products were being tested. If the sample is normally distributed and 220 of the products were identified to be faulty, test the hypothesis that the observation of the res
Adepoju Reply
false
HariPrasad
please answer the ques"following values are obtained from life table T15=3,493,601 and e°15=44.6 then expected number of person alive at exact age 15 will be "
vinay
make it clear
Kagimu
how x minus x bar is equal to zero
Kashif Reply
When the mean (X bar) of the sample and the datapoint-in-context (X) from the same sample are the same, then it (X minus X bar) is equal to 0
Johns
e.g. mean of. sample is 3 and one of the datapoints in that sample is also 3
Johns
a numerical value used as a summary measure for a sample such as a sample mean is known as
rana Reply
differentiate between qualitative and quantitative variables
rana Reply
qualitative variables are descriptive while quantitative are numeric variables
Chisomo
please guys what is the formulas use in calculated statistics please iam new here
Yunisa Reply
Dear Yunisa there are different formulas used in statistics depending on wnat you want to measure. It would be helpful if you can be more specific
LAMIN

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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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