Lyle graphs triangle ABC on coordinate axes. He performs two transformations on this figure that result in the congruent triangl
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Answer:
a) p-hat (sampling distribution of sample proportions)
b) Symmetric
c) σ=0.058
d) Standard error
e) If we increase the sample size from 40 to 90 students, the standard error becomes two thirds of the previous standard error (se=0.667).
Step-by-step explanation:
a) This distribution is called the <em>sampling distribution of sample proportions</em> <em>(p-hat)</em>.
b) The shape of this distribution is expected to somewhat normal, symmetrical and centered around 16%.
This happens because the expected sample proportion is 0.16. Some samples will have a proportion over 0.16 and others below, but the most of them will be around the population mean. In other words, the sample proportions is a non-biased estimator of the population proportion.
c) The variability of this distribution, represented by the standard error, is:
d) The formal name is Standard error.
e) If we divided the variability of the distribution with sample size n=90 to the variability of the distribution with sample size n=40, we have:
If we increase the sample size from 40 to 90 students, the standard error becomes two thirds of the previous standard error (se=0.667).
Answer:
a) the sample size (n) = 156.25≅ 156
Step-by-step explanation:
<u>Step1 </u>:-
Given the two sample sizes are equal so
Given the standard error (S.E) = 0.04
The standard error of the proportion of the given sample size
Step 2:-
here we assume that the proportion of boys and girls are equally likely
p= 1/2 and q= 1/2
squaring on both sides, we get
on simplification, we get
n= 156.25 ≅ 156
sample size (n) = 156
<u>verification</u>:-
Standard error = 0.04