In: Math
A large school district claims that 80% of the children are from low-income families. 130 children from the district are chosen to participate in a community project. Of the 130 only 72% are from low-income families. The children were supposed to be randomly selected. Do you think they really were?
a. The null hypothesis is that the children were randomly chosen. This translates into drawing times
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at random
with replacement
without replacement
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from a null box that contains
b.
130 tickets, 72% marked "1" and 28% marked "0"
Thousands of tickets, 80% marked "1" and 20% marked "0"
Thousands of tickets marked either "1" or "0", but the exact
percentages of each are unknown and estimated from our
sample.
5 tickets, 1 marked "1" and 4 marked "0"
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c. What is the expected value of the percent of 1's in the draws? (Don't type in the % sign)
%
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d. What is the SD of the null box? (Note: We don't have to estimate the SD of the box from the sample SD because we can compute it directly from the percent of 1's in the null box. This is why we never use a t-test for problems that can be translated into 0-1 boxes.)
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e. What is the standard error of the % of 1's in the draws? (Round to 2 decimal places.) %
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f. What is the value of the test statistic z? (Round answer to 2 decimal places.)
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g. What is the p-value? Click here to view the normal
table
%
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h. What do you conclude?
There is very strong evidence to reject the null, and conclude that
the children were not randomly chosen.
We cannot reject the null, it's plausible the children were
randomly chosen.
Let p denotes the true proportion of children who are from low-income families.
h) Conclusion : There is very strong evidence to reject the null, and conclude that the children were not randomly chosen.