A large school district claims that 80% of the children are fromlow-income families. 130 children from the district are chosen toparticipate in a community project. Of the 130 only 72% are fromlow-income families. The children were supposed to be randomlyselected. Do you think they really were?
a. The null hypothesis is that the children were randomlychosen. 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 exactpercentages of each are unknown and estimated from oursample.
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 thedraws? (Don't type in the % sign)
%
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d. What is the SD of the null box? (Note: We don't have toestimate the SD of the box from the sample SD because we cancompute it directly from the percent of 1's in the null box. Thisis why we never use a t-test for problems that can be translatedinto 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 2decimal places.)
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g. What is the p-value? Click here to view the normaltable
%
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h. What do you conclude?
There is very strong evidence to reject the null, and conclude thatthe children were not randomly chosen.
We cannot reject the null, it's plausible the children wererandomly chosen.
