please explain so i can understand!! thank you!! In a study done in Michigan, it
ID: 3055373 • Letter: P
Question
please explain so i can understand!! thank you!!
In a study done in Michigan, it was determined 38 (out of 62) poor children who attended pre-school needed social services later in life compared to 59 (out of 71) poor children who did not attend preschool.
State a +4 99% confidence interval to determine the true difference in the proportion of pre-school attending poor children who need social services to those that do not attend pre-school.
We are [a]% confident that poor children who attend preschool need social services between [b]% and [c]% [d](more/less) often compared to those that do not attend pre-school.
Does this study provide significant evidence that preschool reduces the need for social services later in life?
Ho: [e] Ha: [f]
test statistic: [g] & P-value: [h]
Conclusion:
We [i] the null hypothesis. There [j] (is/is not) evidence at the .01 level that preschool reduces the need for social services later in life.
Explanation / Answer
a)
p1 = 38/62 = 0.6129 , n1 = 62 , p2 = 59/71 = 0.8310 , n2 = 71
z value at 99% = 2.576
CI = ( p1 - p2) +/- z *sqrt(p1 (1 -p1)/n1 + p2 * (1 -p2)/n2)
= (0.6129 - 0.8310) +/- 2.576 * sqrt(0.6129 * (1 -0.6129)/62 + 0.8310 * (1 - 0.8310)/71)
= (-0.4143,-0.0218)
We are 99% confident that poor children who attend preschool need social services between -0.4143 % and -0.0218% (more/less) often compared to those that do not attend pre-school.
e)
H0 : p1 = p2
f)
Ha : p1 < p2
g)
Test statistics:
p = (38 + 59)/(62+71) = 0.7293
z = ( p1 - p2) / sqrt(p * (1 -p) * (1/n1+1/n2))
= (0.6129 - 0.8310) /sqrt(0.7293 *(1-0.7293) * (1/62 + 1/71))
= -2.8240
h)
P value = 0.0023
i)
Conclusion:
We reject the null hypothesis. There is evidence at the .01 level that preschool reduces the need for social services later in life.
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