Answer:
A 90% confidence interval to estimate the mean DRP score in Henrico County Schools is =32±2.7280
i.e. C.I. [29.3,34.7]
Hence the results are not significant.
Step-by-step explanation:
Given:
Total no of students =44
True mean =32
Standard deviation=11
And all 4 students score also given.
To Find:
90 % confidence interval and conclusion on it.
Solution:
Here for C.I. we required mean, standard deviation and no of students.
So mean =32,S.D.=11 and n=44
Therefore , For 90 % interval Zscore is Z=1.645
C.I.=mean±Z[Standard deviation/Sqrt(n)]
=32±1.645[11/Sqrt(44)]
=32±1.645[1.6583]
=32±2.7280
i.e. C.I. [29.3,34.7]
Now Here to commit on calculated interval we should check value of Z-score
So we need to calculate the sample mean.
Sample mean =Sum of all values /Total no of values.
=[40+ 26 +39+ 14+ 42+ 18 +25+ 43+ 46 +27 +19+ 47+ 19 +26+ 35 +34+ 15+ 44 40+ 38+ 31+ 46 +52 +25+ 35 +35+ 33 +29 +34 +41 +49+ 28+ 42+ 47 +35 +48 +22 33+ 41 +51 +27 +14+ 54 +45]/44
=34.86
Z-score=(sample mean -true mean)/[standard deviation/Sqrt(n)]
=(34.86-32)/[11/Sqrt(44)]
Z=1.72465
For ,
P(Z≥1.72465)=0.08544
For 0.05 significance level the results are not significant at p<0.01.
Researcher claimed mean is not correct upto 0.05 significant level
i.e calculated mean and Sample mean are different.
Hence the results are not significant.
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