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.
then vertex is max value
then vertex is min value
