Q24 Historically, biology has been taught through lectures, and assessment of le

Question

Q24 Historically, biology has been taught through lectures, and assessment of learning was accomplished by testing vocabulary and memorized facts. A teacher-developed new curriculum called "Biology: A Community Co (BACC) is standards based, ac- tivity oriented, and inquiry centered. Students taught using the historical and new methods were tested n the traditional sense on biology concepts that featured bio- logical knowledge and process skills. The results of a test on biology concepts were publish in the The American Biology Teacher and are given the following table Sample Standard Mea Size Deviation 5.59 Pretest: all BACC classes 13.38 372 Pretest: all traditional Posttest: all BACC classes 18.50 365 Posttest: traditina 16.50 298 14.06 368 8.03 6.96

Explanation / Answer

a.
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=13.38
Standard deviation( sd )=5.59
Sample Size(n)=372
Confidence Interval = [ 13.38 ± t a/2 ( 5.59/ Sqrt ( 372) ) ]
= [ 13.38 - 1.649 * (0.29) , 13.38 + 1.649 * (0.29) ]
= [ 12.902,13.858 ]

b.
CI = x1 - x2 ± t a/2 * Sqrt ( sd1 ^2 / n1 + sd2 ^2 /n2 )
Where,
x1 = Mean of Sample 1, x2 = Mean of sample2
sd1 = SD of Sample 1, sd2 = SD of sample2
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x1)=13.38
Standard deviation( sd1 )=5.59
Sample Size(n1)=372
Mean(x2)=14.06
Standard deviation( sd2 )=5.45
Sample Size(n2)=368
CI = [ ( 13.38-14.06) ±t a/2 * Sqrt( 31.2481/372+29.7025/368)]
= [ (-0.68) ± t a/2 * Sqrt( 0.1647) ]
= [ (-0.68) ± 1.966 * Sqrt( 0.1647) ]
= [-1.4779 , 0.1179]

c.
Interpretations:
1) We are 95% sure that the interval [-1.4779 , 0.1179] contains no difference between
true population mean U1 - U2, as zero lies b/w those
2) If a large number of samples are collected, and a confidence interval is created
for each sample, 95% of these intervals will contains the difference between
true population mean U1 - U2
3) Since this Cl does contain a zero we can conclude at 0.01 true mean
difference is zero  

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