都係統計學 - Ans.fyi 參考答案

都係統計學

2007-04-03 10:28 am

Question 2:
An examination was given to two classes comprising 40 and 50 students respectively. In the first class, the mean mark was 74 with a standard deviation of 8, while in the second class, the mean mark was 78 with a standard deviation of 7. Is there any significant difference between the performance of the two classes at a level of significance of (i) 5% and (ii) 1%?

回答 (1)

匿名

2007-04-03 5:33 pm

✔ 最佳答案

sample mean x_bar1=74, standard deviation 1 =8, n1=40
sample mean x_bar2=78, standard deviation 2 =7, n2=50

null hypothesis: E(x1)-E(x2)=0
alternative: E(x1)-E(x2) not equal to 0

Since standard deviations are known, compute Z

Z=[(x_bar1-x_bar2)-(E(x1)-E(x2))]/ sqrt{[(standard deviation 1)^2/n1]+[(standard deviation 2)^2/n2]}

Z=[74-78-0]/ sqrt[(64/40) + (49/50)]
= -4/ sqrt(2.58)
= -2.49

(i) significant level=5% (2-sided or 2-tail)
critical value= +/-1.96
|Z| = 2.49 > 1.96
reject null hypothesis.
so there is significant difference between the performance of the two classes if level of significance is 5%.

(ii) significant level=1% (2-sided or 2-tail)
critical value= +/- 2.575
|Z| = 2.49 < 2.575
not reject null hypothesis, that is, (E(x1)-E(x2))=0
so no significant difference between the performance of the two classes if level of significance is 1%.

參考: myself

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