✔ 最佳答案
(1) H0: There is no difference between the mean scores of two classes.
H1: Reject H0
Since σ_1^2 and σ_2^2 are unknown and there is no reason to assume that they are equal. So, we will using the test statistic
Test-statistic
=[(78-77.2)-0]/√(1.8^2/36+2^2/32)
=1.7253 < 1.96
with degree of freedom=62.8516
(refer to the formulas given in table 5.2.2)
http://www.acad.polyu.edu.hk/~machanck/lectnotes/c5_hypo.pdf
So, we can use the normal distribution and conclude that there is no significant evidence to reject H0 at 5% level of significance.
(2) The p-value is 0.042237*2=0.084474. It means that under the hypothesis μ_1= μ_2, there is a probability of 0.084474 to appear the experiment. So, if we set type I error (Reject H0 but actually it is true) at 5%. Then we will not reject H0. However, it we set α=10%. Then we will prefer H1.
(ii) The differences between the stores are
-0.1 1 0.15 0.1 0.2 0.6 0.2 0.4 -0.1 0.2
mean=0.65, standard deviation=0.76974
H0: The mean of difference is larger than 0
H1: reject H0
Test statistic: (0.65-0)/(0.76974/√10)=2.6704
with degree of freedom 10-1=9
Since 2.6704 > 1.833 (p-value=0.0128) , reject H0 and conclude that the strategy can increase the sales.
