only have to do 12 , 14 and #11 on the other file

12.Answer
Step1: State the null and alternative hypothesis.
0
H
: The mean recovery time for those receiving the new treatment are equal to the mean those receiving the standard treatment.
:
0
H
µ1 = µ2
1
H
: The mean recovery time for those receiving the new treatment is less than the mean those receiving the standard treatment.
:
a
H
µ1 < µ2
Step 2: Select the distribution to be use and determine the rejection regions.
The standard deviations of the two populations are unknown and assumed to be equal. The sample size for each brand is not significantly large. Consequently we use the t – distribution to make the test.
Determine the rejection regions.
The < sign in the alternative hypothesis indicates that the test is one tailed.
The significance level is, α = 0.05, Hence,
Area in each tail = α = 0.05
The degree of freedom is given by n1 + n2 – 2 = 7+7-2 = 12
The critical value at degrees of freedom 12 and level of significance 0.05 is -1.782
Rejection region: Reject null hypothesis, if |t| < -1.782
Step 3: Calculate the value of the test Statistic.
Given:
    Treatment
    Control
     
    17.71
    28.71
    mean
    4.46
    7.39
    std. dev.
    7
    7
    n
The value of the test statistic t for
1
X
-
2
X
is computed as;
S p=...