A study was constructed to investigate hypnotism on success in math class. The values are the grade on a test before and after hypnosis for the same students. Student 1 2 3 4 5 6 Before 66 65 90 100 85 81 After 68 95 88 95 90 100 a. Fill in the row for ?? (you should use Lists on your calculator and not one at a time) b. State the null and alternative hypothesis:
A study was constructed to investigate hypnotism on success in math class. The
values are the grade on a test before and after hypnosis for the same students.
Student 1 2 3 4 5 6
Before 66 65 90 100 85 81
After 68 95 88 95 90 100
a. Fill in the row for ?? (you should use Lists on your calculator and not one at a time)
b. State the null and alternative hypothesis:
H0:_________________; HA:___________________________
Run the appropriate test on your calculator and use it to answer the following
c. The test statistic is: ______________________(include if this is a Z or T score)
d.The p-value is
e. The conclusion is: (either reject or fail to reject H0 based on a significance level of .05)
f. Write a sentence that explains what your conclusion means for the data.
(a). Obtain the paired differences:
Given information states that, the investigator has selected six students to test whether or not the hypnotism is effective on the success in math class.
The appropriate test-statistic to test a hypothesis regarding the significant difference between a paired set of n observations (xi, yi) is paired t-test statistic.
In order to achieve the paired t-test statistic, paired difference of all the n set of observations must be obtained.
Thus, in the given problem “Paired difference” is been tested.
Hence, the sampling distribution used in the given scenario is “Student’s t” by assuming that d has an approximately normal distribution.
The following table shows the paired differences:
(b). Null and alternate hypotheses:
The investigator is specifically interested to know if the hypnotism is effective on the success in math class.
Since, d = After – Before, the mean difference (After – Before) for the students (µd) would be positive if the hypnotism treatment is effective.
The null and alternate hypotheses are stated below:
Null hypothesis H0:
H0 : µd = 0
That is, there is no significant difference between the grades in math class before and after the hypnotism.
H1 : µd > 0
That is, the grades in math class are significantly increased after the hypnotism treatment.
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