how long do you think it would take to actually sample, run and complete this Hy

Question

how long do you think it would take to actually sample, run and complete this Hypothesis Test?

A) At the .05 level of significance, test whether or not the average annual income of a NU student after taking Statistics 2 is the same as before taking Statistics 2. Assume the differences follow a normal distribution.

The Hypothesis Test has six steps:

1) State the Null Hypothesis and the Alternate Hypothesis. Since this test is about a student’s income after and before taking Statistics 2, then there exists a relationship or dependency between the two populations. The common thread or relationship is the actual student, whose annual income is earned both after and before taking Statistics 2.

TEST: Is µd = 0?

H0: µd = 0

H1: µd 0

2) State the level of significance. In this example, is .05 or 5%.

3) Take a sample of size n and calculate the sample statistics. In this example, let’s say, there is enough time and money to sample 36 NU students both after and before taking Statistics 2. Thus, n = 36 and includes only the matched-pair differences. The sample of matched pairs reveals a sample mean, d-bar, equal to $3,500 and a sample standard deviation, sd, equal to $450.

Remember that this is a matched-pair test. So, in calculating the sample mean, d-bar, for this test, we match Student 1’s annual income after taking Statistics 2, say $37,300, with his/her annual income before taking Statistics 2, say $36,250. This yields a matched-pair difference of +$1,050. This difference, +$1,050, is the first of 36 matched pairs observed in the sample. These 36 observations are used to calculate d-bar and the sample standard deviation, sd.

4) Determine the appropriate Test Statistic. There exists a t-Distribution, per Lecture 12, given the assumption of a normal distribution of differences and d is unknown. Thus, the Test Statistic is t with df = n -1 and is calculated as follows:

tn-1 = d-bar/(sd/sqrn)

t35 = $3,500/($450/6)

t35 = +46.67

5) Formulate the Decision Rule with the appropriate critical value(s). Since Ho and H1 are set up like A (= versus ) as shown in Lecture 7, then this is a two-tailed test with two critical values and two rejection of Ho regions located in both tails of the t-Distribution. Also, because the level of significance, , is .05 and there exist 35 degrees of freedom, df, the critical values in this t-Distribution are -2.030 and +2.030, which separate the acceptance of Ho region from the rejection of Ho regions. See Figure 1 at the end of this lecture for a graphical representation of the Decision Rule.

6) Make the decision on the Null Hypothesis by fitting the Test Statistic into the Decision Rule. Since the Test Statistic, t35 = +46.67, fits outside of the two critical values -2.030 and +2.030 and lies in the right or positive rejection of Ho region, the Null Hypothesis, Ho, is rejected and H1 is accepted. Thus, µd 0 and there is a significant difference in a student’s annual income after taking Statistics 2 at NU, at the .05 level of significance.

Actually, the estimate made by the statistician after running this Hypothesis Test is as follows: At the .05 level of significance, there is enough statistical evidence to refute the hypothesis that the average annual income of an NU student after taking Statistics 2 is the same as before taking Statistics 2.

NOTE: This matched-pair Hypothesis Test is much more powerful than one in which 36 students in the population before taking Statistics 2 is compared to 36 different students in the population after taking Statistics 2.

Explanation / Answer

For this matched pair t test, it is expected to take atleast 5 years to compute the average annual salary after taking job and obviously Statistics 2.

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.