AS2 (Assignment 2, Unit 4): Computing the Z-test Statistic Research Scenario #1
ID: 3045830 • Letter: A
Question
AS2 (Assignment 2, Unit 4): Computing the Z-test Statistic Research Scenario #1 A researcher hypothesizes that zylex, a new antidepressant, will affect concentration. It is known that scores on a standardized concentration test is normaly distributed with a 50 and a = 12. A random sample of n 16 participants, aged 19-35, are chosen from the State of New Jersey The sample is put on a six month dosage plan of zylex. After six months, all the participants are given a standardized concentration test. The researcher records the data and calculates a sample mean of M-56. Are the data sufficient to conclude that the drug. zylex, does have an effect on concenration? Based on the above research scenario, please answer the following questions 1. What is the appropriate hypothesis test? 2. What two means are you comparing in this test? 3. Please calculate the appropriate hypothesis test using all four steps: Step 1: Step 2: Step 3Explanation / Answer
Solution:-
1)
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: < 50
Alternative hypothesis: > 50
Note that these hypotheses constitute a one-tailed test.
2)
We are comparing population mean, = 50 and the sample mean xbar = 56.
3)
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = s / sqrt(n)
S.E = 3
DF = n - 1
D.F = 15
t = (x - ) / SE
t = 2.0
where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.
The observed sample mean produced a t statistic test statistic of 2.0.
Thus the P-value in this analysis is 0.032.
Interpret results. Since the P-value (0.032) is less than the significance level (0.05), we have to reject the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that the treatment is effective in increasing concentration level.
Yes there is a probability of type I error.
The probability iof type I error is 0.05.
We can decrease the probability of type I error by decreasing the level of significance.