Question

I need some statistics help (this question got deleted)

A researcher hypothesizes that zylex, a new antidepressant, will affect concentration. It is known that scores on a standardized concentration test is normally distributed with a μ= 50 and a σ= 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 concentration?

Based on the above research scenario, please answer the following questions:

1. Name the population: ____________________________________

2. Name the sample: _______________________________

3. What is the independent variable? ________________

4. What is the dependent variable? _

_______________________

5. What is the appropriate hypothesis test? __________________

6. What two means are you comparing in this test? ____________________________

7. Please calculate the appropriate hypothesis test using all four steps:

Step 1:

Step 2:

Step 3:

Step 4: _______________________________

Write the statistical statement for your results: __________________________________

Interpret your results (relating back to the hypothesis): _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________

Is there a probability of Type I error? Yes ______ No ______ If yes, what is the probability of a Type I error? ________

Is yes, how could you have decreased that probability? __________________________________

Is there a probability of Type II error? Yes____ _ No______

If it is appropriate, please calculate effect size: Answer:________

Answer 1

please us the answer below!

1. The population is all participants aged 19-35 who may take zylex.
2. The sample is the 16 participants from New Jersey who took zylex.
3. The independent variable is the dosage plan of zylex.
4. The dependent variable is the standardized concentration test score.
5. The appropriate hypothesis test is a one-sample t-test.
6. The two means being compared are the population mean (μ=50) and the sample mean (M=56).
7.
Step 1: State the null hypothesis and the alternative hypothesis.
Null hypothesis: The six-month dosage plan of zylex has no effect on concentration. μ = 50
Alternative hypothesis: The six-month dosage plan of zylex has an effect on concentration. μ ≠ 50

Step 2: Determine the level of significance (α).
Assuming a 95% confidence level, α = 0.05

Step 3: Determine the test statistic and p-value.
Using a t-distribution with 15 degrees of freedom (n-1), the critical values for a two-tailed test at α = 0.05 are t = ±2.131. The sample mean is M=56, the population mean is μ=50, and the standard deviation is σ=12. The standard error is calculated as σ/√n = 3.0. The t-value is (56-50)/3.0 = 2.0. The p-value for a two-tailed test with t=2.0 and 15 degrees of freedom is approximately 0.06.

Step 4: Make a decision and interpret the results.
Since the calculated t-value of 2.0 does not fall outside the critical values of ±2.131, we fail to reject the null hypothesis. The p-value of 0.06 is greater than the level of significance of 0.05. Therefore, we cannot conclude that zylex has an effect on concentration based on this sample.

The statistical statement for the results is: t(15) = 2.0, p > 0.05.

There is a probability of Type I error, which is the probability of rejecting the null hypothesis when it is actually true. The probability of Type I error is equal to α, which is 0.05 in this case. To decrease the probability of Type I error, we could decrease the level of significance or increase the sample size.

There is also a probability of