Question

These weekly exercises provide the opportunity for you to understand and apply statistical methods and analysis. Unless otherwise stated, use 5% (.05) as your alpha level (cutoff for statistical significance).

#1. Define "power" in relation to hypothesis testing.

#2. Alpha (a) is used to measure the error for decisions concerning true null hypotheses. What is beta (ß) error used to measure?

#3. In the following studies, state whether you would use a one-sample t test or a two-independent-sample t test.

1. A study testing whether night-shift workers sleep the recommended 8 hours per day
2. A study measuring differences in attitudes about morality among Democrats and Republicans
3. An experiment measuring differences in brain activity among rats placed on either a continuous or an intermittent reward schedule

Use SPSS and the data file found in syllabus resources (DATA540.SAV) to answer the following questions. Round your answers to the nearest dollar, percentage point, or whole number.  

Log onto:

https://learners.calsouthern.edu/common/file.aspx?form=syllabus_resource&id=134900

user name Zeenat.Pasha

Password    Healthwealth19

click on course

click left (Resources)

Open Data File 540SAV

#4. Test the age of the participants (AGE1) against the null hypothesis H₀ = 34. Use a one-sample t-test. How would you report the results?

a.         t = -1.862, df = 399, p > .05
b.         t = -1.862, df = 399, p < .05
c.         t = 1.645, df = 399, p > .05
d.         t = 1.645, df = 399, p < .05

#5. What is the mean and standard deviation for the Lifestyle score (L)?

a. 31.22, 7.99
b. 36.19, 8.54
c. 30.03, 7.28
d. 55, 13

#6. The first case shown in the data file is a firefighter with a financial Risk-Taking score (R) of 38. What is his Risk-Taking z-score (hint: you will need to find the Risk-Taking mean and standard deviation)?

a. 0.179
b. -0.223
c. 1.342
d. -1.223

#7. Perform independent sample t-tests on the Lifestyle, Dependency, and Risk-Taking scores (L, D, and R) comparing men and women (GENDER1). Use p < .05 as your alpha level and apply a two-tailed test. On each of the three scales, do men or women have a significantly higher score?

a. Lifestyle: Men, Dependency: Women, Risk-Taking: Men.
b. Lifestyle: Not significantly different, Dependency: Women, Risk-Taking: Men
c. Lifestyle: Women, Dependency: Women, Risk-Taking: Men
d. Lifestyle: Men, Dependency: Men, Risk-Taking: Not significantly different

#8. The median US salary is $50,700, according to US Census data. Using a one-sample t-test, test to see if participant income (INC1) is different from the national average. Use a two-tailed test and an alpha level of 5%.

1. Participant income is significantly greater than the national average
2. Participant income is significantly less than the national average
3. Participant income is not significantly different from the national average
4. Participant income cannot be compared to the national average

Answer 1

Solution:

1) Power in relation to hypothesis testing :

In hypothesis testing power is define as the probability of making a correct decision. Power is the probability of rejecting the null hypothesis when it is false (not true). We know that type II error is the error, committed by not rejecting the null hypothesis when it is not true. And the probability of type II error is known as β. So, we can write it as follows:

β = Prob (not rejecting H_{​​​​​​0} when it is not true)

Hence, (1 - β) =  Prob ( rejecting H_{​​​​​​0} when it is not true)

So, Power is given by (1 - β) i.e. 1 - Prob (type 2 error). It means as the β decreases, the power increases.

2)  β is used to measure the error for decisions concerning false null hypothesis. β is defined as the probability of type II error. And the type II error is the error committed by not rejecting the null hypothesis when it is not true. It means β is used to measure the error for decisions concerning the false null hypothesis. Also (1 - β) is known has power of the test means with the help of β we can measure the power of the test.

3) a. In a study testing whether night-shift workers sleep the recommended 8 hours per day, we shall use one-sample t-test. Here we want to test whether population mean is equal to a hypothetical value or not. Therefore, one-sample t-test will be used.

b. In a study measuring differences in attitudes about morality among Democrats and Republicans, we shall use two-independent-sample t test. Here we have two independent samples one is from Democrats population and other is from Republican population and we want to test that if there is any difference between attitudes about morality among Democrats and Republican or not i.e. we want to test the equality of two population means. To test the equality of two population means we use two-independent-sample t test. Hence, here two-independent-sample t test will be used.

c. In an experiment measuring differences in brain activity among rats placed on either a continuous or an intermittent reward schedule, we shall use two-independent-sample t test. Here, we have two groups of rats one is placed on continuous reward schedule and other is placed on intermittent reward schedule and we want to test if there is any difference between the brain activity of rats in both the groups or not i.e. we want to test the significance of the difference between two sample means. To test the significance of the difference between two sample means we use two-independent-sample t test. Hence, here two-independent-sample t test will be used.