PSYC 381:  Assignment #3

Z-test, Single Sample t-test, & Two Sample t-tests

  1. A researcher tests if the introduction of fluoride to the drinking water will significantly reduce the average number of cavities among children. Last year the average number of cavities was μ = 2.32, with σ = 0.46. This year fluoride was introduced. Thirty six children are sampled, and have an average of 2.07 cavities.  Using α = .05, test the hypothesis. Remember to follow the 4 steps of hypothesis-testing that were outlined in the lecture
  2. In the following studies (a and b) a single sample mean is being compared to a population with a known mean but an unknown variance. Determine what test to conduct for study a and for study b. Decide whether there is a significant difference between means. (If the df is not given in the table, use the t for the closest highest df value). Go through each step of the hypothesis testing procedure. Be sure to show all of your computations.
 

 

  

 

Sample

Size

(N)

  

 

Population

Mean

(μ)

  

 

Sample

Variance

(s2)

  

 

Sample

Mean

(M)

  

 

Tails

(1 or 2-tailed)

  

 

Significance Level

(α)
 

a.

  

44

  

12.35

  

9.00

  

11.00

  

1

(low predicted)

  

.05
 

b.

  

25

  

3.65

  

.40

  

4.01

  

2

  

.01

 

The next test need to be completed by hand and using SPSS – as always you need to follow the steps for testing hypotheses.

An experiment was performed to measure the effect of sleep deprivation on cognitive performance. Sixteen college juniors were randomly selected from a group of volunteers and arbitrarily assigned either to a sleep deprivation group or a control group. The participants in the sleep deprivation group were kept awake for 24 hours; the members of the control group had a normal night’s sleep. Participants were asked to perform a simple mental arithmetic task, and the time it took each participant to complete the task was recorded. The results were as follows:

Sleep Deprivation

Group

 Control

Group
11 13
15 8
13 14
5 11
16 2
20 2
21 17
13 5

 

Do these data indicate a significant difference between the treatments at the .05 level of significance?

  1. Calculate the test by hand. Make sure to follow Steps 1-4 of the hypothesis testing procedure. For hand calculations here is some additional information: Sleep Deprivation group: SS = 181.5; Control Group SS = 224.
  2. Enter the data into SPSS. Save the file as <question4_yourlastname.sav>. Upload the file using the Assignment tool.
  • In SPSS conduct the appropriate statistical test, and ask for descriptive statistics. Print the output, and annotate the printout.

To do this print the SPSS output, annotate directly on the sheet, scan and save as a PDF. You can then upload that to the final assignment document.

  • Submit a single PDF or .doc file that contains your
    hand calculations and your responses to all questions
    and the annotated SPSS output for Question 4.