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T test for independent samples

1. Find the Z -score and percentiles for the following calculations. Interpret your findings:
a) Distribution of scores:
Mean= 80
Standard Deviation=5
Scores are: X= 68, 75, 64 and 54

b) A researcher is testing a null hypothesis at the 0.05 level, would you accept or reject the null hypothesis?
Z= -2.30
Z= 0.78
Z= 1.98
Z= 1.70

c) The level of significance is at 0.05 level of significant. The mean is so
Large that it would occur by chance only 1% of the time. Should the researcher accepts or rejects the null hypothesis?
A) Accept
B) Reject

2. Test score on GRE exams are normally distributed with a mean of 80 and a SD of 20. List the Z scores that you would expect.

a) 68% of the scores is to fall____________ and ___________

b) 96% of the scores is to fall___________and____________

3. Two hundred students were evaluated using a particular scale. The results of the scale showed the mean of 80 and the SD of 5.

a) What is the standard error of the mean?

b) Set up a 95% confidence interval for the mean

c) Set up the 99% confidence interval for the mean

4. How is the null hypothesis often written_______________

a) The types of "error" are defined as _________________

b) The researcher would _____________ the null hypothesis if there are
no significant results.

b) The researcher would ______________ the null hypothesis if there
are significant results.

5. Please provide a statement about the following probabilities.
a) ( p <0.05)______________________________________________
b) ( p<0.01)_______________________________________________

6. List the two (2) types of "errors" that a researcher could make and explain what they mean.

7. Perform a Chi square test for the following 2X2 contingency table:

Parents' Report
Outside Help Neutral Negative Total

No 20 6 23
Yes 14 22 39
Total 34 28 62

a) State the degree of freedom (df)

* The level of significance is 0.05

b) Interpret the results in a statement.
c) Define Critical value______________________________________________

d) Define degree of freedom:__________________________________________

e) The Chi-square (X²) test is known as __________________________________

8. Correctly place the variables in a 2X 2 contingency table for 2 groups of babies born with Down syndrome total 120. One group is mildly retarded, total 40. The second group is severely retarded, total 80. Six (6) mildly retarded babies were born to mother under age 16. Sixty five (65) babies who are severely retarded were born to mother who are age 49 and over. Thirty four (34) babies who are severely retarded were born to mother age 16 and fifteen (15) babies who are mildly retarded were born to mother age 49 and over.

9. In a group of elderly in a community center, the nurse follows their blood pressure during an intervention with group exercise and eating. At the same time, there is another group that does not get the intervention. At the end here is what she finds:
81 in the experimental group: 55 show decrease in B/P, 26 show no improvement
75 in the control group do not get the intervention, 30 show improvement and 45 show no improvement.
a. Calculate the degrees of freedom
b. What is the chi square value?
c. Is there a significant difference between the groups? How do you know?
d. What probability (p value) did you use? Why did you use this one?
e. Write one sentence about what the findings mean.

10. t test

In a group of children with Attention Deficit, the nurse has permission to try a new intervention to see if it can help the kids focus and pay more attention in school. The first group (50 children) is given changes in diet (reduction in sugar and wheat) the other group (65 children) is placed on Ritalin. After 2 weeks the children are given the ADD assessment test. The t value is 8.2.

State the hypothesis in the null form
Is there a significant difference between the two groups?
What is the df?
Write a sentence about why you selected your answer
Write a complete sentence about the findings.


Pulse rate for (control group) Pulse rate for (Experimental group)
70 64
72 66
72 66
76 70
76 70
76 70
76 70
76 70
82 72
82 72
82 72
84 78
Situation: Use the t-test to examine the difference between a control group and an experimental group. The independent variable administered to the experimental group was a form of relaxation therapy. The dependent variable was pulse rate. Pulse rates for the experimental and control groups are presented above.

a. Perform the test for independent samples
b. Write the hypothesis in the null form.
c. Would you accept or reject the null hypothesis?
d. Write a statement to support the findings

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Solution Summary

The solution provides step by step method for the calculation of test statistics for T test . Formula for the calculation and Interpretations of the results are also included.