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# T test for independent samples

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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.

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 complete sentence about the findings.

11.

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

https://brainmass.com/statistics/students-t-test/t-test-for-independent-samples-218789

#### 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.

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## Independent sample t test

A manufacturer claims that the mean lifetime of its fluorescent bulbs is 1050 hours. A homeowner
selects 40 bulbs and finds the mean lifetime to be 1030 hours with a standard deviation of 80 hours.
Test the manufacturer's claim. Use &#945; = 0.05

1. State H0
2. State Ha
3. What is the claim?
4. What is the critical value?
5. What is the standardized test statistic?
6. What is the decision?

A local politician, running for reelection claims the mean prison time for car thieves is less than the required four years. A sample of 80 convicted car thieves was randomly selected and the mean length of prison time was found to be 3.5 years with a standard deviation of 1.25 years. At &#945; = 0.05 test the politician's claim.

7. State H0
8. State Ha
9. What is the claim?
10. What is the critical value?
11. What is the standardized test statistic?
12. What is the decision?

A local brewery distributes beer in bottles labeled 12 ounces. A government agency thinks the brewery is cheating its customers. The agency selects 20 of these bottles and measures their contents and obtains a mean of 11.7 ounces with a standard deviation of 0.7. At &#945; = 0.01 test the claim.

13. State H0
14. State Ha
15. What is the claim?
16. What is the critical value?
17. What is the standardized test statistic?
18. What is the decision?
A medical researcher suspects that the pulse rate of smokers is higher than the pulse rate of non-smokers. Used the sample statistics below to test the researcher's suspicion. Use &#945; = 0.05

Smokers Nonsmokers
n1 = 100 N2 = 100
x bar1 = 84 X bar2 =81
S1 = 4.8 S2= 5.3

19. State H0
20. State Ha
21. What is the claim?
22. What is the critical value?
23. What is the standardized test statistic?
24. What is the decision?

At &#945; = 0.05, test a financial advisor's claim that the difference between the mean dividend rate for listings in the NYSE market and the mean dividend rate for listing in the NASDAQ market is more than 0.75. The sample statistics from randomly selected listings from each market are listed below.

NYSE NASDAQ
n1 = 30 n2 = 50
x bar1 = 2.75% x bar2 =1.66%
S1 = 1.44% S2= 0.63%

25. State H0
26. State Ha
27. What is the claim?
28. What is the critical value?
29. What is the standardized test statistic?
30. What is the decision?

31. Construct a 95% confidence interval for µ1 - µ2. Two samples are randomly selected from each
population . The sample statistics are given below.

n1 = 40 n2 = 35
x bar1 = 12 x bar2 =13
S1 = 2.5 S2= 2.8

A study was conducted to determine if the salaries of elementary school teachers from two neighboring districts are equal. A sample of 15 teachers from each school district was randomly selected. The mean from the first district was \$28,000 with a standard deviation of \$2,300. The mean from second school district was \$30,300 with a standard deviation of \$2,100. Test the claim that the salaries from both district are equal. Assume the variances are equal. Use &#945; = 0.05.

32. State H0
33. State Ha
34. What is the claim?
35. What is the critical value?
36. What is the standardized test statistic?
37. What is the decision?

A local bank claims that the waiting time for its customers to be served is the lowest in the area. A competitor's bank checks the waiting time at both banks. The sample statistics are listed below. Test the local bank's claim assuming the variances are not equal. Use &#945; = 0.05.

Local Bank Competitor Bank
n1 = 15 n2 = 16
x bar1 = 5.3 minutes x bar2 =5.6 minutes
S1 = 1.1 minutes S2= 1.0 minutes

38. State H0
39. State Ha
40. What is the claim?
41. What is the critical value?
42. What is the standardized test statistic?
43. What is the decision?

A manager wishes to determine the relationship between the number of miles (in hundreds of miles) the manager's sales representatives travel per month and the amount of sales (in thousands of dollars) per month.

Miles traveled, x 3 4 4 5 3 6 2 7 3
Sales, y 31 33 78 62 65 61 48 55 120

44. Find the linear regression.
45. Find the correlation coefficient.
46. Find the amount of sales if a sales rep traveled 10 miles.
47. If a sales rep made 80 in sales how many miles had they traveled?
The data below are the final exam scores of 10 randomly selected statistics students and the number of hours they studied for the exam.

Hours, x 3 5 2 8 2 4 4 5 6 3
Scores, y 65 80 60 88 66 78 85 90 90 71

48. Find the linear regression.
49. Find the correlation coefficient.
50. What grade did a student make if they studied 7 hours?
51. If a student made a 100 on the test how many hours had they studied?

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