Broward Community College

Math Dept.

Statistics STA2023

Example of Test # 4

  WRITE THE NAME OF THE PROGRAM YOU ARE USING

1-) A team of eye surgeons has developed a new technique for a risky eye operation to restore the sight of people blinded from a certain disease. Under the old method, it is known that only 30% of the patients who undergo this operation recover their eyesight.

     Suppose that surgeons in various hospitals have performed a total of 225 operations using the new method and that 88 have been successful (the patients fully recovered their sight). Can we justify the claim that the new method is better than the old one? (Use a 1% level  of significance.)

 

2-) The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitude toward school, and study habits of students. Scores range from 0 to 200. The mean score for U.S. college students is about 115, and the standard deviation is about 30. A teacher who suspects that older students have better attitudes toward school gives the SSHA to 20 students who are at least 30 years of age. Their mean score is x = 135.2.

Assuming that σ = 30 for the population of older students, carry out a test of :

                                                                   Ho: μ = 115

                                                                   Ha: μ  > 115

Report the P-value of your test, and state your conclusion clearly.

 3-) Consumer Reports indicated that the mean acceleration time(0 to 60 miles per hour) for the Dodge Intrepid was 10.2 seconds. In most tests of this type, regular unleaded gasoline is used. Suppose that 41 such tests were made using premium unleaded gasoline (octane over 91), and the sample mean acceleration time (0 to 60 miles per hour) was x = 9.7 seconds with sample standard deviation Sx = 2.1 seconds. Does this indicate that premium gasoline tends to reduce average acceleration time (0 to 60 miles per hour)? Use α =0.05.

 

 4-) Here are the Degree of Reading Power (DRP) scores for an Simple Random Sample(SRS) of 44 third-grade students from a suburban school district:

.

40

26

39

14

42

18

25

43

46

27

19

47

19

26

35

34

15

44

40

38

31

46

52

25

35

35

33

29

34

41

49

28

52

47

35

48

22

33

41

51

27

14

54

45

 

DRP scores are approximately normal. The researcher believes that the mean score μ of all third graders in this district is higher than the national mean, which is 32.

(a)     State Ho and Ha to test this suspicion.

(b)     Carry out the test.

 

5-) Use a 0.01 significance level to test the claim that weights of female supermodels vary less than the weights of women in general. The standard deviation of weights of the population of women is 29 lb. Listed below are the weights ( in pounds) of nine randomly selected supermodels.

125 (Taylor) 119 (Auermann) 128 (Schiffer)
128 (MacPherson) 119 (Turlington) 127 (Hall)
105 (Moss) 123 (Mazza) 115 (Hume)

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