**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
S_{x} = 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 H_{o}
and H_{a} 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) |