Elementary Statistics
3rd Edition
ISBN: 9781260373561
Author: Navidi, William
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Question
Chapter 15.2, Problem 11E
a.
To determine
To find:The hypothesis for the test statistic.
a.
Expert Solution
Answer to Problem 11E
The hypothesis are
Explanation of Solution
Given information:
The level of significance is
| Compact | ||||
| 34.5 | 33.7 | 26.1 | 28.5 | 27.4 |
| 30.6 | 31.1 | 28.0 | 33.0 | 33.0 |
| 32.8 | 28.5 | 25.5 | 32.1 | 34.9 |
| Midsize | ||||
| 21.6 | 21.1 | 29. 1 | 24.8 | 28.5 |
| 28.1 | 21.9 | 22.5 | 20.5 | 26.1 |
Calculations:
The hypothesis are,
Therefore, the hypothesis are
b.
To determine
To find:The value of test statistic.
b.
Expert Solution
Answer to Problem 11E
The value of test statistic is
Explanation of Solution
Given information:
The level of significance is
| Compact | ||||
| 34.5 | 33.7 | 26.1 | 28.5 | 27.4 |
| 30.6 | 31.1 | 28.0 | 33.0 | 33.0 |
| 32.8 | 28.5 | 25.5 | 32.1 | 34.9 |
| Midsize | ||||
| 21.6 | 21.1 | 29. 1 | 24.8 | 28.5 |
| 28.1 | 21.9 | 22.5 | 20.5 | 26.1 |
Calculations:
The rank table is shown below.
| Gas mileages | Sample | Rank |
| 20.5 | Midsize | 1 |
| 21.1 | Midsize | 2 |
| 21.6 | Midsize | 3 |
| 21.9 | Midsize | 4 |
| 22.5 | Compact | 5 |
| 24.8 | Midsize | 6 |
| 25.5 | Compact | 7 |
| 26.1 | Midsize | 8.5 |
| 26.1 | Compact | 8.5 |
| 27.4 | Compact | 10 |
| 28 | Compact | 11 |
| 28.1 | Midsize | 12 |
| 28.5 | Midsize | 14 |
| 28.5 | Compact | 14 |
| 28.5 | Compact | 14 |
| 29.1 | Midsize | 16 |
| 30.6 | Compact | 17 |
| 31.1 | Compact | 18 |
| 32.1 | Compact | 19 |
| 32.8 | Compact | 20 |
| 33 | Compact | 21.5 |
| 33 | Compact | 21.5 |
| 33.7 | Compact | 23 |
| 34.5 | Compact | 24 |
| 34.9 | Compact | 25 |
The sum of rank of compact car is
The sum of smaller rank is
The value of
Substitute the values in above equation.
The value of
Substitute the values in above equation.
The z- value is,
Substitute the values in above equation.
Therefore, the value of test statistics is
c.
To determine
To find:The p-value.
c.
Expert Solution
Answer to Problem 11E
The p-valueis
Explanation of Solution
Given information:
The level of significance is
| Compact | ||||
| 34.5 | 33.7 | 26.1 | 28.5 | 27.4 |
| 30.6 | 31.1 | 28.0 | 33.0 | 33.0 |
| 32.8 | 28.5 | 25.5 | 32.1 | 34.9 |
| Midsize | ||||
| 21.6 | 21.1 | 29. 1 | 24.8 | 28.5 |
| 28.1 | 21.9 | 22.5 | 20.5 | 26.1 |
Calculations:
From the table of cumulative
Therefore, the p-value is
d.
To determine
To find:The conclusion for the test.
d.
Expert Solution
Answer to Problem 11E
The median mileage is less for compact car than for the midsize car.
Explanation of Solution
Given information:
The level of significance is
| Compact | ||||
| 34.5 | 33.7 | 26.1 | 28.5 | 27.4 |
| 30.6 | 31.1 | 28.0 | 33.0 | 33.0 |
| 32.8 | 28.5 | 25.5 | 32.1 | 34.9 |
| Midsize | ||||
| 21.6 | 21.1 | 29. 1 | 24.8 | 28.5 |
| 28.1 | 21.9 | 22.5 | 20.5 | 26.1 |
Calculations:
Since, the p-value is
Thus, the hypothesis
Therefore, the median mileage is less for compact car than for the midsize car.
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1- Let A = {A1, A2, ...), in which A, A, = 0, when i j.
a) Is A a π-system? If not, which element(s) should be added to A to become a π-system?
b) Prove that σ(A) consists of the finite or countable unions of elements of A; i.c., A E σ(A) if and
only if there exists finite or countable sequence {n} such that A = U₁An (Hint: Let F be such
class; prove that F is a σ-filed containing A.)
c) Let p ≥ 0 be a sequence of non-negative real numbers with Σip₁ = 1. Using p₁'s, how do you
construct a probability measure on σ(A)? (Hint: use extension theorem.)
2- Construct an example for which P(lim sup A,) = 1 and P(lim inf An) = 0.
In a town with 5000 adults, a sample of 50 is selected using SRSWOR and asked their opinion of a proposed municipal project; 30 are found to favor it and 20 oppose it. If, in fact, the adults of the town were equally divided on the proposal, what would be the probability of observing what has been observed? Approximate using the Binomial distribution. Compare this with the exact probability which is 0.0418.
Chapter 15 Solutions
Elementary Statistics
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