Essential Statistics for the Behavioral Sciences
2nd Edition
ISBN: 9781506386300
Author: Gregory J. Privitera
Publisher: SAGE Publications, Inc
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Chapter 4, Problem 5FP
To determine
To explain:
Thedegree of freedom for the sample variance.
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Let X1, X2, and X3 represent the times necessary to perform three successive repair tasks at a certain service facility. Suppose they are independent, normal rv's with expected values μ₁, μ₂, and μ3 and variances σ₁ ², σ22, and σ32, respectively. (Round
your answers to four decimal places.)
USE SALT
02
(a) If μ₁ = μ₂ = μ3 = 80 and σ.
2
101°
=
2 =
02
03
2
=
15, calculate P(T ≤ 255) and P(210 ≤ To ≤ 255).
P(T ≤ 255)
= 0.5944
P(210 ≤ To ≤ 255) =
(b) Using the μ's and σ's given in part (a), calculate both P(75 ≤ X) and P(78 ≤ X ≤ 82).
(c)
P(75 ≤ X)
P(78 ≤ X ≤ 82)
S
=
=
Using the μ's and σ's given in part (a), calculate P(-10 ≤ X₁ - 0.5X2 - 0.5X3 ≤ 5).
-
P(-10 ≤ X₁ = 0.5X2 - 0.5X3 ≤ 5)
S =
Interpret the quantity P(-10 ≤ X₁1 - 0.5X2 - 0.5X3 ≤ 5).
(d)
If μ1
The quantity represents the probability that X1, X2, and X3 are all between -10 and 5.
The quantity represents the probability that the difference between ✗₁ and the average of X2 and X3 is between -10 and 5.
○ The quantity represents the…
Suppose a company sells bacon in packages that they claim average a weight of 12 ounces. Timothy believes that the actual
average weight of the packages is different than what the company claims, and would like to test this using a significance level of
0.01. He takes a random sample of 31 packages and gets a sample mean of 12.49 ounces and a sample standard deviation of 1.02
ounces.
a) What are the null and alternative hypotheses?
Ho: μ
÷
== 12
÷
HA: M
=
± =
12
b) What is the test statistic? (Round your answer to 3 decimal places, if needed.)
2.678
Your last answer was interpreted as follows:
2.678
c) Using the statistical table, the p-value is 0.01 < p-value < 0.02 →
d) Based on the p-value, Timothy should fail to reject ✰ the null hypothesis.
e) This data does not provide
sufficient evidence to conclude that the actual average weight of the packages is
different from → what the company claims.
Check
The Office of Student Affairs receives numerous appeals from students seeking reevaluation of their enrollment status. The office has observed that, on average, 30% of appeals are successful. Suppose the office has recently received 15 appeals.
Calculate the probability that none of the appeals will be successful.
Determine the probability that exactly three appeals will be successful.
Find the probability that at least two appeals will be successful. At least two appeals means P(x≥2).
Compute the probability that less than half of the appeals will be successful. Less than half means P(x<8) or P(x≤7).
Chapter 4 Solutions
Essential Statistics for the Behavioral Sciences
Ch. 4 - Prob. 1FPCh. 4 - Prob. 2FPCh. 4 - Prob. 3FPCh. 4 - Prob. 4FPCh. 4 - Prob. 5FPCh. 4 - Prob. 6FPCh. 4 - Prob. 7FPCh. 4 - Prob. 8FPCh. 4 - Prob. 9FPCh. 4 - Prob. 10FP
Ch. 4 - Prob. 11CAPCh. 4 - Prob. 12CAPCh. 4 - Prob. 13CAPCh. 4 - Prob. 14CAPCh. 4 - Prob. 15CAPCh. 4 - Prob. 16CAPCh. 4 - Prob. 17CAPCh. 4 - Prob. 18CAPCh. 4 - Prob. 19CAPCh. 4 - Prob. 20CAPCh. 4 - Prob. 21CAPCh. 4 - Prob. 22CAPCh. 4 - Prob. 23CAPCh. 4 - Prob. 24CAPCh. 4 - Prob. 25CAPCh. 4 - Prob. 26CAPCh. 4 - Prob. 27CAPCh. 4 - Prob. 28CAPCh. 4 - Prob. 29PRCh. 4 - Prob. 30PRCh. 4 - Prob. 31PRCh. 4 - Prob. 32PR
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