The likelihood of not rejecting the null hypothesis when the null hypothesis is false is ß, the probability of a type II error. The likelihood of rejecting the null hypothesis when the null hypothesis is false is then 1-6. significance level a, - (mp,+ n₂), (m + n) Refer to the formula for ß as a function of proportions p₁ and P2, where Za/2 is the critical value based PL^,:03) = 0 [²×2√³3 (2+ + +) -10₂ - P2)] - •[-².²√(³ (+ + +) - (0₂ - 02₂)] 0 J Given a 0.01, the critical value for this calculation is Za/220.005- Use the table standard normal curve areas to determine the critical value, rounded to two decimal places. Za/2 20.005 Calculate p using p₁ = 0.50, P₂0.25, and m = n = 100. 5 = (mp₁ + np₂) (m + n) 0.5(100)+1 9- 100 100 Calculated using p₁ -0.50, P₂0.25, and m-n-100, where d₁1-P₁ and 4₂1-P₂¹ (ma,+ na₂) (m + n) (10.5)(100) + (1 -[ a (100) 100 + 100 Calculate , rounding the result to five decimal places. P11+ P₂92 m n 0.50(1-0.50) 0.25(1- 100 (100) 100 0191 292 (ma₁ + a₂), m and in are the sample sizes of Brand A and Brand B samples, respectively, and o-191 (m + n)
The likelihood of not rejecting the null hypothesis when the null hypothesis is false is ß, the probability of a type II error. The likelihood of rejecting the null hypothesis when the null hypothesis is false is then 1-6. significance level a, - (mp,+ n₂), (m + n) Refer to the formula for ß as a function of proportions p₁ and P2, where Za/2 is the critical value based PL^,:03) = 0 [²×2√³3 (2+ + +) -10₂ - P2)] - •[-².²√(³ (+ + +) - (0₂ - 02₂)] 0 J Given a 0.01, the critical value for this calculation is Za/220.005- Use the table standard normal curve areas to determine the critical value, rounded to two decimal places. Za/2 20.005 Calculate p using p₁ = 0.50, P₂0.25, and m = n = 100. 5 = (mp₁ + np₂) (m + n) 0.5(100)+1 9- 100 100 Calculated using p₁ -0.50, P₂0.25, and m-n-100, where d₁1-P₁ and 4₂1-P₂¹ (ma,+ na₂) (m + n) (10.5)(100) + (1 -[ a (100) 100 + 100 Calculate , rounding the result to five decimal places. P11+ P₂92 m n 0.50(1-0.50) 0.25(1- 100 (100) 100 0191 292 (ma₁ + a₂), m and in are the sample sizes of Brand A and Brand B samples, respectively, and o-191 (m + n)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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step 7
![The likelihood of not rejecting the null hypothesis when the null hypothesis is false is ß, the probability of a type II error. The likelihood of rejecting the null hypothesis when the null hypothesis is false is then 1 - ß.
(ma₁ + nq₂)
(m + n)
Refer to the formula for 8 as a function of proportions p₁ and P₂, where Z₁/2 is the critical value based on significance level a, p = (mp₁ + np₂), ā=.
z
(m + n)
862, 103) - + [²^ 2 √(- 3 (2+ + 2 ) – (0, - ²3)] -
√(³ 3 (²+ + ² ) - 10₁ - ³₂³)] _ •
B(P₁, P₂) = $
²a/2√
(P₁-P₂)
Calculate p using p₁ = 0.50, P₂ = 0.25, and m = n = 100.
(mp₁ + np₂)
(m + n)
0.5(100) +
p=
=
a
Given α = 0.01, the critical value for this calculation is Za/2=Z0.005. Use the table of standard normal curve areas to determine the critical value, rounded to two decimal places.
Za/2= ²0.005
0 =
100 + 100
P2
Calculated using p₁ -0.50, P₂ = 0.25, and m = n = 100, where a₁ = 1- P₁ and q₂ = 1 - P₂¹
9=
(ma₁ + ng₂)
(m + n)
(1 - 0.5)(100) + (1 -
+
100 + 100
Calculate σ, rounding the result to five decimal places.
P191
P292
m
n
(100)
0.50(1-0.50)
100
+
0.25(1-[
[ -5-²2√/
[-², 2√/³3 (+ + +) - 6 - 2³
(01
P2) ]
Ō
(100)
100
1
m and n are the sample sizes of Brand A and Brand B samples, respectively, and o =
P191
m
+
P292
n](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e84cf3b-fceb-4a4c-8366-ddb1bf5b2bd5%2F64d3cf6d-a8e2-4e05-9b17-bf5126f1fcc6%2Ffvitde_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The likelihood of not rejecting the null hypothesis when the null hypothesis is false is ß, the probability of a type II error. The likelihood of rejecting the null hypothesis when the null hypothesis is false is then 1 - ß.
(ma₁ + nq₂)
(m + n)
Refer to the formula for 8 as a function of proportions p₁ and P₂, where Z₁/2 is the critical value based on significance level a, p = (mp₁ + np₂), ā=.
z
(m + n)
862, 103) - + [²^ 2 √(- 3 (2+ + 2 ) – (0, - ²3)] -
√(³ 3 (²+ + ² ) - 10₁ - ³₂³)] _ •
B(P₁, P₂) = $
²a/2√
(P₁-P₂)
Calculate p using p₁ = 0.50, P₂ = 0.25, and m = n = 100.
(mp₁ + np₂)
(m + n)
0.5(100) +
p=
=
a
Given α = 0.01, the critical value for this calculation is Za/2=Z0.005. Use the table of standard normal curve areas to determine the critical value, rounded to two decimal places.
Za/2= ²0.005
0 =
100 + 100
P2
Calculated using p₁ -0.50, P₂ = 0.25, and m = n = 100, where a₁ = 1- P₁ and q₂ = 1 - P₂¹
9=
(ma₁ + ng₂)
(m + n)
(1 - 0.5)(100) + (1 -
+
100 + 100
Calculate σ, rounding the result to five decimal places.
P191
P292
m
n
(100)
0.50(1-0.50)
100
+
0.25(1-[
[ -5-²2√/
[-², 2√/³3 (+ + +) - 6 - 2³
(01
P2) ]
Ō
(100)
100
1
m and n are the sample sizes of Brand A and Brand B samples, respectively, and o =
P191
m
+
P292
n
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