1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
zhenek [66]
2 years ago
7

The melting point of each of 16 samples of a certain brand of hydrogenated vegetable oil was determined, resulting in ¯x = 94.32

. Assume that the distribution of the melting point is normal with σ = 1.20. (a) Test H0 : µ = 95 versus Ha : µ 6= 95 using a two-tailed level .01 test. (b) If a level .01 test is used, what is β(94), the probability of a type II error when µ = 94? (c) What value of n is necessary to ensure that β(94) = .1 when α = .01?
Mathematics
1 answer:
Degger [83]2 years ago
4 0

Answer:

Given:

Mean, x' = 94.32

s.d = 1.20

n = 16

a) For null hypothesis:

H0 : u= 95

For alternative hypothesis:

Ha : u≠95

Level of significance, a = 0.01

(Two tailed test)

We reject null hypothesis, h0, if P<0.01 level of significance.

Calculating the test statistic, we have:

Z = \frac{x' - u_0}{s.d / \sqrt{n}} = \frac{94.32-95}{1.20/ \sqrt{16}}

= -2.266

= -2.27

Calculating the P value:

P value = 2P(Z < -2.27)

Using the standard normal table,

NORMSDIST(-2.27)

= 0.0116

P value= 2(0.0116)

= 0.0232

Since P value(0.0232) is greater than level of significance (0.01), we fail to reject the null hypothesis H0.

We can say that there is enough evidence to conclude the data does not support that average melting point differs from the level of 95 at the level of 0.01 significance level.

b) B(u = 94)

= P(when u=94, do not reject H0)

Using the standard nkrmal table, the z-score corresponding to

Z(0.01/2)= 0.005 will be

Z_a_/_2 = 2.58

B(94) = ∅[Z_a_/_2+ \frac{u_0-u}{s.d- \sqrt{n}}] - ∅[-Z_a_/_2+ \frac{u_0-u}{s.d/ \frac{n}}]

B(94) = ∅[2.58+ \frac{95-94}{1.20- \sqrt{16}}] - ∅[-2.58+ \frac{95-94}{1.2/ \frac{16}}]

= ∅(5.91)-∅(0.75)

P(Z≤5.91)-P(Z≤0.75)

From standard normal table, we have:

P(Z≤0.75)=0.7734, P(Z≤5.91)=1

= 1 - 0.7734

= 0.2266

Probability of making type II error when u=94 is 0.2266

c) Probability of committing type II error when u= 94 at a significance level of 0.01 will be =0.10.

B(94) = 0.10

Finding sample size, n for a two tailed test:

n = [\frac{s.d(Z_a_/_2+Z_B)}{u_0-u}]^2

Using standard normal table, Z score corresponding to a/2 = 0.005 cummulative area(1-0.005 = 0.995) is Z= 2.58

Z score corresponding to 0.10 cummulative area(1-0.10 = 0.90) is Z = 1.28

Our sample size n, wil be=

n = [\frac{1.2(2.58+1.28)}{95-94}]^2

= [\frac{4.632}{1}]^2

= 21.46

= 22

Sample size = 22

You might be interested in
Complete the equation, and tell which property you used.<br><br> 8 x (14+7) = _________+ (8 x 7)
melamori03 [73]
By distributive property, 8 x (14 + 7) = (8 x 14) + (8 x 7)
8 0
3 years ago
Fred's sporting goods is providing a $5 discount on a bicycle that costs $80. What is the percentage of the discount?
Sonja [21]

Answer:

6.25%

Step-by-step explanation:

discount/ normal price

5/80

And we are trying to find out the percentage, so

x/100

Set the 2 equations equal to each other

5/80=x/100

Cross multiply

80x=500

Divide by 80 on both sides

x= 6.25

8 0
3 years ago
In an isolated environment, a disease spreads at a rate proportional to the product of the infected and non-infected populations
eimsori [14]

Answer:

Expression: N = C·L·l(t)· T + 20

The initial value problem and solution are expressed as a first order differential equation.

Step-by-step explanation:

First, gather the information:

total population, N = 2 000

Proportionality constant, C = 0.0002

l(t) number of infected individuals = l(t)

healthy individuals = L

The equation is given as follows:

N = C·L·l(t)

However, there is a change with time, so the expression will be:

\frac{dN}{dt} = C·L·l(t)

multiplying both sides  by dt gives:

dN  =   C·L·l(t)

Integrating both sides gives:

\int\limits^a_b {dN} \, dt = \int\limits^a_b {CLl(t)} \, dt

N = C·L·l(t)· T + K

initial conditions:

T= 0, N₀ = (0.01 ₓ 2 000)  = 20

to find K, plug in the values:

N₀ = K

20 = K

At any time T, the expression will be:

<u>N = C·L·l(t)· T + 20</u> Ans

8 0
3 years ago
The first step for deriving the quadratic formula from the quadratic equation, 0 = ax2 + bx + c, is shown. Step 1: –c = ax2 + bx
Goshia [24]

Answer:

Subtract c from each side, using the subtraction property of equality

Step-by-step explanation:

0 = ax^2 + bx + c

Subtract c from each side, using the subtraction property of equality

-c = ax^2 + bx + c-c

-c = ax^2 + bx

4 0
3 years ago
Read 2 more answers
You and your friend drive toward each other. The equation 50h = 190 – 45h represents the number h of hours until you and your fr
Evgesh-ka [11]

Answer:

C. 2 hours

Step-by-step explanation:

50h= 190-45h

50h + 45h = 190

95h = 190.

190÷95= 2h

8 0
3 years ago
Other questions:
  • mark went to two stores to buy a shirt,pants,and shoes. he wants to know which store has the better deal. ( item:shirts $23.89,p
    13·1 answer
  • A baseball team wants to collect at least 160 cans of food for an upcoming food drive. Team members brought 42 cans of food on M
    9·2 answers
  • A company has a $150 budget to provide lunch for its 20 employees. The options are to provide either roast beef sandwiches, whic
    5·2 answers
  • One number is 2 less than a second number. Twice the second number is 9 less than 3 times the first. Find the two numbers.
    5·1 answer
  • A farmer had 6 cows, and all but 6 died. How many are left?
    14·2 answers
  • Item 12
    5·1 answer
  • What is indicated by arrowheads on a line?
    10·1 answer
  • What is the domain of this function?
    12·1 answer
  • What is the solution to this inequality?
    14·1 answer
  • Find the equation of the parabola with points (-3,15), (0,-6), &amp; (2,10)
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!