Name a transversal Name all corresponding angles Name all alternate exterior angles

A new dental bondlng agent. When bonding teeth, orthodontists must maintain a dry field. A new bonding adhesive(called "Smartbon

Gemiola [76]

Answer:

(a) H₀: μ ≥ 5.70 vs. Hₐ:μ < 5.70

(b) The rejection region is (t₀.₀₁,₉ ≤ -2.821).

(c) The value of the test statistic is -4.33.

(d) The true mean breaking strength of the new bonding adhesive is less than 5.70 Mpa.

Step-by-step explanation:

A hypothesis test should be conducted to determine that the if the true mean breaking strength of the new bonding adhesive is less than 5.70 Mpa.

(a)

The hypothesis is:

H₀: The true mean breaking strength of the new bonding adhesive is not less than 5.70 Mpa, i.e. μ ≥ 5.70.

Hₐ: The true mean breaking strength of the new bonding adhesive is less than 5.70 Mpa, i.e. μ < 5.70.

(b)

The alternate hypothesis indicates that the hypothesis test is left-tailed.

The rejection region for the left tailed test will be towards the lower tail of the t-distribution curve.

The significance level of the test is: α = 0.01.

The critical value is:

$t_{\alpha ,(n-1)}=t_{0.01,(10-1)}=t_{0.01,9}$

Use the t-table for the critical value.

$t_{\alpha ,(n-1)}=t_{0.01,9}=-2.821$

Since rejection region is in the lower tail the critical value will be negative.

Thus, the rejection region is (t₀.₀₁,₉ ≤ -2.821).

(c)

The test statistic value is:

$t=\frac{\bar x-\mu}{s/\sqrt{n}}$

Given:

$\bar x=5.07\\s=0.46\\n=10\\\mu=5.70$

Compute the value of the t-statistic as follows:

$t=\frac{\bar x-\mu}{s/\sqrt{n}}=\frac{5.07-5.70}{0.46/\sqrt{10}} =-4.33$

The value of the test statistic is -4.33.

(d)

The value of the test is less than the critical value.

$t=-4.33$

This implies that the test statistic lies in the rejection region.

Hence the null hypothesis will be rejected at 1% significance level.

Conclusion:

As the null hypothesis is rejected it can be concluded that the true mean breaking strength of the new bonding adhesive is less than 5.70 Mpa.

(e)

The conditions required for the t-test for single mean to be valid is:

The data should be continuous.
The parent population should be normally distributed.
The sample should be randomly selected.

5 0

3 years ago

What is the rate of change from -1 to 4?

lana66690 [7]

Answer:

5

Step-by-step explanation:

-1+(1)= 0

0+(4)=4

1+4=5

5 0

3 years ago

Please help me do this one complicated and confused

IrinaK [193]

Answer:

9

Step-by-step explanation:

Area of a triangle=(base*height)/2

1) Input the values

54=(12h)/2

2) Multiply both sides by 2

54*2=(12h/2)2

108=12h

3) Divide both sides by 12

108/12=12h/12

9=h

I hope this helps! Please comment if you have any questions.

3 0

3 years ago

Read 2 more answers

Find the solution to the following system using substitution or elimination:

raketka [301]

Answer:

B) (3,1)

Step-by-step explanation:

y = -2x + 7

y = 3x - 8

3x - 8 = -2x + 7

combine like terms:

5x = 15

divide both sides of the equation by 5:

x = 3

y = 3(3) - 8 = 1

4 0

3 years ago

Al llegar al hotel nos an dado un mapa con los lugares de la ciudad nos dijieron que 5 cm del mapa que representaban 600 metros

Sati [7]

Pregunta completa:

Al llegar al hotel nos an dado un mapa con los lugares de la ciudad nos dijieron que 5 cm del mapa que representaban 600 metros de la realidad hoy queremos ir a un par que que se encuentra a 8 cm del hotel en el mapa. ¿A qué distancia del hotel está la pareja?

Respuesta: 960m

Explicación paso a paso:

Dado que:

5 cm en el mapa equivale a 600 m en tierra Por lo tanto,

8 cm en el mapa será equivalente a:

5 cm en el mapa - - - - - -> 600 m en el suelo 8cm - - - - - - -> y metros en el suelo

Usando la multiplicación cruzada

y × 5 = 8 × 600

5y = 4800 Luego,

y = 4800/5

y = 960m

Por lo tanto, 8 cm en el mapa serán 960 m en realidad.

8 0

3 years ago