What’s the missing number ? help please

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

Gemiola [76]

Answer:

(a) <em>H</em>₀: <em>μ ≥ 5.70 </em><em>vs. </em><em>Hₐ</em>:<em>μ < 5.70</em>

(b) The rejection region is (<em>t₀.₀₁,₉</em> <em>≤ -2.821</em>).

(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:

<em>H</em>₀: The true mean breaking strength of the new bonding adhesive is not less than 5.70 Mpa, i.e. <em>μ ≥ 5.70</em><em>.</em>

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

(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<em>-</em>distribution curve.

The significance level of the test is: <em>α</em> = 0.01.

The critical value is:

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

Use the <em>t-</em>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 (<em>t₀.₀₁,₉</em> <em>≤ -2.821</em>).

(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 <em>t</em>-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.

<u>Conclusion:</u>

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 <em>t-</em>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

Harry paid $35 for a tie and $11 for a T-shirt. He gave the cashier a 100-dollar bill. How much change did he receive from the c

Vaselesa [24]

Answer:

54

Step-by-step explanation: you add 35 and 11 together then subtract 100 by the number you got to get the anwser

4 0

3 years ago

Read 2 more answers

Consider the line shown on the graph. Enter the

Semenov [28]

<h2>Solution -</h2>

From the graph, we concluded that line passes through the points (0, 3) and (1, 4) respectively.

So, slope of the line (m) passing through the points (a, b) and (c, d) is

m = d - b/ c - a

<h3>So, on substituting the values, we get </h3>

m = 4 - 3 / 1 - 0 = 1/1 = 1

Also, line makes an intercept of 3 units in positive direction of y - axis.

So, c = 3

<h3>So, Equation of line is given by</h3>

y = mx + c

y = 1 × x + 3

<h3>Alternative Method :-</h3>

We know, Equation of line passing through the points (a,b) and (c, d) is given by

y - b = d - b / c - a (x - a)

a = 0

b = 3

c = 1

d = 4

<h3>So, on substituting these values in above result, we get :-</h3>

y - 3 = 4 - 3 /1 - 0 ( x - 0 )

y - 3 = 1/1 ( x - 0 )

y - 3 = x

<h3>Different forms of equations of a straight line :-</h3>

1. Equations of horizontal and vertical lines

Equation of line parallel to x - axis passes through the point (a, b) is y = b.

Equation of line parallel to y - axis passes through the point (a, b) is x = a.

<h3>2. Point-slope form equation of line</h3>

Equation of line passing through the point (a, b) having slope m isy - b = m(x - a)

<h3>3. Slope-intercept form equation of line</h3>

Equation of line which makes an intercept of c units on y axis and having slope m is y = mx + c.

<h3>4. Intercept Form of Line</h3>

Equation of line which makes an intercept of a and b units on x - axis and y axis respectively is x/a + y/b = 1.

<h3>5. Normal form of Line</h3>

Equation of line which is at a distance of p units from the origin and perpendicular makes an angle B with the positive X-axis is x cosB + y sinB = p.

<h2 />

8 0

2 years ago

It takes Natalie five hours to tar a roof. Imani can tar the same roof in ten hours. How long would it take them if they worked

tresset_1 [31]

Answer:

C. 3.33 hours

Step-by-step explanation:

Use the algebra work equation:

$\frac{1}{tb}$ = $\frac{1}{t1}$ + $\frac{1}{t2}$ , where tb is the time to work together, t1 is the time it takes one person, and t2 is the time it takes the other person