Which expression would be easier to simplify if you used the associative property to change the grouping

Last year, 46% of business owners gave a holiday gift to their employees. A survey of business owners indicated that 35% plan to

DiKsa [7]

Answer:

a) Number = 60 *0.35=21

b) Since is a left tailed test the p value would be:

$p_v =P(Z$

c) If we compare the p value obtained and using the significance level given $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% the proportion of business owners providing holiday gifts had decreased from the 2008 level.

We can use as smallest significance level 0.044 and we got the same conclusion.

Step-by-step explanation:

Data given and notation

n=60 represent the random sample taken

X represent the business owners plan to provide a holiday gift to their employees

$\hat p=0.35$ estimated proportion of business owners plan to provide a holiday gift to their employees

$p_o=0.46$ is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Part a

On this case w ejust need to multiply the value of th sample size by the proportion given like this:

Number = 60 *0.35=21

2) Part b

We need to conduct a hypothesis in order to test the claim that the proportion of business owners providing holiday gifts had decreased from the 2008 level:

Null hypothesis: $p\geq 0.46$

Alternative hypothesis: $p < 0.46$

When we conduct a proportion test we need to use the z statisitc, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.35 -0.46}{\sqrt{\frac{0.46(1-0.46)}{60}}}=-1.710$

Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a left tailed test the p value would be:

$p_v =P(Z$

Part c

If we compare the p value obtained and using the significance level given $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% the proportion of business owners providing holiday gifts had decreased from the 2008 level.

We can use as smallest significance level 0.044 and we got the same conclusion.

8 0

2 years ago

Triangle L N M is shown. Angle L N M is a right angle. An altitude is drawn from point N to point O on side L M, forming a right

zaharov [31]

Answer:

Therefore the value of k = 6.

Step-by-step explanation:

Given:

LN = m

NM = l

OM = k

NO = 4

LO = 8

LM = 8 + k and

Δ LNM ,Δ LON and Δ MON are right Triangle.

To Find :

Om = k = ?

Solution:

In Right angle Triangle By Pythagoras Theorem we have,

$(\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}$

So, In Right angle Triangle Δ LON we have,

LN² = ON² + OL²

m² = 4² + 8²

m² = 80 ............( 1 )

Now in Right angle Triangle Δ MON we have,

MN² = ON² + MO²

l² = 4² + k² ....................( 2 )

Now In Right angle Triangle Δ LNM we have,

LM² = LN² + MN²

(8 + k)² = m² + l² .................( 3 )

Substituting equation 1 and equation 2 in equation 3

(8+k)² = 80 + 4² + k²

Applying (A+B)² = A² +2AB + B² we get

$64 + 16k+k^{2} = 80+ 16 +k^{2} \\\\16k=96\\\\\therefore k=\frac{96}{16} \\\\\therefore k=6$

Therefore the value of k = 6.

4 0

1 year ago

Read 2 more answers

Which graph represents a function with direct variation? A coordinate plane with a line passing through (negative 4, 0) and (0,

lesya692 [45]

Answer:

A line passing through the points (-1,-4),(0,0) and (1,4)

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

<u><em>Verify each case</em></u>

Part 1) A line passing through the points (-4,0) and (0,-2)

This line not represent a direct variation, because the line not passes through the origin.

Part 2) A line passing through the points (-5,4) and (0,3)

This line not represent a direct variation, because the line not passes through the origin.

Part 3) A line passing through the points (-4,-6) and (0,3)

This line not represent a direct variation, because the line not passes through the origin.

Part 4) A line passing through the points (-1,-4),(0,0) and (1,4)

The line passes through the origin

Find out the value of k

$k=y/x$

For the point (-1,-4)

substitute

$k=-4/-1$

$k=4$

For the point (1,4)

substitute

$k=4/1$

$k=4$

The linear equation is

$y=4x$

This line represent a direct variation

6 0

2 years ago

Read 2 more answers

tankabanditka [31]

Answer:

If we assume that the bottle is cylindrical and we take the same radius (3.26) of both the bottles (bottles only differ in heights) then the larger bottle will hold approximately 701.14 ml of fluid (the answer says 700ml which is very close)

Step-by-step explanation:

Step 1: Formula of volume of a cylinder is pi*r^2*h

where value of pi is 3.14

r is the radius

h is the height of the bottle (height is different for both bottles)

After putting the values and estimated radius for both as 3.26, we get the volume of the taller bottle.

You can extract the radius by following this method:

Volume of a cylinder = pi*r^2*h (now put the value of the known volume and height of the smaller cylinder)

500 = 3.14 * (r)^2 *15

500/(3.14*15) = r^2

10.616 = r^2

Taking sqrt. on both sides

We get r = 3.26

Now put the same value in the formula of volume with the radius and height. You will get the answer for second bottle.

V= 3.14 * (3.26)^2 *21

V= 701.14 (approx)

5 0

2 years ago

Read 2 more answers

Zane is a dangerous fellow who likes to go rock climbing in active volcanoes. one time while inside a volcano, he heard some rum

defon

From the given scenario is this particular item, the equation that can be derived for the distance traveled after x seconds is,
y = d₀ + (4)x
Substituting the known values x and y in order to solve for d₀ will give us an answer of,
13 = d₀ + 4(3)
d₀ = 1
Thus, the answer is 1 m.

5 0

2 years ago