Tienes un triángulo equilátero con lados de 10cm, lo divides en dos partes de manera horizontal tal que el área de ambos figuras resultantes es igual, ¿cuánto vale la distancia del lado x?

Frank can build a fence in twice the time it would take Sandy. Working together, they can build it in 7 hours. How long will it take each of them to do it alone?

Answer

If Frank and Sandy can build the fence in 7 hours, they must be building

1

7

of the fence every hour.

Now, let the amount of time it takes Sandy be

x

hours so that Frank takes

2

x

hours. Sandy can build

1

x

of the fence every hour and Frank can build

1

2

x

of the fence every hour.

We now have the following equation to solve.

1

x

+

1

2

x

=

1

7

2

+

1

2

x

=

1

7

21

=

2

x

x

=

21

2

=

10.50

Thus, Sandy takes

10.50

hours and Frank takes

21

hours.

Answer:

See explanation below

Step-by-step explanation:

Given a mean of 32. The claim here is that the mean is 32.

Therefore, the null hypothesis and alternative hypothesis, would be:

H0 : u = 32

Ha: u ≠ 32

b) When we fail to reject null hypothesis, H0. This means that the mean weight, u = 32

Conclusion:  There is not enough evidence to conclude that there is overfilling or underfilling.

c) When null hypothesis, H0 is rejected. This means the mean weight, u ≠ 32.

Conclusion: There is enough evidence to conclude that overfilling or underfilling exists

The null hypothesis in the sampling is u = 32 and the alternative is that u isn't equal to 32.

It should be noted that based on the information, when the null hypothesis is rejected, it implies that the weight is 32.

Also, there's no enough evidence to conclude that there's either overfilling or underfilling. When the null hypothesis is rejected, it means that the mean weight is not equal to 32.

Learn more about sampling on:

https://brainly.com/question/17831271

Answer:

The downtown angle measures about 22.62° and the town pool angle measures about 67.38°.

The hypotenuse measures 13 miles. Each third measures 4 1/3 miles.

Step-by-step explanation:

Use trigonometric ratios to solve this problem.

a. Find the measure of each acute angle of the right triangle shown.

Let's start with the acute angle that's marked near downtown. We can use the trigonometric ratio tangent to find the measure of this angle. (Remember, tangent = opposite/adjacent!)

We can divide the opposite side from the angle by the adjacent side to find the tangent:

5/12

= 0.4166666...

Now, we do the inverse tangent to find the measure of the angle:

≈ 22.62°

Now, we can find the angle near the town pool. This time, we can use tangent again, but the 12 mi side is the opposite and the 5 mi side is the adjacent:

12/5

= 2.4

Now, calculate the inverse tangent:

≈ 67.38°

b. Find the length of the hypotenuse. Also find the length of each of the three congruent segments forming the hypotenuse.

We can use the Pythagorean theorem to find the length of the hypotenuse. Remember, given legs a and b and hypotenuse c, the Pythagorean theorem states:

a² + b² = c²

Plug the values in this triangle into this equation:

5² + 12² = c²

25 + 144 = c²

169 = c²

13 = c

The hypotenuse measures 13 miles.

Now, we find the length of the three congruent segments that form the hypotenuse. (to be honest, I'm not sure that there are three congruent segments, but oh well, I'll just go with what it says there).

Since all the segments are the same length, we can just divide 13 by 3 to find the length of each of them:

13/3 = 4 1/3.

Each of the segments measures 4 1/3 miles.

Answer: it’s A

Step-by-step explanation:

Answer:

I check the answer was a or Subtract 6 from the x value to get the y value

Answer:

21.6m

Step-by-step explanation:

Brian throws a ball from point 'a'

The ball travels a distance of:

The ball travels a total distance of 0.6m + 1.2m + 1.8m + 2.4m + 3.0m + 3.6m + 4.2m + 4.8m = 21.6m from point 'a' to point 'b'.

Answer:

165 different teams of 3 students can be formed for competitions

Step-by-step explanation:

Combinations of m elements taken from n in n (m≥n) are called all possible groupings that can be made with the m elements so that:

That is, a combination is an arrangement of elements where the place or position they occupy within the arrangement does not matter. In a combination it is interesting to form groups and their content.

To calculate the number of combinations, the following expression is applied:

[tex]C=\frac{m!}{n!*(m-n)!}[/tex]

It indicates the combinations of m objects taken from among n objects, where the term "n!" is called "factorial of n" and is the multiplication of all the numbers that go from "n" to 1.

In this case:

Replacing:

[tex]C=\frac{11!}{3!*(11-3)!}[/tex]

Solving:

[tex]C=\frac{11!}{3!*8!}[/tex]

being:

So:

[tex]C=\frac{39,916,800}{6*40,320}[/tex]

C= 165

165 different teams of 3 students can be formed for competitions

Answer:

There will be 3 teams of 3 students, and one team of 2 students, so there will be 4 teams with one team one student short, but only 3 teams that can hold 3 students

Answer:

Step-by-step explanation:

Hello!

There was a special program funded, designed to reduce crime in 8 areas of Miami.

The number of crimes per area was recorded before and after the program was established in each area. This is an example of a paired data situation. For each are in Miami you have recorded a pair of values:

X₁: Number of crimes recorded in one of the eight areas of Miami before applying the special program.

X₂: Number of crimes recorded in one of the eight areas of Miami after applying the special program.

Area: (Before; After)

A: (14; 2)

B: (7; 7)

C; (4; 3)

D: (5; 6)

E: (17; 8)

F: (12; 13)

G: (8; 3)

H; (9; 5)

To apply a paired sample test you have to define the variable "difference":

Xd= X₁ - X₂

I'll define it as the difference between the crime rate before the program and after the program.

If the original populations have a normal distribution, we can assume that the  variable defined from them will also have a normal distribution.

Xd~N(μd; σd²)

If the crime rate decreased after the special program started, you'd expect the population mean of the difference between the crime rates before and after the program started to be less than zero, symbolically μd<0

The hypotheses are:

H₀: μd≥0

H₁: μd<0

α: 0.01

[tex]t= \frac{X[bar]_d-Mu_d}{\frac{S_d}{\sqrt{n} } } ~~t_{n-1}[/tex]

To calculate the sample mean and standard deviation of the variable difference, you have to calculate the difference between each value of each pair:

A= 14 - 2= 12

B= 7 - 7= 0

C= 4 - 3= 1

D= 5 - 6= -1

E= 17 - 8= 9

F= 12 - 13= -1

G= 8 - 3= 5

H= 9 - 5= 4

∑Xdi= 12 + 0 + 1 + (-1) + 9 + (-1) + 5 + 4= 29

∑Xdi²= 12²+0²+1²+1²+9²+1²+5²4²= 269

X[bar]d= 29/8= 3.625= 3.63

[tex]S_d=\sqrt{\frac{1}{n-1}[sumX_d^2-\frac{(sumX_d)^2}{n} ] } = \sqrt{\frac{1}{7}[269-\frac{29^2}{8} ] } = 4.84[/tex]

[tex]t_{H_0}= \frac{3.63-0}{\frac{4.86}{\sqrt{8} } } = 2.11[/tex]

This test is one-tailed to the left and so is the p-value, under a t with n-1= 8-1=7 degrees of freedom, the probability of obtaining a value as extreme as the calculated value is:

P(t₇≤-2.11)= 0.0364

The p-value is greater than the significance level, so the decision is to not reject the null hypothesis. Then at a 1% significance level, you can conclude that the special program didn't reduce the crime rate in the 8 designated areas of Miami.

I hope it helps!

Using the t-distribution, it is found that since the p-value of the test is 0.048 > 0.01, there is not enough evidence to conclude that there has been a decrease in the number of crimes since the inauguration of the program.

At the null hypothesis, it is tested if there has been no reduction, that is, the subtraction of the mean after by the mean before is at least 0, hence:

[tex]H_0: \mu_A - \mu_B \geq 0[/tex]

At the alternative hypothesis, it is tested if there has been a reduction, that is, the subtraction of the mean after by the mean before is negative, hence:

[tex]H_1: \mu_A - \mu_B < 0[/tex]

For both before and after, the mean, standard deviation of the sample(this is why the t-distribution is used) and sample sizes are given by:

[tex]\mu_B = 9.5, s_B = 4.504, n_B = 8[/tex]

[tex]\mu_A = 5.875, s_A = 3.5632, n_A = 8[/tex]

The standard errors are given by:

[tex]s_A = \frac{3.5632}{\sqrt{8}} = 1.2596[/tex]

[tex]s_B = \frac{4.504}{\sqrt{8}} = 1.5924[/tex]

For the distribution of differences, the mean and standard error are given by:

[tex]\overline{x} = \mu_A - \mu_B = 5.875 - 9.5 = -3.625[/tex]

[tex]s = \sqrt{s_A^2 + s_B^2} = \sqrt{1.2596^2 + 1.5924^2} = 2.0304[/tex]

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

Hence:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

[tex]t = \frac{-3.625 - 0}{2.0304}[/tex]

[tex]t = -1.7854[/tex]

The p-value is found using a t-distribution calculator, with t = -1.7854, 8 + 8 - 2 = 14 df and a left-tailed test with a significance level of 0.01, as we are tested if the mean is less than a value.

Since the p-value of the test is 0.048 > 0.01, there is not enough evidence to conclude that there has been a decrease in the number of crimes since the inauguration of the program.

You can learn more about the use of the t-distribution to test an hypothesis at https://brainly.com/question/13873630

Answer:

x = 48

Step-by-step explanation:

Since it's given that these two shapes are similar, you can set up a proportion to solve for x, like so:

[tex]\frac{27}{18} =\frac{72}{x}[/tex]

Cross multiply:

[tex]\frac{27x}{1296}[/tex]

Divide 1296 by 27:

x = 48

Answer:

7 3/10

Step-by-step explanation:

7.3=7+0.3= 7+ 3/10= 7 3/10

Answer:

d. Because of the small sample size of differences in times required between machine A and machine B, the distribution of differences for all workers must be normal.

Step-by-step explanation:

A paired t- test conclusion is said to be valid if one of the assumptions that must be satisfied is that: the distribution of the differences must be normal in most cases for which the sample size is small.

From the given information:

the sample size n = 15 ;which is far less than 30

Therefore;we require the distribution of differences in times required between machine A and machine B for all workers to be normal.

From the first option; it is incorrect because even if the sample size is small; the distribution of sample means of the differences will be normal but in the first option ; it is stated that the differences cannot be normal. That makes the first option to be incorrect.

From the second option; is not correct because the sample size (for differences) is 15 and therefore that is a minimal sample which makes the Central Limit Theorem to be invalid and not applicable here.

From the third option; we all know that the sample size is small and not large since it is lesser than 30.

Answer:

46

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

8 + 15 + 17 = 40

**Hope this helped!!**

**If I was right then please mark brainliest!!**

Answer:

[tex]4a^3(5a^3-11)[/tex]

Step-by-step explanation:

→Take out the GCF (Greatest Common Factor). The GCF is [tex]4a^3[/tex] because both [tex]-44a^3[/tex] and [tex]20a^6[/tex] can be divided by it, like so:

[tex]-44a^3+20a^6[/tex]

[tex]4a^3(5a^3-11)[/tex]

9.4 units.

Because,

Formula for arc length is 2times pie times radius times angle divided by 360.

Answer:

The answer is option 2.

Step-by-step explanation:

You have to use length or arc formula, Arc = θ/360×2×π×r where θ represents degrees and r is radius. Then substitute the following values into the formula :

[tex]arc = \frac{θ}{360} \times 2 \times \pi \times r[/tex]

Let θ = 45,

Let r = 12,

[tex]arc = \frac{45}{360} \times 2 \times \pi \times 12[/tex]

[tex]arc = \frac{1}{8} \times 24\pi[/tex]

[tex]arc = 9.42 \: units \: (3s.f)[/tex]

Answer:

a) 0.505,0.995

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 12, \pi = \frac{9}{12} = 0.75[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.75 - 1.96\sqrt{\frac{0.75*0.25}{12}} = 0.505[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.75 + 1.96\sqrt{\frac{0.75*0.25}{12}} = 0.995[/tex]

So the correct answer is:

a) 0.505,0.995

The interval of the data if, The mean of 73.5 years and the standard deviation of 6.5 years, is  (67,80) so, option D is correct.

Mean is a measurement of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value."

Given:

The mean of 73.5 years and the standard deviation of 6.5 years,

the middle 99.7% of ages of residents living at the facility,

Calculate the interval as shown below,

The coordinates of x in the interval = Mean - Standard deviation

The coordinates of x in the interval = 73.5 - 6.5

The coordinates of x in the interval = 67

The coordinates of y in the interval =  Mean + Standard deviation

The coordinates of y in the interval = 73.5 + 6.5

The coordinates of y in the interval = 80

Thus, the interval will be (67, 80).

To know more about mean:

https://brainly.com/question/2810871

#SPJ5

Answer:

Change in temperature = -9 degrees

Step-by-step explanation:

Given

[tex]Start Temperature = 10 deg[/tex]

[tex]Change = 3 deg/hr[/tex]

[tex]Time= 3hr[/tex]

Required

Change in temperature;

First, the total change in 3 hours has to be solved for. This is done as follows:

[tex]Total Change = Change* Time[/tex]

[tex]Total Change = 3 deg/hr * 3 hr[/tex]

[tex]Total Change = 9 deg[/tex]

From the question, we understand that the temperature dropped.

So,  we can conclude that the temperature changed by -9 degrees;

This means that at the end of the third hour is temperature is 1 degrees

Answer:

B) 0.0069

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 8.4, \sigma = 1.8, n = 40, s = \frac{1.8}{\sqrt{40}} = 0.2846[/tex]

Find the probability that their mean rebuild time exceeds 9.1 hours.

This is 1 subtracted by the pvalue of Z when X = 9.1. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{9.1 - 8.4}{0.2846}[/tex]

[tex]Z = 2.46[/tex]

[tex]Z = 2.46[/tex] has a pvalue of 0.9931

1 - 0.9931 = 0.0069

So the answer is B.

Answer:

1.625 when convert it to 1.6 pounds

Step-by-step explanation:

The given bag of mill shrugged 1. 625 pounds.

1.625 ≈ 1.6 poundest to the nearest tenth.

Given information:

We can use the Law of Sines to find angle B:

Substitute the given values:

Now, solve for angle B:

Now that we have angle B, we can find angle C using the fact that the sum of the interior angles in a triangle is always 180°:

Now, we can use the Law of Sines again to find the length of the other side (side c) opposite angle C:

Substitute the given values:

Now, solve for side c:

To the nearest meter, the other side length of the triangular lot is approximately 617 m. But, since there is not an option for the answer, the closest option is C. 616 m.

________________________________________________________

Answer:

  289 m  or  617 m

Step-by-step explanation:

You want the third side length of a triangle with side lengths 450 m and 200 m, with an angle of 28°.

The man's claim does not say which side the given angle is opposite. There are two possibilities. (1) It is opposite the unknown side; (2) it is opposite the side of length 450 m. (No triangle is possible having an angle of 28° opposite the shorter given side.)

If the angle is opposite the unknown side, the law of cosines can be used to find the third side length:

  c² = a² + b² - 2ab·cos(C)

  c² = 450² +200² -2·450·200·cos(28°) ≈ 83569.43

  c ≈ √83569.43 ≈ 289 . . . . meters

The other side length could be 289 meters.

The third side could also be figured using the law of sines.

  a/sin(A) = b/sin(B) = c/sin(C)

  450/sin(28°) = 200/sin(B)

  B = arcsin(200/450·sin(28°)) ≈ 12.043°

Then angle C is ...

  C = 180° -28° -12.043° = 139.957°

and side 'c' is ...

  c = 450·sin(139.957°)/sin(28°) ≈ 617 . . . . meters

The other side length could be 617 meters.

__

Additional comment

The problem tells us "one side" is 450 m, and it tells us the angle opposite "one side" is 28°. If both of the descriptors "one side" are referring to the same side, then Solution 2 is the intended one.

The description can be written in a less ambiguous way. As is, we are not sure that the second use of "one side" is referring to any side in particular. Hence the two possibilities.

<95141404393>

Answer:

42%

Step-by-step explanation:

Given: P(M) = 0.52, P(A) = 0.33, and P(M and A) = 0.27.

Find: P(not M and not A).

P(not M and not A) = 1 − P(M or A)

P(not M and not A) = 1 − (P(M) + P(A) − P(M and A))

P(not M and not A) = 1 − (0.52 + 0.33 − 0.27)

P(not M and not A) = 1 − 0.58

P(not M and not A) = 0.42

Treating these probabilities as Venn probabilities, it is found that there is a 0.42 = 42% probability of a random student being chosen who is a female and is not between the ages of 18 and 20.

-------------------------

The events are:

-------------------------

-------------------------

The probability of a random student being chosen who is a female and is not between the ages of 18 and 20 is given by:

[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B)[/tex]

Inserting the probabilities we found:

[tex]P(A \cap B) = 0.48 + 0.67 - 0.73 = 0.42[/tex]

0.42 = 42% probability of a random student being chosen who is a female and is not between the ages of 18 and 20.

A similar problem is given at https://brainly.com/question/21421475

Answer:

[tex]P(21<X<28)=P(\frac{21-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{28-\mu}{\sigma})=P(\frac{21-24}{3}<Z<\frac{28-24}{3})=P(-1<z<1.33)[/tex]

And we can find the probability with this difference

[tex]P(-1<z<1.33)=P(z<1.33)-P(z<-1)[/tex]

And using the normal standard distribution or excel we got:

[tex]P(-1<z<1.33)=P(z<1.33)-P(z<-1)=0.908-0.159=0.749[/tex]

Step-by-step explanation:

Let X the random variable that represent the soft drink machine outputs of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(24,3)[/tex]  

Where [tex]\mu=24[/tex] and [tex]\sigma=3[/tex]

We want to find this probability:

[tex]P(21<X<28)[/tex]

The z score is given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Using this formula we got:

[tex]P(21<X<28)=P(\frac{21-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{28-\mu}{\sigma})=P(\frac{21-24}{3}<Z<\frac{28-24}{3})=P(-1<z<1.33)[/tex]

And we can find the probability with this difference

[tex]P(-1<z<1.33)=P(z<1.33)-P(z<-1)[/tex]

And using the normal standard distribution or excel we got:

[tex]P(-1<z<1.33)=P(z<1.33)-P(z<-1)=0.908-0.159=0.749[/tex]

Answer:

[tex]2\dfrac{11}{12}[/tex]

Step-by-step explanation:

The first step is to ensure that all of the fractions have a common denominator.

[tex]3\dfrac{1}{3}+\left( -2\dfrac{1}{4} \right) + 1\dfrac{5}{6}= \\\\3\dfrac{4}{12} - 2\dfrac{3}{12} +1 \dfrac{10}{12}= \\\\1\dfrac{1}{12}+1\dfrac{10}{12}= \\\\\boxed{2\dfrac{11}{12}}[/tex]

Hope this helps!

Answer:

0.1069 = 10.69%

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

[tex]\mu = 45, \sigma = 10[/tex]

Between 57 and 69

This is the pvalue of Z when X = 69 subtracted by the pvalue of Z when X = 57. So

X = 69

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{69 - 45}{10}[/tex]

[tex]Z = 2.4[/tex]

[tex]Z = 2.4[/tex] has a pvalue of 0.9918

X = 57

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{57 - 45}{10}[/tex]

[tex]Z = 1.2[/tex]

[tex]Z = 1.2[/tex] has a pvalue of 0.8849

0.9918 - 0.8849 = 0.1069 = 10.69%

Answer:

u=3

Step-by-step explanation:

(8u + 8)5 = 160

40u + 40 = 160

40u = 120

u = 3

Answer:

[tex]6x^2-2x-6[/tex]

Step-by-step explanation:

[tex]f(x)=6x^2-4 \\\\g(x)=2x+2 \\\\(f-g)(x)= (6x^2-4)-(2x+2)=6x^2-2x-6[/tex]

Hope this helps!

Answer:

The percent increase was of 464%.

Step-by-step explanation:

To find the percent increase, first we find how much the current amount is of the original amount. Then, we subtract the current amount from the original amount.

Percentage of current amount:

We solve this using a rule of three.

The original amount(94 cities), was 100% = 1.

The current amount(530 cities) is x. So

94 cities - 1

530 cities - x

94x = 530

x = 530/94

x = 5.64

5.64 = 564% of the original amount

What was the percent​ increase?

The current amount is 564%

The original amount is 100%

564 - 100 = 464

The percent increase was of 464%.

Answer:

Step-by-step explanation:

The data is incorrect. The correct data is:

Deluxe standard

39 27

39 28

45 35

38 30

40 30

39 34

35 29

Solution:

Deluxe standard difference

39 27 12

39 28 11

45 35 10

38 30 8

40 30 10

39 34 5

35 29 6

a) The mean difference between the selling prices of both models is

xd = (12 + 11 + 10 + 8 + 10 + 5 + 6)/7 = 8.86

Standard deviation = √(summation(x - mean)²/n

n = 7

Summation(x - mean)² = (12 - 8.86)^2 + (11 - 8.86)^2 + (10 - 8.86)^2 + (8 - 8.86)^2 + (10 - 8.86)^2 + (5 - 8.86)^2 + (6 - 8.86)^2 = 40.8572

Standard deviation = √(40.8572/7

sd = 2.42

For the null hypothesis

H0: μd = 10

For the alternative hypothesis

H1: μd ≠ 10

This is a two tailed test.

The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 7 - 1 = 6

2) The formula for determining the test statistic is

t = (xd - μd)/(sd/√n)

t = (8.86 - 10)/(2.42/√7)

t = - 1.25

We would determine the probability value by using the t test calculator.

p = 0.26

Since alpha, 0.05 < than the p value, 0.26, then we would fail to reject the null hypothesis.

b) Confidence interval is expressed as

Mean difference ± margin of error

Mean difference = 8.86

Margin of error = z × s/√n

z is the test score for the 95% confidence level and it is determined from the t distribution table.

df = 7 - 1 = 6

From the table, test score = 2.447

Margin of error = 2.447 × 2.42/√7 = 2.24

Confidence interval is 8.86 ± 2.24