Can someone plz help me solved this problem I need help plz help me! Will mark you as brainiest!

Answer:

B, C, E, & F

Step-by-step explanation:

Option A is incorrect because the equation Ax = b is referred to as a matrix equation, not a vector equation.

Option B is correct. If Ax = b has a solution, vector b will a linear combination of columns of matrix A.

Option C is correct. In a matrix equation, product Ax when defined, is a sum of products.

Option D is incorrect. If an augmented matrix [Ab] had a pivot position in every row, there could be a pivot in the last column which would make it inconsistent.

Option E is correct. If the columns of an m×n matrix A span[tex] R^m[/tex], then the equation Ax=b is consistent for each b in

Option F is correct. IfA is an m x n matrix whose columns do not span, then the equation Ax = b is inconsistent for some b in [tex] R^m[/tex]

Options B, C, E, and F are correct.

Answer:

a) H0:μ=55,000 H1:μ>55,000

b) Yes, since we can can reject the null hypothesis

Step-by-step explanation:

a) The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

For this case;

Null hypothesis is that the starting salary will be equal to $55,000/year.

H0:μ=55,000

Alternative hypothesis is that the starting salary will be greater than $55,000/year.

H1:μ>55,000

b) Decision Rule;

P-value > significance level --- accept Null hypothesis

P-value < significance level --- reject Null hypothesis

For this case;

P-value = 0.0392

α = 0.05

Since P-value < 0.05, we can reject null hypothesis.

Therefore, we can accept alternative hypothesis which is the starting salary will be greater than $55,000/year, so the student should pursue an actuary career because the starting salary will be greater than $55,000/year.

- Yes, since we can can reject the null hypothesis

Answer:it is b

Step-by-step explanation:

Answer:

Between 0.01 and 0.20

Step-by-step explanation:

I am going to use the normal approximation to the binomial to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed samples can be 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.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

In this problem, we have that:

[tex]n = 500, p = 0.05[/tex]

So

[tex]\mu = E(X) = np = 500*0.05 = 25[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{500*0.05*0.95} = 4.8734/tex]

Find the probability of winning at least 30 times.

Using continuity correction, this is [tex]P(X \geq 30 - 0.5) = P(X \geq 29.5)[/tex]. So this is 1 subtracted by the pvalue of Z when X = 29.5. Then

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

[tex]Z = \frac{29.5 - 25}{4.8734}[/tex]

[tex]Z = 0.92[/tex]

[tex]Z = 0.92[/tex] has a pvalue of 0.8212

1 - 0.8212 = 0.1788

So the correct option is:

Between 0.01 and 0.20

Answer:

[tex]t=\frac{59.4-55}{\frac{3.239}{\sqrt{10}}}=4.296[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=10-1=9[/tex]  

The p value for this case is given by:

[tex]p_v =P(t_{(9)}>4.296)=0.001[/tex]  

And for this case the p value is lower than the significance level so we have enough evidence to reject the null hypothesis and then we can conclude that true mean is higher than 55.

Step-by-step explanation:

Information given

We have the following data: 54 55 58 59 59 60 61 61 62 65

The sample mean and deviation can be calculated with the following formulas:

[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex]s=\sqrt{\frac{\sum_{i=1}^n (X-i -\bar x)^2}{n-1}}[/tex]

[tex]\bar X=59.4[/tex] represent the sample mean

[tex]s=3.239[/tex] represent the sample standard deviation

[tex]n=10[/tex] sample size  

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic  

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to test if the true mean is higher than 55, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 55[/tex]  

Alternative hypothesis:[tex]\mu > 55[/tex]  

Replacing the info given we got:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

And replacing the info given we got:

[tex]t=\frac{59.4-55}{\frac{3.239}{\sqrt{10}}}=4.296[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=10-1=9[/tex]  

The p value for this case is given by:

[tex]p_v =P(t_{(9)}>4.296)=0.001[/tex]  

And for this case the p value is lower than the significance level so we have enough evidence to reject the null hypothesis and then we can conclude that true mean is higher than 55

Answer:

Distance from the base of the cliff to the point on the ground = 7608 feet

Step-by-step explanation:

Given: Height of the cliff is 532 feet, angle of depression from the top of the cliff to a point on the ground is equal to 4 degrees.

To find: distance from the base of the cliff to the point on the ground

Solution:

In ΔABC,

[tex]\angle ACB=4^{\circ}[/tex]  (Alternate interior angles)

For any angle [tex]\theta[/tex], [tex]\tan \theta =[/tex] side opposite to angle/side adjacent to angle

[tex]\tan C=\frac{AB}{BC}[/tex]

Put [tex]AB=532\,,\,\angle C=4^{\circ}[/tex]

[tex]\tan 4^{\circ}=\frac{532}{BC}\\\\BC=\frac{532}{\tan 4^{\circ}}\\\\=7607.95\\\\\approx 7608\,\,feet[/tex]

Distance from the base of the cliff to the point on the ground = 7608 feet

Answer:

part a: 52%

part b: 0.4

part c: 0.24

Step-by-step explanation:

For part one, you find the frequency of the number of people that are less that 20. You add the number of tics in each bar and you divide by the total.

so for part a it is (7+6+9+4)/ (7+6+9+4+4+12+8)

for part b you add up the values that are greater than 25(less than 35)

(12+8)/total

part c you find the number of people between 25 and 30

that's 12

over total

12/total

Answer:

n = -1

Step-by-step explanation:

So first subtract 9 to both sides

8n = -n - 9

Now you want the n on one side and the constant on the other

so add the single n to the n side

9n = -9

Divide 9 to both sides to solve for n

n = -1

Answer:

a rigt angle is a total of 90 degrees so subtratct 51 from 90 and you get 39 degrees.

Answer:

40%

Step-by-step explanation:

you need to divide 80 by 8 to get 10 and then divide 32 by 8 aswell. this gives you 4/10 which is equivalent to 40/100 or 40%

Candidate percent scored is, 40%.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

A candidate scored 32 marks out of 80.

Now, Total marks = 80

And, A candidate score = 32

Hence, The percent score is,

⇒ 32 / 80 × 100

⇒ 3200 / 80

⇒ 40%

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Answer:

bh

6, 17

102

51

Step-by-step explanation:

Answer:

1/2 (bh)

1/2(17)(6)

51

Answer:

d = 2[tex]\sqrt{17}[/tex]

Step-by-step explanation:

P1 (-5, 4) P2 (-3, -4)

Use the distance formula: d = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }[/tex]

Plug in the values and simplify

d = [tex]\sqrt{(-3 + 5)^{2} + (-4 -4)^{2} }[/tex]

d = [tex]\sqrt{(2)^{2} + (-8)^{2} }[/tex]

d = [tex]\sqrt{4 + 64 }[/tex]

d = [tex]\sqrt{68}[/tex]

d = 2[tex]\sqrt{17}[/tex]

I hope this helps :)

Answer:

49

Step-by-step explanation:

Positive 49 not -49

Answer:

Height of the Dom is 112.18 m.

Step-by-step explanation:

The tallest church tower in the Netherlands is the Dom Tower in Utrecht. The angle of elevation to the top of the tower is 77° when 25.9 m from the base. It is required to find the height of the Dom Tower. Let its height is h. So, using trigonometric formula to find it as :

[tex]\tan\theta=\dfrac{h}{b}\\\\\tan(77)=\dfrac{h}{25.9}\\\\h=\tan(77)\times 25.9\\\\h=112.18\ m[/tex]

So, the height of the Dom is 112.18 m.

Answer:

Step-by-step explanation:

If the profit realized by the company is modelled by the equation

P (x) = −0.5x² + 120x + 2000, marginal profit occurs at dP/dx = 0

dP/dx = -x+120

P'(x) = -x+120

Company's marginal profit at the $100,000 advertising level will be expressed as;

P '(100) = -100+120

P'(100) = 20

Marginal profit at the $100,000 advertising level is $20,000

Company's marginal profit at the $140,000 advertising level will be expressed as;

P '(140) = -140+120

P'(140) = -20

Marginal profit at the $140,000 advertising level is $-20,000

Based on the marginal profit at both advertising level, I will recommend the advertising expenditure when profit between $0 and $119 is made. At any marginal profit from $120 and above, it is not advisable for the company to advertise because they will fall into a negative marginal profit which is invariably a loss.

Answer:

Probability that one of the giftcards will go to a student athlete and one will go to a freshman = 26.4%

Step-by-step explanation:

At Central High School, 55% of students play a school sport. Also, 24% of the student population is in ninth grade. No ninth graders are allowed to play school sports. If two students are selected at random to receive a gift card, what is the probability that one will go to a student athlete and one will go to a freshman? Write the answer as a percent rounded to the nearest tenth of a percent.

Solution

Probability that a student plays a school sport, that is, probability that a student is a student athlete = P(S) = 55% = 0.55

Probability that a student is in the ninth grade, that is, probability that a student is a freshman = P(F) = 24% = 0.24

It was given that no freshman is allowed to play sports, hence, it translates that the event that a student is a student athlete and the event that a student is a freshman are mutually exclusive.

P(S n F) = 0

If two students are then picked at random to receive a gift card, we require the probability that one will go to a student athlete and one will go to a freshman.

Probability that the first one goes to a student athlete = P(S) = 0.55

Probability that the second one goes to a freshman ≈ 0.24

Probability that the first one goes to a freshman = P(F) = 0.24

Probability that the second one goes to a student athlete ≈ 0.55

Probability that one will go to a student athlete and one will go to a freshman

= (0.55 × 24) + (0.24 × 0.55)

= 0.132 + 0.132

= 0.264

= 26.4% in percent to the nearest tenth.

Hope this Helps!!

a) The percentage of women meeting the height requirement is approximately 99.99%.

b) The percentage of men meeting the height requirement is approximately 99.95%.

c) The new height requirements are at least 58.5 inches and at most 71.8 inches.

a) To find the percentage of women meeting the height requirement of being between 4ft 9in (57 inches) and 6ft 4in (76 inches), we need to calculate the proportion of women within this range using the normal distribution.

First, we standardize the height requirement using the formula:

Z = (X - μ) / σ

where X is the value (height), μ is the mean, and σ is the standard deviation.

For the lower limit (57 inches):

Z_lower = (57 - 63.3) / 2.7 ≈ -2.33

For the upper limit (76 inches):

Z_upper = (76 - 63.3) / 2.7 ≈ 4.70

Using a standard normal distribution table or calculator, we can find the area between -2.33 and 4.70. This represents the percentage of women meeting the height requirement.

The percentage of women meeting the height requirement is approximately 99.99%.

b) Similarly, for men meeting the height requirement of being between 4ft 9in (57 inches) and 6ft 4in (76 inches), we standardize the values:

For the lower limit (57 inches):

Z_lower = (57 - 67.3) / 2.8 ≈ -3.68

For the upper limit (76 inches):

Z_upper = (76 - 67.3) / 2.8 ≈ 3.11

Using the standard normal distribution table or calculator, we find the area between -3.68 and 3.11.

The percentage of men meeting the height requirement is approximately 99.95%.

c) To find the new height requirements that exclude the tallest 5% of men and the shortest 5% of women, we need to determine the corresponding Z-scores.

For men:

Z_upper_men = Z(0.95) ≈ 1.645

For women:

Z_lower_women = Z(0.05) ≈ -1.645

Using these Z-scores, we can calculate the new height requirements:

For the new lower limit:

X_lower = Z_lower_women * σ + μ

For the new upper limit:

X_upper = Z_upper_men * σ + μ

Substituting the values:

X_lower = -1.645 * 2.7 + 63.3 ≈ 58.53 inches

X_upper = 1.645 * 2.8 + 67.3 ≈ 71.78 inches

Therefore, the new height requirements are at least 58.5 inches and at most 71.8 inches.

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a) The percentage of women meeting the height requirement is 99.99%.

b) The percentage of men meeting the height requirement is 99.95%.

c) The new height requirements are at least 58.5 inches and at most 71.8 inches.

a) For women meeting the height requirement:

Given: Mean (μ) = 63.3 in.

Standard Deviation (σ) = 2.7 in.

So, Minimum height requirement:

= 4 ft 9 in

= 4 * 12 + 9

= 57 inches

and, Maximum height requirement:

= 6 ft 4 in

= 6 * 12 + 4

= 76 inches

We will calculate the Z-scores for these heights using the formula:

Z = (x - μ) / σ

For the minimum height requirement:

[tex]Z_{min[/tex] = (57 - 63.3) / 2.7 ≈ -2.33

For the maximum height requirement:

[tex]Z_{max[/tex] = (76 - 63.3) / 2.7 ≈ 4.70

So, the the area between -2.33 and 4.70.

Thus, the percentage is  99.99%.

b) For men meeting the height requirement:

Given: Mean (μ) = 67.3 in., Standard Deviation (σ) = 2.8 in.

Minimum height requirement: 4 ft 9 in = 57 inches

Maximum height requirement: 6 ft 4 in = 76 inches

For the minimum height requirement:

[tex]Z_{min[/tex]= (57 - 67.3) / 2.8 ≈ -3.68

For the maximum height requirement:

[tex]Z_{max[/tex] = (76 - 67.3) / 2.8 ≈ 3.11

So, the area between -3.68 and 3.11.

Thus, the percentage is 99.95%.

c) For the new height requirements:

For men:

[tex]Z_{upper_{men[/tex] = Z(0.95) ≈ 1.645

For women:

[tex]Z_{lower_{women[/tex] = Z(0.05) ≈ -1.645

For the new lower limit:

[tex]X_{lower} = Z_{lower}_{women} \sigma+ \mu[/tex]

For the new upper limit:

[tex]X_{upper} = Z_{upper}_{men} \sigma+ \mu[/tex]

Substituting the values:

[tex]X_{lower} = -1.645 * 2.7 + 63.3[/tex]

           = 58.53 inches

and, [tex]X_{upper} = 1.645 * 2.8 + 67.3[/tex]

                     = 71.78 inches

Therefore, the new height at least 58.5 inches and at most 71.8 inches.

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Answer:

Find the sales (in units) needed to earn a profit of $262,500

Step-by-step explanation:

hope this is helpful to you bro

4books=6.28inches

30books=?

(30x6.28)/4

47.1 inches

47.1 inches

Answer:

Step-by-step explanation:

What function ?

Answer:

3 1/2 gallons or 56 cups

Step-by-step explanation:

1. Analyze the questions.

We have 3 gallons, and we add another 1/2 gallon. This means that our equation must be 3 + 1/2.

2. Solve.

3 + 1/2 = 3 1/2 gallons

3. Convert.

1 gallon = 16 cups

1 * 3 1/2 gallons = 16 * 3 1/2 cups

3 1/2 gallons = 56 cups

Answer: 3 1/2

                           Hope this helped! :D

Answer:

a) N(2617, 586)

b) 0.3613 = 36.13% probability that the customer consumes less than 2409 calories.

c) 0.4013 = 40.13% of the customers consume over 2764 calories

d) 3981 calories.

Step-by-step explanation:

Problems of normally distributed samples can be 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, we have that:

[tex]\mu = 2617, \sigma = 586[/tex]

a. What is the distribution of X?

Here we first place the mean, then the standard deviation.

N(2617, 586)

b. Find the probability that the customer consumes less than 2409 calories.

This is the pvalue of Z when X = 2409. So

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

[tex]Z = \frac{2409 - 2617}{586}[/tex]

[tex]Z = -0.355[/tex]

[tex]Z = -0.355[/tex] has a pvalue of 0.3613

0.3613 = 36.13% probability that the customer consumes less than 2409 calories.

c. What proportion of the customers consume over 2764 calories?

This is 1 subtracted by the pvalue of Z when X = 2764. So

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

[tex]Z = \frac{2764 - 2617}{586}[/tex]

[tex]Z = 0.25[/tex]

[tex]Z = 0.25[/tex] has a pvalue of 0.5987

1 - 0.5987 = 0.4013

0.4013 = 40.13% of the customers consume over 2764 calories

d. The Piggy award will given out to the 1% of customers who consume the most calories. What is the fewest number of calories a person must consume to receive the Piggy award?

Top 1%, so the 100-1 = 99th percentile.

The 99th percentile is the value of X when Z has a pvalue of 0.99. So it is X when Z = 2.327. So

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

[tex]2.327 = \frac{X - 2617}{586}[/tex]

[tex]X - 2617 = 2.327*586[/tex]

[tex]X = 3980.6[/tex]

Rounding to the nearest calorie, 3981 calories.

Answer:

5^15

Step-by-step explanation:

(5^10)(5^5)= 5^10+5= 5^15

Answer:

2x+11

Step-by-step explanation:

2(x+3)+5

Distribute

2x+ 6 +5

Combine like terms

2x+11

Answer:

2x + 11

Step-by-step explanation:

First distribute 2 to the x + 3

2x + 6 + 5

Combine the constants

6+5=11

2x + 11

The simplified expression is 2x + 11

Answer:

The slope of AB is

different than the

slope of BC.

Step-by-step explanation:

Answer:

L(xyz) = ( 1 , 3 , -7 )

L = x + 3y - 7z -3

Step-by-step explanation:

f (x,y,z) = xy + 2yz - 3xz

f (3,1,0) = (3) (1) + 2 (1) (0) - 3 (3) (0)

f (3,1,0) = 3

fx = y - 3z

f (3,1,0) = (1) - 3 (0)

fx = 1

fy = x + 2z

f (3,1,0) = (3) - 2 (0)

fy = 3

fz = 2y - 3x

f (3,1,0) = 2 (1) - 3 (3)

fz = -7

Answer:

a) x = 30°

b) mRS = x = 30°

mST = 4x = 4(30°) = 120°

mTU = 4x = 4(30°) = 120°

mUR = 3x = 3(30°) = 90°

Question:

The complete question as found on Chegg website:

In the diagram below, secants PT and PU have been drawn from exterior point P such that the four arcs

intercepted have the following ratio of measurements:

mRS : mST :MTU : mUR=1:4:4:3

(a) If mRS = x, then write an equation that could be used to solve for x

and find the value of x.

(b) State the measure of each of the four arcs.

mRS =

mST =

MTU

MUR =

Step-by-step explanation:

Find attached the diagram related to the question

mRS : mST : mTU : mUR = 1:4:4:3

Since mRS = x

Writing the ratios of the measure of angle in terms of mRS:

mST = 4× mRS = 4×x = 4x

mTU = 4× mRS = 4×x = 4x

mUR= 3× mRS = 3×x = 3x

The sum of measure the 4 measures of arc = 360° (sum of angle in a circle)

mRS + mST + mTU + mUR = 360°

x + 4x + 4x + 3x = 360

12x = 360

x = 360/12

x = 30°

b) The measure of angle

mRS = x = 30°

mST = 4x = 4(30°) = 120°

mTU = 4x = 4(30°) = 120°

mUR = 3x = 3(30°) = 90°

Answer:

Step-by-step explanation:

Hello!

The variable is

X: average mass of a sample of rocks collected in the waters of a region. (measured in grams)

Variables can be:

Quantitative: they represent number, any characteristic that can be "counted" is a quantitative variable, the most common examples are weight, volume, temperature, height, etc...

There are two types of quantitative variables:

⇒ Discrete variables: The only take certain values within the interval of definition of the variable, for example "number of sales" or "money in a wallet"

⇒ Continuous variables: They can take any value within an interval, in this example that you are working with mass, depending on the precision of the scale the mass can have infinite decimal values.

Qualitative: they represent characteristics that cannot be counted, meaning, they are not represented by numbers. There are many attributes that are qualitative variables, for example: colors, race of an animal, phenotypes, types of business, etc...

1)

The variable in this example is Quantitative, it takes numerical values, and the correct option is:

D. Quantitative, because numerical values, found by either measuring or counting, are used to describe the data.

2)

The values of mass of the rocks can take any value within the range of definition of the variable, they only depend on the precision of the scale used to weight the rocks.

B. Interval, because the differences in the data can be meaningfully measured, but the data do not have a true zero point.

3)

A standard 52-card deck contains 13 cards for each suit (clubs, diamonds, hearts and spades)

To calculate the probability of choosing a card at random and it being a Diamond, supposing that all cards are equally probable, you have to divide the total number of diamonds by the total number of cards in the deck:

P(diamond)= 13/52= 0.25

For items 4) and 5) the contingency tables are attached.

4)

a. and b. are conditional probabilities, to calculate them you have to apply the following formula: [tex]P(A|B)= \frac{P(AnB)}{P(B)}[/tex]

This means that the probability of the event "A" given that event "B" has occurred is equal to the probability of the intersection between events "A" and "B" divided by the probability of event "B"

a. P(A|C)= [tex]\frac{P(AnC)}{P(C)}[/tex]

To calculate the probability of the intersection P(A∩C) you have to divide the observations where both events cross by the total of observations on the table:

P(A∩C)= 10/50= 0.20

The probability of C is found in the margins of the table, in this case you have to divide the total of observations for event C by the total of observations of the table:

P(C)= 21/50= 0.42

Now you can calculate the asked probability:

[tex]P(A|C)= \frac{0.2}{0.42}= 0.48[/tex]

b. P(C|A)= [tex]\frac{P(AnC)}{P(A)}[/tex]

From item a. we already know that P(A∩C)= 10/50= 0.20

The probability of event A is  in the margin of the table and you calculate it as:

P(A)= 27/50= 0.54

Then:

[tex]P(C|A)= \frac{0.20}{0.54} = 0.37[/tex]

c. P(BE)

This symbolized the probability of the events "B" and "E" occurring at the same time, you can also symbolize it as P(B∩E)

To calculate the probability of B and E happening you have to do as follows:

P(B∩E)= 8/50= 0.16

5)

a. P(C|A)= 0.37 (As calculated in 4b.)

b. P(BE) and c. P(EB) ⇒ Both expressions symbolize the intersection between events "B" and "E", P(B∩E)= P(E∩B)= 0.16 (As calculated in 4c.)

I hope this helps!

Answer:

Step-by-step explanation:

The question is incomplete. The missing data is:

30, 155, 205, 235, 180, 235, 70, 250, 135, 145, 225, 230, 30

Solution:

Mean = (30 + 155 + 205 + 235 + 180 + 235 + 70 + 250 + 135 + 145 + 225 + 230 + 30)/13 = 163.5

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

n = 13

Summation(x - mean)² = (30 - 163.5)^2 + (155 - 163.5)^2 + (205 - 163.5)^2+ (235 - 163.5)^2 + (180 - 163.5)^2 + (235 - 163.5)^2 + (70 - 163.5)^2 + (250 - 163.5)^2 + (135 - 163.5)^2 + (145 - 163.5)^2 + (225 - 163.5)^2 + (230 - 163.5)^2 + (30 - 163.5)^2 = 73519.25

Standard deviation = √(73519.25/13) = 75.2

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ ≤ 150

For the alternative hypothesis,

µ > 150

It is a right tailed test.

a) Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.

Since n = 13,

Degrees of freedom, df = n - 1 = 13 - 1 = 12

t = (x - µ)/(s/√n)

Where

x = sample mean = 163.5

µ = population mean = 150

s = samples standard deviation = 75.2

t = (163.5 - 150)/(75.2/√13) = 0.65

The lower the test statistic value, the higher the p value and the higher the possibility of accepting the null hypothesis.

b) We would determine the p value using the t test calculator. It becomes

p = 0.26

Since alpha, 0.05 < than the p value, 0.26, then we would fail to reject the null hypothesis. Therefore, At a 5% level of significance, the sample data does not show significant evidence that the mean number of friends for the student population at the college who use the social media website is larger than 150.

c)

1.The test statistic value is the difference between the sample mean and the null hypothesis value.