Answer:
[tex]14.2-2.03\frac{6.4}{\sqrt{35}}=12.004[/tex]
[tex]14.2+2.03\frac{6.4}{\sqrt{35}}=16.396[/tex]
We are 95% confidence that the true mean for the delay time is between (12.004 and 16.396)
Step-by-step explanation:
Information given
[tex]\bar X=14.2[/tex] represent the sample mean for the delay time
[tex]\mu[/tex] population mean
s=6.4 represent the sample standard deviation
n=35 represent the sample size
Confidence interval
The confidence interval for the true parameter of interest is given by:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom, given by:
[tex]df=n-1=35-1=34[/tex]
The Confidence level is 0.95 or 95%,and the significance is [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical value for this case is [tex]t_{\alpha/2}=2.03[/tex]
And replacing we got:
[tex]14.2-2.03\frac{6.4}{\sqrt{35}}=12.004[/tex]
[tex]14.2+2.03\frac{6.4}{\sqrt{35}}=16.396[/tex]
We are 95% confidence that the true mean for the delay time is between (12.004 and 16.396)
The traveler is disputing the claim about the variance. The hypothesis test is a right-tailed test. The result of the test does not provide enough evidence to dispute the airline's claim.
Explanation:109. The traveller is disputing the claim about the variance.
110. A sample standard deviation of 15 minutes is the same as a sample variance of 225 minutes.
112. H-o: The variance is 150 minutes or less.
113. d-f = 24
114. chi-square test statistic = 35.172
115. p-value = 0.082
116. Graph the situation:
Horizontal axis: VarianceMean: 150 minutesTest statistic: 225 minutesShade the p value: right tail117. Let a = 0.05
Decision: Fail to reject the null hypothesis
Conclusion: There is not enough evidence to dispute the airline's claim about the variance being 150 minutes or less.
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There is growing concern over a possible causal link between consumption of diet soda and obesity. In 2013, Gallup took a nationally representative sample of 2027 adults and asked them about their soda consumption. In the sample, 920 adults described themselves as overweight, and 300 of them said that they mostly drink diet soda. The remaining 1107 adults described themselves as about right weight, and 225 of them said that they mostly drink diet soda. We plan to test the following hypotheses: The pooled sample proportion of individuals who mostly drink diet soda is: a. 0.2491 b. 0.2033 c. 0.5000 d. 0.2590 e. 0.3261
Answer:
d. 0.2590
Step-by-step explanation:
In this problem, we have that:
A sample of 2027 adults.
920 overweight, and of those, 300 said they drink mostly diet soda.
1107 right weight, of those 225 said that they mostly drink diet soda.
Of 2027 adults, 300+225 = 525 said that they mostly drink diet soda.
The pooled sample proportion of individuals who mostly drink diet soda is:
525 of 2027
525/2027 = 0.2590
So the correct answer is:
d. 0.2590
A recipe calls for 3 teaspoons of orange juice. A can of orange juice is 20 fluid ounces. How many teaspoons of juice are in the can? My child needs help and I don't get it. Help!
Answer:
Step-by-step explanation:
You have to look up (google) the number of ml in a fluid ounce. It equals 29.57 ml approximately.
Next you must look up the number of mL in a teaspoon. The conversion factor turns out to be 4.93 mL = 1 teaspoon.
1 fluid ounce = 29.57 mL
20 fluid ounces = x mL
1/20 = 29.57 /x
x = 20*29.57
x = 591.4 mL
1 teaspoon = 4.93 mL
x teaspoons = 591.4
4.93 * x = 591.4
4.93 * x/4.93 = 591.4 / 4.93
x = 119.96
"A sample of 64 hotels in Atlanta was selected in order to determine whether or not the average room price is significantly different from $110. The average price of the rooms in the sample was $112. The population standard deviation is known to be $16. Use a 0.05 level of significance. Use this information to answer Questions 16 to 19. What should be the appropriate null and alternative hypotheses for the purpose of your analysis?"
Answer:
The null and alternative hypothesis are:
[tex]H_0: \mu=110\\\\H_a:\mu\neq 110[/tex]
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the average room price in Atlanta is significantly different from $110 (P-value=0.317) .
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the average room price in Atlanta is significantly different from $110.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=110\\\\H_a:\mu\neq 110[/tex]
The significance level is 0.05.
The sample has a size n=64.
The sample mean is M=112.
The standard deviation of the population is known and has a value of σ=16.
We can calculate the standard error as:
[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{16}{\sqrt{64}}=2[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{112-110}{2}=\dfrac{2}{2}=1[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as:
[tex]P-value=2\cdot P(z>1)=0.317[/tex]
As the P-value (0.317) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the average room price in Atlanta is significantly different from $110.
Please, answer, I need help.
Answer:
bib
peep
ewe
kayak
racecar
level
noon
An insurance company is interested in conducting a study to to estimate the population proportion of teenagers who obtain a driving permit within 1 year of their 16th birthday. A level of confidence of 99% will be used and an error of no more than .04 is desired. There is no knowledge as to what the population proportion will be. The size of sample should be at least _______. 289
Answer:
The size of the sample should be at least 1037.
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].
The margin of error of the interval is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
A level of confidence of 99% will be used and an error of no more than .04 is desired. There is no knowledge as to what the population proportion will be. The size of sample should be at least
We need a sample size of at least n.
n is found when [tex]M = 0.04[/tex]
We don't know the proportion of the population, so we use [tex]\pi = 0.5[/tex]
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 2.575\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.04\sqrt{n} = 2.575*0.5[/tex]
[tex]\sqrt{n} = \frac{2.575*0.5}{0.04}[/tex]
[tex](\sqrt{n})^{2} = (\frac{2.575*0.5}{0.04})^{2}[/tex]
[tex]n = 1036.03[/tex]
Rounding up
The size of the sample should be at least 1037.
A light bulb consumes 600 watt hours per day. How many Watt hours? Does it consume in 3 days and 12 hours?
Answer:
2100 Watt Hours
Step-by-step explanation:
600 Watt hours is consumed by the bulb every day.
3 Days and 12 Hours = 3 1/2 Days
To find how many Watt hours was consumed in 3 1/2 days we must multiply both of the numbers.
600 x 3 1/2 = 2100
Therefore, we can conclude that 2100 Watt Hours are consumed in 3 Days and 12 Hours.
Answer the questions below about the function whose derivative is f prime (x )equalsStartFraction (x minus 2 )(x plus 8 )Over (x plus 1 )(x minus 5 )EndFraction , xnot equalsminus1, 5. a. What are the critical points of f? b. On what open intervals is f increasing or decreasing? c. At what points, if any, does f assume local maximum and minimum values?
Answer:
Step-by-step explanation:
a) you have that:
[tex]f'(x)=\frac{(x-2)(x+8)}{(x+1)(x-5)},\ \ x\neq -1,5[/tex]
The derivative of a function equals to zero allows you to find the critical points:
[tex]f'(x)=0\\\\(x-2)(x+8)=0\\\\x_1=2\\\\x_2=-8[/tex]
x=2,8 are the critical points
b) To know the behavior if f it is necessary to know where are f is indeterminated. The derivative give to you information about the slope of f. For x=-1,5 you have an infinite slope. Hence, for that values of x you have two indetermination s of f(x.)
However, if you see the atacched images you can obser that the original function (that is obtained with the intgegral) does not have available values for x<5 due to the logrithms. Hence, there are no critical points
The function only increases after x=5 from -infinity to +infinity
c) there are no local maximum neither local minimum
What is the median of this data set 14,18,31,34,44,50
A triangle with a base of 10 units and height of 8 units. Find the area of the triangle. The area of the triangle is square units.
Answer: 40 units
Step-by-step explanation: just did got it right.
Olive's garden is only 10 yd to the second power and the watermelon plants she wants to grow requires 2.5 yd to the second power each, how many watermelon plants can she grow
Answer:
4
Step-by-step explanation:
Garden area: 10 yd²
Each watermelon plant area: 2.5 yd²
No. of plants:
10/2.5 = 4
what is the length of the diameter of the circle
Answer:
6 cm
Step-by-step explanation:
3 is the radius
the radius is half of the diameter
to find the diameter from the radius you have to multiply it by 2
3×2
=6
Describe the key features of polynomial function
g(x) = x^3 − x^2 − 4x + 4, including the end behavior, y-intercept, and zeros.
Answer:
Zeros: x = 1 , − 2 , 2 End Behavior: Falls to the left and rises to the right.
Y-intercept: (0,4)
Step-by-step explanation:
mark me brainliest
What is the slope for y= -1/2x -3
Answer:
-1/2
Step-by-step explanation:
Note the slope intercept form:
y = mx + b
y = (x , y)
m = slope
x = (x , y)
b = y-intercept.
In this case, the number that replaces the m (slope) is -1/2, which is your answer.
~
Answer:
m= -1/2
Step-by-step explanation:
This equation is in slope intercept form:
y=mx+b
where m is the slope and b is the y intercept
We have the equation:
y= -1/2x -3
If we compare the 2 equations:
y=-1/2x -3
y=mx+b
The slope must be -1/2, since x is being multiplied by -1/2
Andres is offered a job as manager of a health club. The job will pay $3,100 per month, paid semimonthly. Along with the base salary, the company offers to pay half the cost of medical insurance and will match Andres' contribution to a retirement plan up to a total of $3,500. If the full cost of the medical insurance is $450 per month and Andres plans to contribute the full $3,500 every year to a retirement plan, what is the actual annual value of this job to Andres?
Andres' job has an actual annual value of $43,400. This figure was obtained by summing his base salary, the company's health insurance contribution, and the company's retirement plan contribution.
Explanation:To calculate the actual annual value of the job offer to Andres, we need to take into account his base salary, the company's contribution towards medical insurance, and the company's matching contribution to his retirement plan. Andres receives a base salary of $3,100 per month and gets paid semimonthly, which equates to an annual salary of $3,100 x 12 = $37,200.
The company pays half of Andres' $450 monthly medical insurance expense. So, that will be $450/2 = $225 per month, and over a year, that's $225 x 12 = $2,700.
Lastly, the company matches Andres' contribution to his retirement plan up to $3,500 annually.
To get the total value, add all these figures up: $37,200 (base salary) + $2,700 (health insurance contribution) + $3,500 (retirement contribution) = $43,400.
So, the actual annual value of Andres' job is $43,400.
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100 points plz answer.....What is the volume of the prism?
8m
6m
14m
Answer:
672m
Step-by-step explanation:
L*W*H
8*6*14
672m
what is 250 divided by 17
Which statement correctly describes the diagram? On a coordinate plane, triangle A is reflected across the x-axis to form triangle B. Triangle A is rotated to form triangle C. Triangle B is a reflection of triangle A across the x-axis. Triangle C is not a reflection of triangle A.. Triangle B is a reflection of triangle A across the y-axis. Triangle C is a reflection of triangle A across the line y = x + 3. Triangle B is a reflection of triangle A across the y-axis. Triangle C is not a reflection of triangle A. Triangle B is a reflection of triangle A across the x-axis. Triangle C is a reflection of triangle A across the line y = x + 3.
Answer:
Your answer would be Triangle B is a reflection of triangle A across the x-axis. Triangle C is not a reflection of triangle A.
Explanation
B is a reflection of the x-axis.
But triangle C is not a reflection because if you fold the image with the y-axis line in the middle then you would see that triangle C doesnt match the placement of triangle A.
hope this helps
give brainliest if you please
Answer:
Without the picture of diagram, based on your description:
Triangle A is reflected across the x-axis to form triangle B.
Triangle A is rotated to form triangle C.
Option A: Triangle B is a reflection of triangle A across the x-axis.
It is correct because "Triangle A is reflected across the x-axis to form triangle B" => Triangle B is a reflection of triangle A across the x-axis
Option B: Triangle C is not a reflection of triangle A
It is correct because "Triangle A is rotated to form triangle C"
Option C: Triangle B is a reflection of triangle A across the y-axis
It is incorrect, because "Triangle A is reflected across the x-axis to form triangle B" => Triangle B is a reflection of triangle A across the x-axis, not y-axis.
Option D: Triangle C is a reflection of triangle A across the line y = x + 3
It is incorrect, because "Triangle A is rotated to form triangle C" => triangle C is a result of rotation, not reflection.
Hope this helps!
:)
There is a cuboids box with the
length 4, width 2 and height 3. Now
I will have to calculate the area of
the box. So what will be the area?
g A realtor is trying to predict the selling price of houses in Greenville (in thousands of dollars) as a function of Size (measured in thousands of square feet) and whether or not there is a fireplace (FP is 0 if there is no fireplace, 1 if there is a fireplace). Part of the regression output is provided below, based on a sample of 20 homes. Some of the information has been omitted. hh Which statement is supported by the regression output? Select one: At α = .05, FP is not a significant predictor in a two-tailed test FP is a more significant predictor than Size A large house with no fireplace will sell for more than a small house with a fireplace a fireplace adds around $6476 to the selling price of the average house
Answer:
size=13.80966
Step-by-step explanation:
Missing information:
size=13.80966
Since p-value of FP is less than 0.05 so it is significant to the model.
If all other things remain constant then a fire place add approximately $6476 to the selling price of the average house. So statement "A fireplace adds around $6476 to the selling price of the average house." is supported by the model.
It is impossible to definitively determine the correct statement without the actual regression output. While we can make educated guesses about the significance of the 'Fireplace' variable and its impact on the house's selling price, further information like t-values, p-values, and standard errors is required to make a detailed and accurate estimate.
Explanation:With the information provided, it is impossible to definitively determine which of the four options are correct without the actual regression output. However, if it were provided and the p-value for the Fireplace's coefficient is higher than 0.05, we could say at α = .05, FP is not a significant predictor in a two-tailed test. If the regression coefficient for the Fireplace is $6,476 and it is significant, then a fireplace adds around $6476 to the selling price of the average house is correct. However, declaring that FP is a more significant predictor than Size or that a large house with no fireplace will sell for more than a small house with a fireplace, would require further information that goes beyond the coefficients themselves, including the standard errors, t-values, and p-values associated with each coefficient.
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Which image shows a translation of the green quadrilateral JKLM three units to the right and one unit down?
Answer:
The second option shows the correct translation of 3 units to the right and 1 unit down.
If f(x) = 3/x+2 - sqrtx-3 , complete the folowing statement f(19)=____
Answer:-27/7
Step-by-step explanation:
f(x)=3/(x+2) -√(x-3)
f(19)=3/(19+2)-√(19-3)
f(19)=3/21 - √(16)
f(19)=1/7-4/1
f(19)=(1 x 1 - 7 x 4)/7
f(19)=(1-28)/7
f(19)=-27/7
To calculate f(19), we would substitute x with 19 in the function f(x) and simplify. However, the function provided is incomplete or incorrect, and therefore, a solution cannot be confidently provided.
To solve the problem f(19), we have to substitute the value of x with 19 into the provided function f(x). However, based on the question provided, the function seems to be incomplete or incorrectly stated.
If we had a correct form of the function f(x), the process would involve replacing any instance of x with 19 and simplifying the resulting expression according to the rules of arithmetic and algebra.
Example Process with Hypothetical Function
Let's assume the function is given correctly as f(x) = 3/(x+2) - √{x-3}. Then, we would calculate:
Step 1: Substitute x with 19: f(19) = 3/(19+2) - √{19-3}
Step 2: Simplify the expression: f(19) = 3/21 - √{16}
Step 3: Complete the calculations: f(19) = 1/7 - 4
Step 4: Find the common denominator and subtract: f(19) = -27/7
However, since we do not have the correct function, I am unable to confidently provide the solution to f(19).
Suppose that you are interested in the average GPA for all KCTCS students. In order to conduct the study you take a sample of 1500 students. This is an example of what branch of statistics?
Inferential
Descriptive
Inductive
Deductive
Answer:
Descriptive
Step-by-step explanation:
Descriptive statistics uses the data that helps to analyse, describe, and elaborate data accurately. It also provides information regarding the population through graphs or tables. Four types of descriptive statistics are measures of frequency, measures of central tendency, measures of dispersion, and measures of position.
The given example in question is descriptive statistics.
Adelia ate lunch and wanted to leave her waitress a 15% tip. her meal cost $8.95. How much money should Adeila leave for the tip?
Answer:
15% of 8.95 is 1.3425
Step-by-step explanation:
Answer:
$1.34
Hope this helped :)
1.
Write a polynomial function in factored form with zeros at -2, 5, and 6.
Answer:
f(x) = (x + 2) (x − 5) (x − 6)
Step-by-step explanation:
f(x) = (x − (-2)) (x − 5) (x − 6)
f(x) = (x + 2) (x − 5) (x − 6)
(a) What is the matrix representation of G, with vertices in numerical (ascending) order? (b) Consider using the Greedy Coloring Algorithm to color G, where the randomly generated vertex order is [4,3,1,6,7,5,2] and a randomly generated color order is [red, blue, green, purple, onyx, heather, fuchsia]. What color is the vertex 2 at the end of the algorithm?
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
100 POINTS
PLEASE PROVIDE STEPS AND GRAPH.
GRAPH USING DESMOS IF POSSIBLE.
Answer:
A) (-2, 8), (4, 8)
B) See attachment.
C) 36 square units
Step-by-step explanation:
Part AGiven functions:
[tex]\begin{cases}f(x)=x^2-2x\\g(x)=8\end{cases}[/tex]
To find the x-coordinates of the points where the two functions intersect, set the equations equal to each other and solve for x:
[tex]f(x)=g(x)\\\\x^2-2x=8\\\\x^2-2x-8=0\\\\x^2-4x+2x-8=0\\\\x(x-4)+2(x-4)=0\\\\(x+2)(x-4)=0\\\\\\x+2=0 \implies x=-2\\\\x-4=0 \implies x=4[/tex]
As points on the function g(x) have a y-coordinate of 8, the solutions to f(x) = g(x) are:
[tex]\Large\boxed{(-2,8)\;\textsf{and}\;(4,8)}[/tex]
[tex]\dotfill[/tex]
Part BThe function g(x) is a horizontal line parallel to the x-axis that intercepts the y-axis at (0, 8).
We are given that function f(x) is a concave up parabola with roots at (0, 0) and (2, 0). From Part A, we know that the parabola intersects g(x) at points (-2, 8) and (4, 8).
To help sketch the graph of function f(x), we can find its vertex and y-intercept.
The x-coordinate of the vertex of a quadratic function in the form y = ax² + bx + c is x = -b/2a. In this case, a = 1 and b = -2, so the x-coordinate of the vertex is:
[tex]x = -\dfrac{-2}{2(1)}=\dfrac{2}{2}=1[/tex]
To find the y-coordinate of the vertex, substitute x = 1 into f(x):
[tex]f(1)=(1)^2-2(1)=1-2=-1[/tex]
Therefore, the vertex of f(x) is at point (1, -1). The axis of symmetry of a parabola is the x-coordinate of the vertex, so in this case, the axis of symmetry is x = 1.
To find the y-intercept, substitute x = 0 into the function and solve for y:
[tex]f(0)=(0)^2-2(0)=0-0=0[/tex]
Therefore, the y-intercept of f(x) is the origin (0, 0).
[tex]\dotfill[/tex]
Part CThe area of the region R bounded by f(x) and g(x) on the interval [-2, 4] is given by the integral:
[tex]\displaystyle R = \int_{-2}^{4} \left[ g(x) - f(x) \right] \; dx[/tex]
Substitute g(x) = 8 and f(x) = x² - 2x:
[tex]\displaystyle R = \int_{-2}^{4} \left[8-(x^2-2x)\right] \; dx \\\\\\ R = \int_{-2}^{4} \left[8-x^2+2x\right] \; dx[/tex]
Evaluate the Integral
[tex]\displaystyle R = \left[8x-\dfrac{x^{2+1}}{2+1}+\dfrac{2x^{1+1}}{1+1}\right]^4_{-2} \\\\\\ R = \left[8x-\dfrac{x^{3}}{3}+x^2\right]^4_{-2} \\\\\\ R=\left(8(4)-\dfrac{(4)^{3}}{3}+(4)^2\right)-\left(8(-2)-\dfrac{(-2)^{3}}{3}+(-2)^2\right) \\\\\\ R=\left(32-\dfrac{64}{3}+16\right)-\left(-16+\dfrac{8}{3}+4\right) \\\\\\ R=\dfrac{80}{3}+\dfrac{28}{3} \\\\\\ R=\dfrac{108}{3}\\\\\\ R=36[/tex]
Therefore, the area of the region R bounded by f(x) and g(x) is:
[tex]\Large\boxed{\textsf{$36$ square units}}[/tex]
1. Find the Length of Line AD A(6, 2) D(-3, -2)
Answer:
5
Step-by-step explanation:
[tex]\sqrt{(2-(-2))^{2} + (6-(-3))^2}[/tex]
=[tex]\sqrt{4^{2} + 3^{2} } \\[/tex]
=[tex]\sqrt{25}[/tex]
=5
HELP! So confused.
I need help finding the measurement of the unknown vertical angles.
(2x+40)°=(4x+10)° are already known. If somebody could explain it to me, that'd be amazing. Thank you!
Answer:
hjjjkkkkk(hmmmm jhhjjjjjjuu
Answer: x=15
Step-by-step explanation: use distributive property:
2x + 40=4x + 10
40=2x + 10
30= 2x
15=x
Question 7 ( 6 Marks)
Three crayons are held together with an elastic band. The diagram below shows the end of
the crayons and the elastic band. Each of the crayons has diameter of 10 mm. Find the
length of the elastic band in this position.
Answer:
Total length of the elastic band in this stretched position = 61.43 mm
Step-by-step explanation:
The complete Question with the image is attached to this solution
The second image shows the break down of the angle subtended by the elastic band over the crayons at the centre of the circle formed by the crayon's circular shape.
The elastic band extends over 3 of such length of an arc and covers a length of 2 × radius in the spaces between the contact with each crayon. This is also shown in the second attached image.
So, the length of the band will be a sum of 3 diameters and 3 of those arc lengths
Length of an arc is given by
L = (θ/360) × πD
θ = 120°
D = 10 mm
L = (1/3) × 10π = (10π/3) mm
But there are 3 of those, So, total length of the arcs = 3 × (10π/3) = (10π) mm
Length of those 3 diameter regions = 3×10 = 30 mm
Total length of the elastic band in this stretched position = 30 + 10π = 30 + 31.43 = 61.43 mm
Hope this Helps!!!
A researcher wants to check the claim that convicted burglars spend an average of 18.7 months in jail. She takes a random sample of 11 such cases from court files and finds that the data was normally distributed and average jail time was 15.5 months with a standard deviation of 5.7 months. Is the reported claim correct? (use a 0.05 level of significance)
Answer:
[tex]t=\frac{15.5-18.7}{\frac{5.7}{\sqrt{11}}}=-1.862[/tex]
The degrees of freedom are given by:
[tex]df=n-1=11-1=10[/tex]
The p value would be given by:
[tex]p_v =2*P(t_{(10)}<-1.862)=0.0922[/tex]
We see that the p value is higher than the significance level so we don't have enough evidence to ocnclude that the true mean is different from 18.7 months in jail at 5% of significance.
Step-by-step explanation:
Information given
[tex]\bar X=15.5[/tex] represent the sample mean for the jail time
[tex]s=5.7[/tex] represent the sample standard deviation
[tex]n=11[/tex] sample size
[tex]\mu_o =18.7[/tex] represent the value that we want to compare
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value for the test
System of hypothesis
We want to check the hypothesis if the true mean for the jail time is equal to 18.7 or no, the system of hypothesis are:
Null hypothesis:[tex]\mu = 18.7[/tex]
Alternative hypothesis:[tex]\mu \neq 18.7[/tex]
Since we don't know the population deviation the statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Rreplacing we got:
[tex]t=\frac{15.5-18.7}{\frac{5.7}{\sqrt{11}}}=-1.862[/tex]
The degrees of freedom are given by:
[tex]df=n-1=11-1=10[/tex]
The p value would be given by:
[tex]p_v =2*P(t_{(10)}<-1.862)=0.0922[/tex]
We see that the p value is higher than the significance level so we don't have enough evidence to ocnclude that the true mean is different from 18.7 months in jail at 5% of significance.