Answer: 56.9 years to 63.1 years.
Step-by-step explanation:
Confidence interval for population mean (when population standard deviation is unknown):
[tex]\overline{x}\pm t_{\alpha/2}{\dfrac{s}{\sqrt{n}}}[/tex]
, where [tex]\overline{x}[/tex]= sample mean, n= sample size, s= sample standard deviation, [tex]t_{\alpha/2}[/tex]= Two tailed t-value for [tex]\alpha[/tex].
Given: n= 24
degree of freedom = n- 1= 23
[tex]\overline{x}[/tex]= 60 years
s= 7.4 years
[tex]\alpha=0.05[/tex]
Two tailed t-critical value for significance level of [tex]\alpha=0.05[/tex] and degree of freedom 23:
[tex]t_{\alpha/2}=2.0687[/tex]
A 95% confidence interval on the true mean age:
[tex]60\pm (2.0686){\dfrac{7.4}{\sqrt{24}}}\\\\\approx60\pm3.1\\\\=(60-3.1,\ 60+3.1)\\\\=(56.9,\ 63.1)[/tex]
Hence, a 95% confidence interval on the true mean age. : 56.9 years to 63.1 years.
Translate the statements into a confidence interval for p. Approximate the level of confidence. In a survey of 8451 U.S. adults, 31.4% said they were taking vitamin E as a supplement. The survey's margin of error is plus or minus 1%.
Answer:
The confidence interval is [tex]0.304 < p < 0.324[/tex]
Step-by-step explanation:
From the question we are told
The sample proportion [tex]\r p = 0.314[/tex]
The margin of error is [tex]E = 0.01[/tex]
The confidence interval for p is mathematically represented as
[tex]\r p - E < p < \r p + E[/tex]
=> [tex]0.314 - 0.01 < p < 0.314 + 0.01[/tex]
=> [tex]0.304 < p < 0.324[/tex]
Sarah needs to go to five different stores. How many ways can she go to two of them before lunch?
Answer:
10
Step-by-step explanation:
Solution 1: At first, you might think that because there are 5 ways to choose the first store and 4 ways to choose the second store, the answer is 5 * 4 = 20 but this is over-counting by a factor of 2. Say that two of the stores are A and B. If she went to A then B, that's the same as going to B then A since you still go to the same stores, therefore, the answer is 20 / 2 = 10.
Solution 2: We need to find the number of ways to choose 2 stores from 5, we can do this by calculating ₅C₂ which equals:
5! / 2! * 3!
= 5 * 4 * 3 * 2 * 1 / 2 * 1 * 3 * 2 * 1
= 5 * 4 / 2 * 1
= 10
What is the area of the house (including the drawing room, TV room, balcony, hallway, kitchen, and bedroom)?
Answer:
A
Step-by-step explanation:
Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.)
an = (−3^n)/(4n!)
Answer:
[tex]a_{i} = \frac{(-3)^{i}}{4\cdot i!}[/tex] converges.
Step-by-step explanation:
The convergence analysis of this sequence is done by Ratio Test. That is to say:
[tex]r = \frac{a_{n+1}}{a_{n}}[/tex], where sequence converges if and only if [tex]|r| < 1[/tex].
Let be [tex]a_{i} = \frac{(-3)^{i}}{4\cdot i!}[/tex], the ratio for the expression is:
[tex]r =-\frac{3}{n+1}[/tex]
[tex]|r| = \frac{3}{n+1}[/tex]
Inasmuch [tex]n[/tex] becomes bigger, then [tex]r \longrightarrow 0[/tex]. Hence, [tex]a_{i} = \frac{(-3)^{i}}{4\cdot i!}[/tex] converges.
A website developer wished to analyze the clicks per day on their newly updated website. Let the mean number of clicks per day be μ. If the website developer wants to know if the number of clicks per day is different than 200 clicks a day, on average, what are the null and alternative hypotheses?
Answer:
Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 200 clicks a day
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 200 clicks a day
Step-by-step explanation:
We are given that a website developer wished to analyze the clicks per day on their newly updated website.
The website developer wants to know if the number of clicks per day is different than 200 clicks a day, on average.
Let [tex]\mu[/tex] = mean number of clicks per day.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 200 clicks a day
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 200 clicks a day
Here, the null hypothesis states that the mean number of clicks per day is 200 clicks a day.
On the other hand, the alternate hypothesis states that the mean number of clicks per day is different than 200 clicks a day.
Hence, this is the correct null and alternative hypotheses.
Answer: Null Hypothesis [tex]H_0:\mu=200[/tex]
Alternate Hypothesis[tex]H_a:\mu\neq200[/tex]
Step-by-step explanation:
Let [tex]\mu[/tex] be the mean number of clicks per day.
Given, a website developer wished to analyze the clicks per day on their newly updated website.
The website developer wants to know if the number of clicks per day is different than 200 clicks a day, on average.
i.e. he wants to check either [tex]\mu=200\text{ or }\mu\neq 200[/tex]
Since a null hypothesis is a hypothesis believes that there is no difference between the two variables whereas an alternative hypothesis believes that there is a statistically significant difference between two variables.
So, Null Hypothesis [tex]H_0:\mu=200[/tex]
Alternate Hypothesis[tex]H_a:\mu\neq200[/tex]
Hence, the required null and alternative hypotheses.
Null Hypothesis [tex]H_0:\mu=200[/tex]
Alternate Hypothesis[tex]H_a:\mu\neq200[/tex]
If xy = 1 what is the arithmetic mean of x and y in terms of y? Please show work as detailed as possible
Answer:
(1+y^2) /2y
Step-by-step explanation:
arithmetic mean is the average of x and y
(x+y)/2
Using the equation
xy = 1
and solving for x
x = 1/y
Replacing x in the first equation
(1/y + y) /2
Multiply by y/y
(1/y + y) /2 * y/y
(1/y + y)*y /2y
(1+y^2) /2y
Answer two questions about Equations A and B: A.5x=20 \ B.x=4 1) How can we get Equation B from Equation A? Choose 1 answer: (Choice A) Multiply/divide both sides by the same non-zero constant (Choice B,) Multiply/divide both sides by the same variable expression (Choice C) Add/subtract the same quantity to/from both sides (Choice D) Add/subtract a quantity to/from only one side
Answer:
Multiply/divide both sides by the same non-zero constant
Step-by-step explanation:
5x = 20
Divide each side by 5
5x/5 = 20/5
x = 4
To obtain (B) from (A) "Multiply/divide both sides by the same non-zero constant"
Given the equations :
5x = 20 ___ (A)x = 4 _____ (B)To obtain the value ; x = 4 from A
We multiply (A) by the same non-zero constantHere, the constant value which can be used is 5 in other to isolate 'x'
5x/5 = 20/5
x = 4
Therefore, to obtain (B) from (A) "Multiply/divide both sides by the same non-zero constant"
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A number is chosen at random from 1 to 50. Find
the probability of selecting multiples of 10.
Step by step.
Answer:
1/10
Step-by-step explanation:
There are 5 numbers in the range that are multiples of 10: 10, 20, 30, 40, 50. The probability of choosing one of those at random from the set of 50 numbers is ...
5/50 = 1/10
An operator wants to determine the standard deviation for a machine relative to its ability to produce windshield wipers conforming within their specifications. To do this, she wants to create a p-chart. Over a month's time, she tests 100 units every day and records the number of manufacturing defects. The average proportion of non-conforming windshield wipers is found to be 0.042. What is the standard deviation of this sample
Answer:
the standard deviation of the sample is less than 0.1
Step-by-step explanation:
Given that :
The sample size n = 100 units
The average proportion of non-conforming windshield wipers is found to be 0.042 which is the defective rate P-bar
The standard deviation of the machine([tex]S_p[/tex]) can be calculated by using the formula:
[tex]S_p =\dfrac{ \sqrt{ \overline P \times (1 - \overline P)} }{n}[/tex]
[tex]S_p =\dfrac{ \sqrt{0.042 \times (1 -0.042)} }{100}[/tex]
[tex]S_p =\dfrac{ \sqrt{0.042 \times (0.958)} }{100}[/tex]
[tex]S_p =\dfrac{ \sqrt{0.040236} }{100}[/tex]
[tex]S_p =\dfrac{ 0.2005891323 }{100}[/tex]
[tex]S_p =0.002[/tex]
Thus , the standard deviation of the sample is less than 0.1
For a given confidence level, t ? df is larger than z ? . Explain how t ∗ df being slightly larger than z ∗ affects the width of the confidence interval.
Answer:
Answer is below
Step-by-step explanation:
The width of the CI is directly proportional to critical value. When t* is greater than z value, the t value would then cause the margin of error to be larger and this will in turn cause the width of the confidence interval to be larger.
Greater t*df than z* gives us a bigger margin of error. This would in turn give bigger width of confidence interval. t distribution has greater width confidence interval compared to z distribution.
The width of confidence interval is a function of the margin of error. If the critical value of t(t*) is slightly larger than the critical value of z(z*), then the width of the confidence interval will be larger.
The margin of error is the product of the critical value and the standard error. Therefore, given the same standard error value, the value of the margin of error will increases based on the value of the critical value.
Since, t* is slightly larger than z*, then the confidence interval, t will be wider.
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Question 1 (Multiple Choice Worth 4 points)
(08.01) Looking at the spread of your data best fits which step of the statistical process?
Answer:
The answer is "Analysis the information by chart and number processes".
Step-by-step explanation:
They already have articulated a query and also gathered information unless you are searching only at the distribution of your results. Those who are ready to analyze your results for all are there.
A projectile is fired vertically upward from a height of 300
300
feet above the ground, with an initial velocity of 900
900
ft/sec. Recall that projectiles are modeled by the function h(t)=−16t2+v0t+y0
h
(
t
)
=
−
16
t
2
+
v
0
t
+
y
0
. Write a quadratic equation to model the projectile's height h(t)
h
(
t
)
in feet above the ground after t seconds.
Step-by-step explanation:
It is given that, a projectile is fired vertically upward from a height of 300 feet above the ground, with an initial velocity of 900 ft/s.
The general equation with which a projectile are modled by the function is given by :
[tex]h(t)=-16t^2+v_ot+y_o[/tex]
y₀ is the initial height above the ground
v₀ = initial velocity
So,
[tex]h(t)=-16t^2+900t+300[/tex]
This is the quadratic equation that models the projectile height in feet above the ground after t seconds.
qaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
Answer:
32.8 miles
Step-by-step explanation:
Amy is driving to Seattle. Suppose that the remaining distance to drive (in miles) is a linear function of her driving time (in minutes). When graphed, the function gives a line with a slope of -0.95. See the figure below. Amy has 48 miles remaining after 31 minutes of driving. How many miles will be remaining after 47 minutes of driving?
Answer: The general equation of a line is given as y = mx + c, where m is the slope of the line and c is the intercept on the y axis. Given that the slope is -0.95, substituting in the general equation :
y = -0.95x + c
Amy has 48 miles remaining after 31 minutes of driving, to find c, we substitute y = 48 and x = 31. Therefore:
48 = -0.95(31) + c
c = 48 + 0.95(31)
c = 48 + 29.45
c = 77.45
The equation of the line is
y = -0.95x + 77.45
After 47 minutes of driving, the miles remaining can be gotten by substituting x = 47 and finding y.
y = -0.95(47) + 77.45
y = -44.65 + 77.45
y = 32.8 miles
Take thus quote, and embed (introduce) it into a complete sentence: "TV plots
and characters tended to be simple" The author is Ostergaard.
Oregon State University is interested in determining the average amount of paper, in sheets, that is recycled each month. In previous years, the average number of sheets recycled per bin was 59.3 sheets, but they believe this number may have increase with the greater awareness of recycling around campus. They count through 79 randomly selected bins from the many recycle paper bins that are emptied every month and find that the average number of sheets of paper in the bins is 62.4 sheets. They also find that the standard deviation of their sample is 9.86 sheets. What is the value of the test-statistic for this scenario
Answer:
The test statistic is [tex]t = 2.79[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 59.3[/tex]
The sample size is [tex]n = 79[/tex]
The sample mean is [tex]\= x = 62.4[/tex]
The standard deviation is [tex]\sigma = 9.86[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\= x - \mu }{ \frac{ \sigma}{ \sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 62.2 - 59.3 }{ \frac{ 9.86}{ \sqrt{ 79} } }[/tex]
[tex]t = 2.79[/tex]
State whether the data described below are discrete or continuous, and explain why.
The widths (in centimeters) of different paintings in an art museum
nothing
Choose the correct answer below.
A. The data are continuous because the data can only take on specific values.
B. The data are discrete because the data can only take on specific values.
C. The data are discrete because the data can take on any value in an interval.
D. The data are continuous because the data can take on any value in an interval.
What is the solution to the system of equations? -2x-3y+z=-6, z=6, 3x-y+z=13
Answer:
B is the correct answer.
Step-by-step explanation:
-2x+3y+z=-6
z=6
-2x+3y+6=-6
-2x+3y=-12
-2(3)+3(2)
-6+6=0 A is incorrect
-2(3)+3(-2)=-12
-6-6=-12
B is the correct answer.
I am not going to show C or D, because you have the right answer. Hope this helps you. Thank you.
one of these marbles is picked at random. what is the probability that a blue marble is picked?
A.1/3
B.2/5
C.1/2
D.1/4
Answer:
1/3
Step-by-step explanation:
there are twelve marbles total. there are 4 blue marbles.
4/12 = 1/3
Which of the following is an example of closure? (1 point)
The equation 5 - 5 = 0 is an example of the natural numbers being closed under subtraction
The equation 1.5 +1.6 = 3.1 is an example of the rational numbers being closed under addition
The equation 4 - 6 = -2 is an example of the whole numbers being closed under subtraction
The equation 1+0= 1 is an example of the natural numbers being closed under addition
Answer:
The equation 1+0=1
Step-by-step explanation:
Other options are not eligible because
1 option -Natural numbers cannot be closed under subtraction
2 option-The equation is not having proper rational numbers, they are decimals
3 option-Whole numbers cannot be closed under subtraction
Thank you!
Each corner of a rectangular prism is cut off. Two (of the eight) cuts are shown. How many edges does the new figure have? Assume that the planes cutting the prism do not intersect anywhere in or on the prism. EXPLAIN PLS
Answer:
36
Step-by-step explanation:
Each cut creates a triangular face where the corner used to be. That face adds three edges to the figure. The 8 cuts add a total of 8×3 = 24 edges to the 12 edges the prism already had.
The new figure has 12+24 = 36 edges.
In the diagram, ∆ABC and ∆DBE are similar. What is the scale factor of the dilation that will map the preimage ΔABC onto the image ΔDBE? A. 1.33 B. 0.75 C. 0.66 D. 0.55
Answer:
B
Step-by-step explanation:
Calculate the ratio of corresponding sides, image to preimage, that is
scale factor = [tex]\frac{DE}{AC}[/tex] = [tex]\frac{12.09}{16.12}[/tex] = 0.75 → B
The scale factor of the dilation will be 1.33. Then the correct option is A.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
There is no effect of dilation on the angle.
In the diagram, ∆ABC and ∆DBE are similar.
Then the scale factor of the dilation that will map the preimage ΔABC onto the image ΔDBE will be
⇒ 16.12 / 12.09
⇒ 1.33
Then the correct option is A.
More about the dilation link is given below.
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In order to study the mean blood pressure of people in his town, Richard samples the population by dividing the residents by age and randomly selecting a proportionate number of residents from each age group. Which type of sampling is used?
a. Convenience sampling
b. Cluster sampling
c. Stratified sampling
d. Systematic sampling
Answer:
C Stratified sampling
Step-by-step explanation:
Stratified sampling : Stratified sampling is a type of sampling technique in which the total population is divided into smaller groups or strata to complete the sampling process. The strata is formed based on some common characteristics in the data of the population.
One of the advantage of stratified random sampling is that it covers important population characteristics in the sample.
Suppose that you are standing 150 feet from a building and the angle of elevation to the top of the building is 42°. What is the building's height?
Answer:
135.06 feet
Step-by-step explanation:
Since the side of the building makes a right triangle with the ground and you know one side length and the degree angle between you and the top of the building we can use trigonometric function to find the height of the building. So since we know one side other than the hypotenuse we can use tangent to solve. Tangent is the opposite side over the adjacent side of the known angle.
opposite side = x
adjacent side = 150 feet
angle = 42°
tan(42°) = x/150 feet
150 feet * tan(42°) = x
x = 135.06 feet
A racecar is traveling at a constant speed of 150 miles per hour. How many feet does it travel in 5 seconds? Remember that 1 mile is 5280 feet.
Answer:
distance covered in 5 seconds
= 1.4283 *10^10 feet
Step-by-step explanation:
A racecar is traveling at a constant speed of 150 miles per hour.
One mile = 5280 feet
150 miles= 5290*150
150 miles= 793500 feet
A racecar is traveling at a constant speed of 793500 feet per hour.
Converting 793500 feet per hour to feet per seconds .
793500 feet per hour
= 793500*60*60 feet per seconds
=2856600000 feet per second
In 5 seconds , distance covered
= 2856600000 *5
distance covered in 5 seconds
= 1.4283 *10^10 feet
Is math a feature of the universe or a feature of human creation?
Answer:
a feature of the universe
Step-by-step explanation:
Math is a feature of the universe because what we call math is just a way of explaining how things work.
Bob cycles 5.4 km every morning.how many feet are in 5.4 km, given that 1 mile=1.609 km and 1 mile=5,280 feet?
Answer:
17,720 ft
Step-by-step explanation:
5.4 km * (1 mile)/(1.609 km) * (5280 ft)/(1 mile) = 17,720 ft
Given a population with a mean of µ = 100 and a variance of σ2 = 1600, the central limit theorem applies when the sample size is n ≥ 25. A random sample of size n = 50 is obtained. • What are the mean and variance of the sampling distribution for the sample means? • What is the probability that ¯X > 110?
Answer:
The probability that the sample mean is more than 110 is 0.0384.
Step-by-step explanation:
According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the sampling distribution of the sample mean will be approximately normally distributed.
Then, the mean of the sampling distribution of sample mean is given by:
[tex]\mu_{\bar x}=\mu[/tex]
And the variance of the sampling distribution of sample mean is given by:
[tex]\sigma^{2}_{\bar x}=\frac{\sigma^{2}}{n}[/tex]
The information provided is:
[tex]n=50\\\\\mu=100\\\\\sigma^{2}=1600[/tex]
Since n = 50 > 30, the central limit theorem can be applied to approximate the sampling distribution of sample mean by the normal distribution.
The mean variance of the sampling distribution for the sample mean are:
[tex]\mu_{\bar x}=\mu=100\\\\\sigma^{2}_{\bar x}=\frac{\sigma^{2}}{n}=\frac{1600}{50}=32[/tex]
That is, [tex]\bar X\sim N(100, 32)[/tex].
Compute the probability that the sample mean is more than 110 as follows:
[tex]P(\bar X>110)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}>\frac{110-100}{\sqrt{32}})[/tex]
[tex]=P(Z>1.77)\\=1-P(Z<1.77)\\=1-0.96164\\=0.03836\\\approx 0.0384[/tex]
*Use a z-table.
Thus, the probability that the sample mean is more than 110 is 0.0384.
Many stores run "secret sales": Shoppers receive cards that determine how large a discount they get, but the percentage is revealed by scratching off that black stuff only after the purchase has been totaled at the cash register. The store is required to reveal (in the fine print) the distribution of discounts available. Determine whether the following probability assignment is legitimate?
10% off 20% off 30% off 50% off
a. 0.2 0.2 0.2 0.2
b. 0.5 0.3 0.2 0.1
c. 0.8 0.1 0.05 0.05
d. 0.75 0.25 0.25 -0.25
e. 1 0 0 0
Answer:
b
Step-by-step explanation:
it makes the most senses the lower the discount the higher the chance
The average daily volume of a computer stock in 2011 was ų=35.1 million shares, according to a reliable source. A stock analyst believes that the stock volume in 2014 is different from the 2011 level. Based on a random sample of 30 trading days in 2014, he finds the sample mean to be 32.7 million shares, with a standard deviation of s=14.6 million shares. Test the hypothesis by constructing a 95% confidence interval. Complete a and b A. State the hypothesis B. Construct a 95% confidence interval about the sample mean of stocks traded in 2014.
Answer:
a
The null hypothesis is [tex]H_o : \mu = 35 .1 \ million \ shares[/tex]
The alternative hypothesis [tex]H_a : \mu \ne 35.1\ million \ shares[/tex]
b
The 95% confidence interval is [tex]27.475 < \mu < 37.925[/tex]
Step-by-step explanation:
From the question the we are told that
The population mean is [tex]\mu = 35.1 \ million \ shares[/tex]
The sample size is n = 30
The sample mean is [tex]\= x = 32.7 \ million\ shares[/tex]
The standard deviation is [tex]\sigma = 14.6 \ million\ shares[/tex]
Given that the confidence level is [tex]95\%[/tex] then the level of significance is mathematically represented as
[tex]\alpha = 100-95[/tex]
[tex]\alpha = 5\%[/tex]
=> [tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table
The value is [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{ \sigma }{\sqrt{n} }[/tex]
substituting values
[tex]E = 1.96 * \frac{ 14.6 }{\sqrt{30} }[/tex]
[tex]E = 5.225[/tex]
The 95% confidence interval confidence interval is mathematically represented as
[tex]\= x -E < \mu < \= x +E[/tex]
substituting values
[tex]32.7 - 5.225 < \mu < 32.7 + 5.225[/tex]
[tex]27.475 < \mu < 37.925[/tex]
A cubical sandbox has a volume of 91.125 cubic inches. What is the side length of the
sandbox?
Hey there! I'm happy to help!
To find the volume of a cube, you simply cube the side length (multiply it by itself three times). This is because all of the sides of a cube are the same and if you multiply the length by the width by the height it is the same number multiplied by itself three times.
We already know that the volume is 91.125 cubic inches. To find the side length, we simply do the cube root on our calculator, which tells us what number we cube to get 91.125.
∛91.125=4.5
Therefore, the side length of the sandbox is 4.5 inches.
I hope that this helps! Have a wonderful day! :D
