A set of 12 numbers has an arithmetic mean of 20. if the numbers 10 and 14 are removed from the set, what is the arithmetic mean of the 10 numbers remaining in the set?

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A set of 12 numbers has an arithmetic mean of 20. if the numbers 10 and 14 are removed from the set, what is the arithmetic mean of the 10 numbers remaining in the set?

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asked 2021-05-05

A random sample of \( n_1 = 14 \) winter days in Denver gave a sample mean pollution index \( x_1 = 43 \).
Previous studies show that \( \sigma_1 = 19 \).
For Englewood (a suburb of Denver), a random sample of \( n_2 = 12 \) winter days gave a sample mean pollution index of \( x_2 = 37 \).
Previous studies show that \( \sigma_2 = 13 \).
Assume the pollution index is normally distributed in both Englewood and Denver.
(a) State the null and alternate hypotheses.
\( H_0:\mu_1=\mu_2.\mu_1>\mu_2 \)
\( H_0:\mu_1<\mu_2.\mu_1=\mu_2 \)
\( H_0:\mu_1=\mu_2.\mu_1<\mu_2 \)
\( H_0:\mu_1=\mu_2.\mu_1\neq\mu_2 \)
(b) What sampling distribution will you use? What assumptions are you making? NKS The Student's t. We assume that both population distributions are approximately normal with known standard deviations.
The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.
The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.
(c) What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate.
(Test the difference \( \mu_1 - \mu_2 \). Round your answer to two decimal places.) NKS (d) Find (or estimate) the P-value. (Round your answer to four decimal places.)
(e) Based on your answers in parts (i)−(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level \alpha?
At the \( \alpha = 0.01 \) level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
At the \( \alpha = 0.01 \) level, we reject the null hypothesis and conclude the data are statistically significant.
At the \( \alpha = 0.01 \) level, we fail to reject the null hypothesis and conclude the data are statistically significant.
At the \( \alpha = 0.01 \) level, we reject the null hypothesis and conclude the data are not statistically significant.
(f) Interpret your conclusion in the context of the application.
Reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Fail to reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver. (g) Find a 99% confidence interval for
\( \mu_1 - \mu_2 \).
(Round your answers to two decimal places.)
lower limit
upper limit
(h) Explain the meaning of the confidence interval in the context of the problem.
Because the interval contains only positive numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.
Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, we can not say that the mean population pollution index for Englewood is different than that of Denver.
Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.
Because the interval contains only negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is less than that of Denver.

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asked 2020-12-17

For each of the following sequences: @ identify if the sequence is arithmetic, geometric or quadratic’. Justify your response. @ assuming the first item of each sequence is a1, give an expression for aj. (In other words, find a formula for the i-th term in the sequence). @ if the sequence is arithmetic or geometric, compute the sum of the first 10 terms in the sequence \(i 2,-12, 72, -432, 2592,...\)
\(ii 9, 18, 31, 48, 69, 94,...\)
\(iii 14, 11.5, 9, 6.5, 4, 1.5,...\)

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asked 2021-02-14

In the arrangement shown in Figure P14.40, an object of mass,m = 2.0 kg, hangs from a cordaround a light pulley. The length of the cord between pointP and the pulley is L = 2.0 m.(a) When thevibrator is set to a frequency of 145Hz, a standing wave with six loops is formed. What must be thelinear mass density of the cord in kg/m? (b) How many loops (ifany) will result if m is changed to 2.88 kg?
(c) How many loops (if any) will result if m is changed to72.0 kg?

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asked 2020-11-29

Prove the Arithmetic-Geometric Mean Inequality If \(\displaystyle{a}_{{1}}{a}_{{2}},\ldots,{a}_{{n}}\) are nonnegative numbers, then their arithmetic mean is \(\displaystyle{\frac{{{a}_{{1}}+{a}_{{2}}+\ldots+{a}_{{n}}}}{{{n}}}},\) and their geometric . The avthmetic-geometic mean is \(\displaystyle\sqrt{{{n}}}{\left\lbrace{a}_{{1}},{a}_{{2}},\ldots{a}_{{n}}\right\rbrace}.\) The arithmetic-geometric mean equality states that the geometric mean is always less than or equal to the arithmetic mean. In this problem we prove this in the case of two numbers andy. (a) If x and y are nonnegative and \(\displaystyle{x}\leq{y},{t}{h}{e}{n}{x}^{{2}}\leq{y}^{{2}}.\) [Hint: First use Rule 3 of Inequalities to show that \(\displaystyle{x}^{{2}}\leq{x}{y}{\quad\text{and}\quad}{x}{y}\leq{y}^{{2}}.\) ] (b) Prove the arithmetic-geometric mean inequality \(\displaystyle\sqrt{{{x}{y}}}\leq{\frac{{{x}+{y}}}{{{2}}}}\)

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asked 2020-12-03

1. Is the sequence \(0.3, 1.2, 2.1, 3, ...\) arithmetic? If so find the common difference.
2. An arithmetic sequence has the first term \(a_{1} = -4\) and common difference \(d = - \frac{4}{3}\). What is the \(6^{th}\) term?
3. Write a recursive formula for the arithmetic sequence \(-2, - \frac{7}{2}, -5, - \frac{13}{2} ...\) and then find the \(22^{nd}\) term.
4. Write an explicit formula for the arithmetic sequence \(15.6, 15, 14.4, 13.8, ...\) and then find the \(32^{nd}\) term.
5. Is the sequence \(- 2, - 1, - \frac{1}{2},- \frac{1}{4},...\) geometric? If so find the common ratio. If not, explain why.

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asked 2021-03-27

Water is being boiled in an open kettle that has a 0.500-cm-thick circular aluminum bottle with a radius of 12.0cm. If the water boils away at a rate of 0.500 kg/min,what is the temperature of the lower surface of the bottom of the kettle? Assume that the top surface of the bottom of the kettle is at \(\displaystyle{100}^{\circ}\) C.

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asked 2021-04-20

A teenager pushes tangentially on a small hand-drivenmerry-go-round and is able to accelerate it from rest to afrequency of 20 rpm in 8.0s. Assume the merry-go-round is auniform disk of radius 2.0m and has a mass of 600kg, and twochildren (each with a mass of 20kg) sit opposite each other on theedge.
A) Calculate the torque required to produce theacceleration, neglecting frictional torque.
B) What force is required at the edge?

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asked 2021-06-09

The following table represents the Frequency Distribution and Cumulative Distributions for this data set: 12, 13, 17, 18, 18, 24, 26, 27, 27, 30, 30, 35, 37, 41, 42, 43, 44, 46, 53, 58 Class Frequency Relative Cumulative Frequency Frequency 10 but less than 20 5 20 but less than 30 4 30 but less than 4 4 40 but less than 50 5 50 but less than 60 2 TOTAL What is the Relative Frequency for the class: 20 but less than 30? State you answer as a value with exactly two digits after the decimal. for example 0.30 or 0.35

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asked 2021-05-13

A boy is to sell lemonade to make some money to afford some holiday shopping. The capacity of the lemonade bucket is 1. At the start of each day, the amount of lemonade in the bucket is a random variable X, from which a random variable Y is sold during the day. The two random variables X and Y are jointly uniform.
Find and sketch the CDF and the pdf of 'Z' which is the amount of lemonade remaining at the end of the day. Clearly indicate the range of Z

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asked 2021-05-18

1. S1 and S2, shown above, are thin parallel slits in an opaqueplate. A plane wave of wavelength λ is incident from the leftmoving in a direction perpendicular to the plate. On a screenfar from the slits there are maximums and minimums in intensity atvarious angles measured from the center line. As the angle isincreased from zero, the first minimum occurs at 3 degrees. Thenext minimum occurs at an angle of-
A. 4.5 degrees
B. 6 degrees
C. 7.5 degrees
D. 9 degrees
E. 12 degrees

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Answer 1

For a set of positive numbers \(x_{1},\ x_{2},\ \cdots,\ X_{n}\), the arithmetic mean is given as \(\text{Arithmetic Mean}=\ \frac{x_{1}\ +\ x_{2}\ +\ \cdots\ +\ x_{n}}{n}\) Now, set of 12 numbers which includes 10 and 14 has an arithmetic mean of 20. Let x be the sum of the remaining 10 numbers. \(AM =\ \frac{x\ +\ 10\ +\ 14}{12} = 20\)
\(\frac{x\ +\ 24}{12}=20\)
\(x=240\ -\ 24=216\) Now, we find the arithmetic mean of the remaining 10 numbers whose sum is 216. \(\therefore\ \frac{x}{10}=\ \frac{216}{10}=21.6\)

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A set of 12 numbers has an arithmetic mean of 20. if the numbers 10 and 14 are removed from the set, what is the arithmetic mean of the 10 numbers remaining in the set?

A set of 12 numbers has an arithmetic mean of 20. if the numbers 10 and 14 are removed from the set, what is the arithmetic mean of the 10 numbers remaining in the set?

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