Since A and B are mutually exclusive, we have

P(A or B)=P(A)+P(B)=0.5+0.4=0.9

P(A or B)=P(A)+P(B)=0.5+0.4=0.9

Question

asked 2021-02-14

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.

asked 2021-03-30

A potential difference of 480V is established between largeparallel, metal plates. Let the potential of one plate be 480V andthe other be 0V. The plates are separated by d = 1.70cm.

a) Sketch the equipotential surfaces that correspond to 0, 120,240, 360, and 480 V.

b) In your sketch, show the electric field lines. Does yoursketch confirm that the field lines and surfaces are mutually perpendicular?

a) Sketch the equipotential surfaces that correspond to 0, 120,240, 360, and 480 V.

b) In your sketch, show the electric field lines. Does yoursketch confirm that the field lines and surfaces are mutually perpendicular?

asked 2020-11-10

If two events A and B are independent and you know that P(A)=0.3, what is the value of P(A|B)?

asked 2020-10-27

Let A and B be events with P(A)=0.6, P(B)=0.4, and \(\displaystyle{P}{\left({B}{\mid}{A}\right)}={0.4}\). Find P(A and B).

asked 2021-01-24

If you used a random number generator for the numbers from 1 through 20 to play a game, what is the theoretical probability of getting each of these outcomes? a. A multiple of 3 or a multiple of 7, P(multiple of 3 or multiple of 7) b. P( even or odd) c. P(prime or 1) d. How did you find the probabilities of these events?

asked 2021-01-02

Suppose you roll a number cube. Find the probability. P(3 or 4)

asked 2021-01-28

Data is being processed from 35 data sources. Each dataset may or may or net generate dataset at the beginning of each timeslot, the probability that any individual source actually generates a dataset is 0.004,and the data sources are independent. In each time slot we can process up to two datasets. Now, the processing is real time with the processed results only being considered if they are done within the time slot. Determine the probability that all incoming datasets can be processed in any particular time slot?

asked 2021-03-07

This problem is about the equation

dP/dt = kP-H , P(0) = Po,

where k > 0 and H > 0 are constants.

If H = 0, you have dP/dt = kP , which models expontialgrowth. Think of H as a harvesting term, tending to reducethe rate of growth; then there ought to be a value of H big enoughto prevent exponential growth.

Problem: find acondition on H, involving \(\displaystyle{P}_{{0}}\) and k, that will prevent solutions from growing exponentially.

dP/dt = kP-H , P(0) = Po,

where k > 0 and H > 0 are constants.

If H = 0, you have dP/dt = kP , which models expontialgrowth. Think of H as a harvesting term, tending to reducethe rate of growth; then there ought to be a value of H big enoughto prevent exponential growth.

Problem: find acondition on H, involving \(\displaystyle{P}_{{0}}\) and k, that will prevent solutions from growing exponentially.

asked 2021-01-27

Charlie and Clare are playing a number-guessing game. Charlie picked two numbers between 1 and 5. To win the game, Clare must guess both his numbers in three lines. Her guesses, simulated using a random-number generator are shown in the table. If Charlie's numbers are 1 and 3, what is the experimental probability that Clare won?