Six people are in a room, 3 men and 3 women, and two individuals are selected.

What is the probability of both being women, given that one is a woman?

What is the probability of both being women, given that one is a specific woman?

Question: 9 hypertension patients in a clinic use an experimental drug for treatment. The systolic blood pressure reading for these patients before and after using the drug are as follows:

Assume that blood pressure has a standard deviation of 5 mmHg. Do you think the drug works?

After solving the problem;

1-) Choose the treshold value on your own.

2-) Explain briefly why you choose that numbers as treshold

3-) Make comments on the result of hypothesis test.

Thank you for everything.

Photon Technologies, Inc., a manufacturer of batteries for mobile phones, signed a contract with a large electronics manufacturer to produce three models of lithium-ion battery packs for a new line of phones. The contract calls for the following:

Photon Technologies can manufacture the battery packs at manufacturing plants located in the Philippines and Mexico. The unit cost of the battery packs differs at the two plants because of differences in production equipment and wage rates. The unit costs for each battery pack at each manufacturing plant are as follows:

The PT-100 and PT-200 battery packs are produced using similar production equipment available at both plants. However, each plant has a limited capacity for the total number of PT-100 and PT-200 battery packs produced. The combined PT-100 and PT-200 production capacities are 175,000 units at the Philippines plant and 160,000 units at the Mexico plant. The PT-300 production capacities are 75,000 units at the Philippines plant and 100,000 units at the Mexico plant. The cost of shipping from the Philippines plant is $0.21 per unit, and the cost of shipping from the Mexico plant is $0.18 per unit.

Discuss the problems of using a self-report questionnaire with smokers in a smoking cessation clinic. What percentage might be motivated to indicate that they had stopped when in fact they were still smoking? What would constitute

A CI is desired for the true average stray-load loss μ (watts) for a certain type of induction motor when the line current is held at 10 amps for a speed of 1500 rpm. Assume that stray-load loss is normally distributed with σ = 2.2. (Round your answers to two decimal places.)

(a) Compute a 95% CI for μ when n = 25 and x = 56.7.

(answer,answer) watts

(b) Compute a 95% CI for μ when n = 100 and x = 56.7.

(answer,answer) watts

(c) Compute a 99% CI for μ when n = 100 and x = 56.7.

(answer,answer) watts

(d) Compute an 82% CI for μ when n = 100 and x = 56.7.

(answer,answer) watts

(e) How large must n be if the width of the 99% interval for μ is to be 1.0? (Round your answer up to the nearest whole number.)

4. A study was conducted to determine the effects of two factors on the latherability of soap. The two factors were type of water (tap or distilled) and glycerol (present or absent). The outcome measured was the amount of foam produced (in milliliters). The experiment was repeated three times for each combination of the factors. The results are as follows.

Analyze the data using a=.05.

Conduct the following tests. It may not be necessary to perform all tests. Use a =.05. Please show all work

1. Test for Interaction

H₀:

H_a:

Test statistic value:

p-value:

State your conclusion:

b.Test for the effect of glycerol

H₀:

H_a:

Test statistic value:

p-value:

State your conclusion:

c.Test for the effect of type of water

H₀:

H_a:

Test statistic value:

p-value:

State your conclusion:

Americans receive an average of 20 Christmas cards each year. Suppose the number of Christmas cards is normally distributed with a standard deviation of 6. Let X be the number of Christmas cards received by a randomly selected American. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(,)

b. If an American is randomly chosen, find the probability that this American will receive no more than 19 Christmas cards this year.  

c. If an American is randomly chosen, find the probability that this American will receive between 21 and 25 Christmas cards this year.  

d. 73% of all Americans receive at most how many Christmas cards? (Please enter a whole number)

. A recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percent. Suppose that a survey of 100 local seniors and 100 national seniors is conducted to see if the proportion of drug and alcohol use is higher locally than nationally. Locally, 65 seniors reported using drugs or alcohol within the past month, while 60 national seniors reported using them.

Hardly a day goes by without some new poll being published. Polls influence the choice of candidates and the direction of their policies, especially during election campaigns. For example, the Gallup Organization polled 1012 American adults, asking them, ``Do you think there should or should not be a law that would ban the possession of handguns, except by the police and other authorized persons?'' Of 1012 randomly chosen respondents, 374 said that there should be such a law. Construct a 95% confidence interval for the population proportion of all American adults who think there should be such a law.

A sociologist was hired by a large city hospital to investigate the relationship between the number of unauthorized days that employees are absent per year and the distance (miles) between home and work for the employees. A sample of 10 employees was chosen, and the following data were collected.

a. Which is the independent/explanatory variable?

b. Which is the dependent/response variable?

Enter the data into an Excel spreadsheet.

c. Create a scatterplot for these data. How would you interpret the scatterplot?

Run a regression analysis using Data Analysis/Regression Tool and use the output to answer the following questions:

d. What is the correlation between distance to work and days absent? What does it say about the strength of the relationship?

e. What is the coefficient of determination? How would you interpret it?

f. Write the hypotheses for the test of the slope.

g. What is the p-value for the test of the slope? How would you interpret the p-value?

h. What is the regression formula resulting from this analysis between Distance to Work and Days Absent?

i. Use your formula to predict the number of days absent for an employee who lives 9 miles from work.

j. Use your formula to predict the number of days absent for an employee who lives 17 miles from work.

Jorge Jones, a recent management graduate has a new job as a shelf stocker at the local Shop and Stop (bad job market). In order to maintain some of the knowledge he gained in college, Jorge wants to apply regression analysis to predict weekly sales on the cereal aisle.

He believes there would be a relationship between the shelf space that a particular product takes up and the sales of that product. Jorge has gathered the following data:

a. Which is the independent/explanatory variable?

b. Which is the dependent/response variable?

Enter the data into an Excel spreadsheet.

c. Create a scatterplot for these data. How would you interpret the scatterplot?

Run a regression analysis using Data Analysis/Regression Tool and use the output to answer the following questions:

d. What is the value of the correlation coefficient? How would you interpret it?

e. What is the value of the coefficient of determination? How would you interpret it?

f. Write the hypotheses for the test of the slope.

g. What is the p-value for the test of the slope? How would you interpret the p-value?

h. What is the regression formula resulting from this analysis between Shelf Space and Weekly Sales?

i. Use the regression formula to estimate the Weekly Sales for a product that has a Shelf space of 23.

j. Use the regression formula to estimate the Weekly Sales for a product that has a Shelf space of 8.

For the standard normal distribution, find the value of c such that:

P(z > c) = 0.0025

Solve the problem.

A one-sided confidence interval for p can be written as p <  + E or p >  - E where the margin of error E is modified by replacing z_/2 with z. If a teacher wants to report that the fail rate on a test is at most x with 90% confidence, construct the appropriate one-sided confidence interval. Assume that a simple random sample of 70 students results in 5 who fail the test.

a) p < 0.032

b) p < 0.122

c) p > 0.032

d) p < 0.111

A statistics professor at a large university hypothesizes that students who take statistics in the morning typically do better than those who take it in the afternoon. He takes a random sample of 36 students who took a morning class and, independently, another random sample of 36 students who took an afternoon class. He finds that the morning group scored an average of 72 with a standard deviation of 8, while the evening group scored an average of 68 with a standard deviation of 10. The population standard deviation of scores is unknown but is assumed to be equal for morning and evening classes. Let µ1 and µ2 represent the population mean final exam scores of statistics' courses offered in the morning and the afternoon, respectively. Compute the appropriate test statistic to analyze the claim at the 1% significance level.

We draw a random sample of size 36 from a population with standard deviation 3.2. If the sample mean is 27, what is a 95% confidence interval for the population mean?