Rhino viruses typically cause common colds. In a test of the effectiveness of​ echinacea, 38 of the 45 subjects treated with echinacea developed rhinovirus infections. In a placebo​ group, 87 of the 101 subjects developed rhinovirus infections. Use a 0.05 significance level to test the claim that echinacea has an effect on rhinovirus infections. Complete parts​ (a) through​ (c) below.

Identify the test statistic.:

Z equals negative 0.27 ​(Round to two decimal places as​ needed.)

Identify the​ P-value. ​:

P-value equals 0.788 ​(Round to three decimal places as​ needed.)

What is the conclusion based on the hypothesis​ test? The​ P-value is greater than the significance level of a= 0.05​, so fail to reject the null hypothesis. There is not sufficient evidence to support the claim that echinacea treatment has an effect. :

b. Test the claim by constructing an appropriate confidence interval.

The 95​% confidence interval is nothing less than left parenthesis p 1 minus p 2 right parenthesis less than nothing. :

___<(P1-P2)>___ ?

So what does P1 and P2 equal?

Assume that a hypothesis test will be conducted using significance level α = .01 and alternative hypothesis Ha: μ : ≠ 19.3.

Furthermore, we will use the following sample data: n = 12, x-bar = 18.8, and s = 2.1.

1. A statistic is an unbiased estimator of a population parameter. This means that ...

A. ... the population mean is equal to the mean of the parameter.

B. ... the population is normal and the population mean is equal to the statistic.

C. ... the population is normal, the population mean is equal to the statistic mean, and the population standard deviation is equal to the parameter standard deviation.

D. ... the statistic mean is equal to the parameter.

2. An online survey was conducted to study cyberbullying in the UK. It was reported that 62% of young people had received nasty private messages on a social network. You randomly sample four young people from the network and ask them if they received nasty messages on the network. Find the probability that the number who received these messages is three.

A. .85 B. .36 C. .74 D. .18

3. The number of particles large enough to initiate a crack on an aircraft wing follows a Poisson distribution with mean 0.5 per square centimeter. Find the probability that a 100 square centimeter section has more than 60 of these particles.

A. .270 B. .207 C. .072 D. .027

6. In a survey of 1430 undergraduate students, 1087 reported that they had one or more credit cards. Give a 95% confidence interval for the proportion of all college students who have at least one credit card.

A. 73% to 79% B. 70% to 82% C. 65% to 60% D. 74% to 78%

7. A study compared the proportions of young women and men who use Instagram. Out of 537 women, 328 used Instagram, whereas out of 532 men, 234 used the service. Find a 95% confidence interval for the difference between the proportions of men and women who use Instagram.

A. .09 to .25 B. .10 to .24 C. .11 to .23 D. .12 to .22

8. As a result of the computation of a confidence interval with a 95% confidence level, it is reported that the proportion of American families that own more than one car is 12.4% with a margin of error of 2%. In light of this, we are 95% confident that the largest the actual proportion of such families can be is:

A. 14.4% B. 12.6% C. 12.42% D. 16.4%

The Bank of Canada takes several measures to protect Canadian Economy. One of the tools Bank of Canada uses to adjust monetary policies is changing the interest rate. Increasing in interest rate would reduce how much Canadian borrow and spend. This will affect the housing market, as the increased interest rate means lower ability to borrow. A real estate advisor, however, thinks the Ottawa real estate market is hot and that an increase in interest rate would not lower the prices of houses. He assesses the likelihood of Bank of Canada’s action and its effect on house prices in Ottawa:

The likelihood of an increase in the average price of houses in Ottawa if the interest rate increases = 0.15

The likelihood of an increase in the average price of houses in Ottawa if the interest rate maintains the same level = 0.75

The chance of Bank of Canada’s maintaining the current interest rate = 0.65

We are certain that the Bank of Canada does not lower the interest rate in the near future. Bank of Canada believes to strengthen the Economy, the current interest rate should be maintained or increase. If you notice an increase in the price of houses, what probability do you assign to the event that Bank of Canada increased the interest rate?

Male and female populations of

humpback whaleshumpback whales

under 80 years old are represented by age in the table below. Complete parts​ (a) through​ (d).

Age. Males. Females

​0-9 (13). (10)

​10-19 (11) (10)

​20-29 (18) (16)

​30-39 (18) (16)

​40-49 (25) (23)

​50-59 (22) (25)

​60-69 (19) (15)

​70-79 (14) (12)

Find the population mean and standard deviation of age for males and females.

An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 4.2 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 170 engines and the mean pressure was 4.4 pounds/square inch. Assume the standard deviation is known to be 1.0. A level of significance of 0.02 will be used. Determine the decision rule.

Enter the decision rule

Someone witnesses a crime involving a taxi. The witness tells the police that the taxi was blue. The police know that 80% of witnesses are correct and also that 12% of all of the taxis that could have been involved are blue while the rest are green. What is the probability that the taxi was in fact blue? Write your answer out to two decimal places so that 1% is .01, 99% is .99, etc. "base rate fallacy taxi"

A sample of 40 observations results in a sample mean of 436. The population standard deviation is known to be 121.

1. Construct a 95% confidence interval for the population mean.
2. Does the sample evidence enable to conclude that the population mean is greater than 400 with the 5% significance level? Conduct the test based on the critical value approach.
3. Does the sample evidence enable to conclude that the population mean is greater than 400 with the 5% significance level? Conduct the test based on the p-value approach.
4. Does the sample evidence enable to conclude that the population mean is greater than 400 with the 10% significance level? Conduct the test based on the p-value approach.
5. Does the sample evidence enable to conclude that the population mean is different from 400 with the 5% significance level? Conduct the test based on the p-value approach.

A stockbroker has a large number of clients. The proportion of clients with whom she does not communicate during a given month has the beta distribution with parameters α = 6 and β = 2. Determine the probability that, during a given month, the percentage of clients with whom the broker does not communicate will be

a) at least 60%.

b) between 70% and 80%.

A research reports a comparison of 2 methods for predicting the strength of 9 different types of steel. The following table shows the results of this research. a) We wish to determine whether there is any difference in the predicted mean strength for the two methods at 1% alpha level. b) Solve part (a) by Minitab and report the results.

a) We wish to determine whether there is any difference in the predicted mean strength for the two methods at 1% alpha level.

b) Solve part (a) by Minitab and report the results.

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

The National Council of Small Businesses is interested in the proportion of small businesses that declared Chapter 11 bankruptcy last year. Since there are so many small businesses, the National Council intends to estimate the proportion from a random sample. Let p be the proportion of small businesses that declared Chapter 11 bankruptcy last year.

(a) If no preliminary sample is taken to estimate p, how large a sample is necessary to be 99% sure that a point estimate p̂ will be within a distance of 0.09 from p? (Round your answer up to the nearest whole number.)
small businesses

(b) In a preliminary random sample of 30 small businesses, it was found that thirteen had declared Chapter 11 bankruptcy. How many more small businesses should be included in the sample to be 99% sure that a point estimate p̂ will be within a distance of 0.090 from p? (Round your answer up to the nearest whole number.)
more small businesses

Let's say you have a bag of 100 marbles. There are an equal number of five different colors. You are curious to know what the probability would be if you dipped your hand in and grabbed out 5 of the same color marble. In this scenario, the underlying success rate = _______.

**Please show work!

What price do farmers get for their watermelon crops? In the third week of July, a random sample of 44 farming regions gave a sample mean of x = $6.88 per 100 pounds of watermelon. Assume that σ is known to be $1.92 per 100 pounds.

(a) Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop. What is the margin of error? (Round your answers to two decimal places.)

(b) Find the sample size necessary for a 90% confidence level with maximal error of estimate E = 0.39 for the mean price per 100 pounds of watermelon. (Round up to the nearest whole number.)
farming regions

(c) A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop. What is the margin of error? Hint: 1 ton is 2000 pounds. (Round your answers to two decimal places.)

HW 9: Linear Regression and Correlation Analysis

INSTRUCTIONS: Please modify the Excel sheet attached to complete this assignment. Turn in the following work including: 1) written formulas, 2) values from Excel plugged into formulas, and 3) final answer.

Scenario: A graduate student has administered a pro-inflammatory substance, lipopolysaccharide (LPS), to rats in the form of a pill (several doses – 0 mg or placebo, 1.25 mg, 2.5 mg, 5.0 mg, and 10 mg). She then determines the blood concentration of a particular protein that is thought to be upregulated due to LPS called Inflammo using ELISA. Find the linear model and the correlation coefficient of the experimental data on Blackboard labeled “HW9 Raw Data”.

(10pts)Equation for Linear Model:

(10pts)Correlation Coefficient:

(10pts)Does the linear model describe the relationship between LPS and Inflammotin concentration well?

(10pts)If so, what type of correlation exists between LPS dosage and Inflammo concentration?

Equations/formulas (30 pts)(Attach work):

The data from exercise 3 follow.

The estimated regression equation is ŷ = 7.6 + .9x.

1. What is the value of the standard error of the estimate (to 4 decimals)?
   
2. What is the value of the t test statistic (to 2 decimals)?
   
   
   What is the p-value?
   - Select your answer -less than .01between .01 and .02between .02 and .05between .05 and .10between .10 and .20between .20 and .40greater than .40Item 3
   
   What is your conclusion (α = .05)?
   - Select your answer -Conclude a significant relationship exists between x and yCannot conclude a significant relationship exists between x and yItem 4
3. Use the F test to test for a significant relationship. Use α = .05.
   
   Compute the value of the F test statistic (to 2 decimals).
   
   
   What is the p-value?
   - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 6
   
   What is your conclusion?