Let Y have the lognormal distribution with mean 78.8 and variance 160.20. Compute the following probabilities. (You may find it useful to reference the z table. Round your intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answers to 4 decimal places.)

1. Find the equation of a linear regression line for the data where age is the independent variable, x, and time is the dependent variable. (Enter a mathematical expression. Round your numerical answers to three decimal places.)

ŷ =

2. Using the equation from part (a), estimate the number of hours a person 30 years old spends on the internet. (Enter a number. Round your answer to the nearest hour.)

3. Find the linear correlation coefficient. (Enter a number. Round your answer to the nearest four decimal places.)

R=

A random sample of n = 500 observations from a binomial population produced x = 250 successes. Find a 90% confidence interval for p. (Round your answers to three decimal places.)

Interpret the interval:

A. In repeated sampling, 90% of all intervals constructed in this manner will enclose the population proportion.

B. 90% of all values will fall within the interval.

C. In repeated sampling, 10% of all intervals constructed in this manner will enclose the population proportion.

D. There is a 10% chance that an individual sample proportion will fall within the interval.

E. There is a 90% chance that an individual sample proportion will fall within the interval.

4) A medical researcher is interested in knowing what percentage of the U.S. population has a certain gene. The researcher collect a random sample of 510 people from across the country, and tests them for the gene. The gene was present in 42 of the 510 people tested.

a) Find a 90% confidence interval for the true proportion of people in the U.S. with the gene.

b) Provide the right endpoint of the interval as your answer.

Round your answer to 4 decimal places.

Consider the following hypothesis test:

H0: p ≥ 0.75

Ha: p < 0.75

A sample of 300 items was selected. Compute the p-value and state your conclusion for each of the following sample results. Use α = .05.

Round your answers to four decimal places.

a. p = 0.67   p-value _____?

b. p = 0.75 p-value _____?

c. p = 0.7 p-value _____?

d. p = 0.77 p-value _____?

Let X1,..., Xn be an i.i.d. sample from a geometric distribution with parameter p.

U = ( 1, if X1 = 1, 0, if X1 > 1)

find a sufficient statistic T for p.

find E(U|T)

. For n = 2 look at the smallest and largest sample means. How close is each of these sample means to the population mean? Use the formula x − . This difference is called the sampling error.

Do the same for n = 3 and n = 4. What do you notice as n gets larger?

A common test for tuberculosis (TB) is a skin test, where protein is injected into a person’s arm and the person tests positive for TB if a rash develops. The probability of the person testing negative when they have TB is 1% (false negative). In some cases, a rash can develop even if the person does not have TB (false positive). Assume the probability of a false positive is 5%. Only 4 in 10,000 people have TB.

(a) Let T + mean “tests positive”, T − mean “tests negative”, and D mean “has the disease TB”. Use proper probabilistic notation to write three probabilities that are directly given in the information above.

(b) Draw a tree diagram (based upon the conditional information that is given) to show all possibilities. Fill in all probabilities along the tree.

(c) What is the probability that a randomly selected person will test positive for TB? Show all work, and use proper notation. You may leave your answer numerically unsimplified.

(d) What is the probability that a randomly selected person who tests positive actually has TB? Show all work, and use proper notation. You may leave your answer numerically unsimplified.

. For the questions, your report should include the formulated hypotheses, steps of calculation and formulas, your answers and conclusions, and the results from Excel.

A retail company has started a new advertising campaign in order to increase sales. In the past, the mean spending in both the 18–35 and 35+ age groups was at most $70.00. a. Formulate a hypothesis test to determine if the mean spending has statistically increased to more than $70.00.

b. After the new advertising campaign was launched, a marketing study found that the sample mean spending for 400 respondents in the 18–35 age group was $73.65, with a sample standard deviation of $56.60. Is there sufficient evidence to conclude that the advertising strategy significantly increased sales in this age group with significance level of 5%?

c. For 600 respondents in the 35+ age group, the sample mean and sample standard deviation were $73.42 and $45.44, respectively. Is there sufficient evidence to conclude that the advertising strategy significantly increased sales in this age group with significance level of 5%?

Question:

If all other factors are constant, explain in detail (in your own words) what happens to the standard error of estimate as the correlation moves closer to zero. The regression equation is intended to be the "best fitting" straight line for a set of data. What is the criterion for the best fitting? Explain in detail in your own words. Note: While the majority of your answers should be in your own words, you may cite sources to support your rationale.

The Answer I got:

The standard error to estimate decrease because the data point is closer to line. *The best fitting line is determined by the error between the predicted Y values on the line and the actual Y values in the data.

-I NEED THIS ANSWER TO BE LONGER AND TO BE EXPLAINED IN DETAIL

A retail company has started a new advertising campaign in order to increase sales. In the past, the mean spending in both the 18–35 and 35+ age groups was at most $70.00.

a. Formulate a hypothesis test to determine if the mean spending has statistically increased to more than $70.00.

b. After the new advertising campaign was launched, a marketing study found that the sample mean spending for 400 respondents in the 18–35 age group was $73.65, with a sample standard deviation of $56.60. Is there sufficient evidence to conclude that the advertising strategy significantly increased sales in this age group with significance level of 5%?

c. For 600 respondents in the 35+ age group, the sample mean and sample standard deviation were $73.42 and $45.44, respectively. Is there sufficient evidence to conclude that the advertising strategy significantly increased sales in this age group with significance level of 5%?

A chocolate chip cookie manufacturing company recorded the number of chocolate chips in a sample of 50 cookies. The mean is 22.26 and the standard deviation is 2.28.Construct a

95% confidence interval estimate of the standard deviation of the numbers of chocolate chips in all such cookies.

2. At a zoo, Biteyfloofers have a mean length of 11” and standard devation 2.5”, while Fluffersnappers have a mean length of 10” and standard deviation 2”. Both follow an approx. normal distribution. (a) Which is more unusual, a Fluffersnapper that is 12” long or a Biteyfloofer that is 12”? (b) Which would seem longer relative to their populations, a 9” Fluffersnapper or a 9.5” Biteyfloofer? (c) Use the empirical rule to compare the middle 95% of heights for each creature.

In a study of Americans from a variety of professions were asked if they considered themselves left-handed, right-handed, or ambidextrous.

The results are given below:

1. Test for an association between handedness and career for these five professions. What do you conclude at the 5% significance level? What do you conclude at the 1% confidence level? Make sure you show all the steps.

2. Can we conclude, at the 5% significance level, that left-handedness is equally distributed among the five professions? Make sure you show all the steps.

Exhibit 2

Current statistics show that, about 5% of the patients who are infected with the Novel Coronavirus are in serious or critical condition, and need ventilators and oxygen facilities. Suppose this is the population proportion. (The questions related to this Exhibit are designed so that you can see how statistical analyses can be used to fight against pandemics.)

Question 7

Refer to Exhibit 2. Assume that in the City of Gotham, in the first week of outbreak, 256 citizens are tested positive for COVID-19. At least how many ventilators should be prepared to meet the possible demand. (Round up to the nearest integer that is larger than the result.)

Question 8

Refer to Exhibit 2. Suppose the No. 1 district of the City of Gotham has 8100 residents living in it. If you were the head of the health department of the No. 1 district. To cope with the possible all-infection outbreak of COVID-19 in your district, you prepared 600 ventilators. Assuming in the worst case scenario, what is the probability that your prepared medical equipments are overwhelmed by the serious conditioned patients who are in need of the ventilators? (Round up to nearest four decimal place.)

Question 9

Refer to Exhibit 2. In the first week of out break, the total number of confirmed cases in the No. 1 district of Gotham is 96. Out of these 96 cases, no one has developed serious conditions yet. But you want to use the normal approximation method to estimate a probability that, from these 96 infected patients, more than 10 cases develop a serious condition. Are you able to do so? Why or why not? If yes, please provide the probability value you estimated. (In four decimal places.)

Question 10

Refer to Exhibit 2. In the second week, the total number of confirmed cases in the No. 1 district of Gotham increased to 196. You want to use this sample of 196 cases and the normal approximation method to estimate the probability that, from these 196 patients, more than 19 cases develop a serious condition. Are you able to do so? Why or why not? If yes, please provide the probability value you estimated. (In four decimal places.)

Question 11

Refer to Exhibit 2. Suppose that you are the head of the health department in the City of Zion. You DO NOT know the population proportion of seriously conditioned cases among the people who infected with the COVID-19. But now you have a sample of 625 cases who tested positive of COVID-19, out of these 625 patients, 28 developed serious conditions. What is your estimation of the proportion of seriously conditioned patients? (Round to the nearest four decimal place.)

Question 12

Refer to Exhibit 2. Continue from Question 11. Construct a 88% confidence interval (CI) for the proportion you estimated in Question 11. What is the Lower Confidence Limit of your CI? (Round to the nearest four decimal place.)

Question 13

Refer to Exhibit 2. Continue from Question 12. What is the Upper Confidence Limit of your CI? (Round to the nearest four decimal place.)