An article suggests the lognormal distribution as a model for SO₂ concentration above a certain forest. Suppose the parameter values are μ = 1.9 and σ = 0.8.

(a) What are the mean value and standard deviation of concentration? (Round your answers to three decimal places.)

(b) What is the probability that concentration is at most 10? Between 5 and 10? (Round your answers to four decimal places.)

Assume that each sample is a simple random sample obtained from a population with a normal distribution.

a. n= 93 mean=3.90968 s=0.51774 Construct a 99​% confidence interval estimate of the standard deviation of the population from which the sample was obtained.

b. n=93 mean=4.09355 s=0.59194 Repeat part​ (a).

How do you find values on a chi-square table when the degrees of freedom are a value not commonly found on standard chi-square tables? (In this case, 92)

The American Housing Survey reported the following data on the number of times that owner-occupied and renter-occupied units had a water supply stoppage lasting 6 or more hours in the past 3 months.

Do not round intermediate calculations. Round your answers to two decimal places.

a. Define a random variable x = number of times that owner-occupied units had a water supply stoppage lasting 6 or more hours in the past 3 months and develop a probability distribution for the random variable. (Let x = 4 represent 4 or more times.)

b. Compute the expected value and variance for x.

c. Define a random variable y = number of times that renter-occupied units had a water supply stoppage lasting 6 or more hours in the past 3 months and develop a probability distribution for the random variable. (Let y = 4 represent 4 or more times.)

d. Compute the expected value and variance for y.

A researcher believes that college students today have different IQ scores than in previous years. To investigate this belief, he randomly samples 41 currently enrolled students and records their IQ scores. The scores have a mean of 111 and a standard deviation of 12.4. A local census taken 10 years ago shows that the mean IQ of students enrolled during that time was 115.

The degrees of freedom for this sample is                            [ Select ]                       ["41", "40", "39", "38", "-2.201", "-2.407", "2.704", "2.021", "-2.07", "+2.07", "-0.32", "+0.32", "reject the null hypothesis", "fail to reject the null hypothesis", "IQ is probably different", "IQ is not different"]         

Using a two tailed alpha level of .01, the appropriate critical value is                             [ Select ]                       ["41", "40", "39", "38", "-2.201", "-2.407", "2.704", "2.021", "-2.07", "+2.07", "-0.32", "+0.32", "reject the null hypothesis", "fail to reject the null hypothesis", "IQ is probably different", "IQ is not different"]         

The obtained value of the appropriate statistic is                            [ Select ]                       ["41", "40", "39", "38", "-2.201", "-2.407", "2.704", "2.021", "-2.07", "+2.07", "-0.32", "+0.32", "reject the null hypothesis", "fail to reject the null hypothesis", "IQ is probably different", "IQ is not different"]         

What is your decision?                             [ Select ]                       ["41", "40", "39", "38", "-2.201", "-2.407", "2.704", "2.021", "-2.07", "+2.07", "-0.32", "+0.32", "reject the null hypothesis", "fail to reject the null hypothesis", "IQ is probably different", "IQ is not different"]         

Is the IQ of currently enrolled college students different than in previous years?                            [ Select ]                       ["41", "40", "39", "38", "-2.201", "-2.407", "2.704", "2.021", "-2.07", "+2.07", "-0.32", "+0.32", "reject the null hypothesis", "fail to reject the null hypothesis", "IQ is probably different", "IQ is not different"]         

A telephone service representative believes that the proportion of customers completely satisfied with their local telephone service is different between the Midwest and the West. The representative's belief is based on the results of a survey. The survey included a random sample of 760 midwestern residents and 680 western residents. 37% of the midwestern residents and 46% of the western residents reported that they were completely satisfied with their local telephone service. Find the 90% confidence interval for the difference in two proportions.

1. Find the point estimate that should be used in constructing the confidence interval.

2.  Find the margin of error. Round your answer to six decimal place

It is known that 83% of all new products introduced in grocery stores fail (are taken off the market) within 2 years. If a grocery store chain introduces 70 new products, find the following probabilities. (Round your answers to four decimal places.)

(a) within 2 years 47 or more fail

(b) within 2 years 58 or fewer fail

(c) within 2 years 15 or more succeed

(d) within 2 years fewer than 10 succeed

1. A student researcher works at ski resort. For a student project, they would like to know whether the proportion of skiers on a particular day is about the same as the proportion of snowboarders. They take a stratified random sample, looking at each of the 3 chair lifts and randomly selecting every other chair of people to mark whether they are a skier (1) or a snowboarder (0). Which test is most appropriate to test whether the proportion of skiers is not 0.50?

           [ Choose ] Two Sample t test Matched Pairs t test Multiple Regression Analysis Simple Linear Regression Single-factor ANOVA One Proportion z Test         

2. A team of engineers perform an experiment to test the strength of four cable types made from different materials. They would like to see whether any of the cable types have an average strength that is stronger than the others. They test the strength of seven cables for each cable type and compare the averages of the four groups. What type of procedure is appropriate to tell if there is a difference between the average strength between the cable types?

           [ Choose ] Two Sample t test Matched Pairs t test Multiple Regression Analysis Simple Linear Regression Single-factor ANOVA One Proportion z Test         

3. In order to attract wasps into a trap, a group of researchers are interested in the effectiveness of two different types of wasp attractants. They set up an experiment with “Wasp Bait A” and “Wasp Bait B” and randomly assign 40 identical traps to receive one of two attractants. After a significant time period, the average number of wasps per trap are compared between the two attractants. What procedure will best test the difference in the average number of trapped wasps among the two attractants?

           [ Choose ] Two Sample t test Matched Pairs t test Multiple Regression Analysis Simple Linear Regression Single-factor ANOVA One Proportion z Test         

4. Often students claim they forget much of the information they learn from a course soon after the course ends. In an educational study, researchers would like to estimate the average difference in scores from a test taken at the conclusion of a course and again 6 months after the conclusion of the course. Specifically, they would like to see whether the average difference between the two test scores is other than 0. What type of procedure is appropriate for this scenario?

           [ Choose ] Two Sample t test Matched Pairs t test Multiple Regression Analysis Simple Linear Regression Single-factor ANOVA One Proportion z Test         

5. A real estate website would like to build a model and test to see which factors are good at predicting the selling price of homes on their site. They would like to predict house sale price based on several factors including number of bedrooms, number of bathrooms, age of home, square footage and more. What type of analysis would be appropriate for this scenario?

           [ Choose ] Two Sample t test Matched Pairs t test Multiple Regression Analysis Simple Linear Regression Single-factor ANOVA One Proportion z Test

A study of the effect of television commercials on 12-year-old children measured their attention span, in seconds. The commercials were for clothes, food, and toys.

1. Complete the ANOVA table. Use 0.05 significance level. (Round the SS and MS values to 1 decimal place and F value to 2 decimal places.)

2. Find the values of mean and standard deviation. (Round the mean and standard deviation values to 3 decimal places.)

3. Is there a difference in the mean attention span of the children for the various commercials?

4. Are there significant differences between pairs of means?

Three admission test preparation programs are being evaluated. Suppose the scores obtained by a sample of 20 people who used the programs provided the following data.

Use the Kruskal-Wallis test to determine whether there is a significant difference among the three test preparation programs. Use α = 0.05.

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

For this activity, select a recurring quantity from your OWN life for which you have monthly records at least 2 years (including 24 observation in dataset at least). This might be the cost of a utility bill, the number of cell phone minutes used, or even your income. If you do not have access to such records, use the internet to find similar data, such as average monthly housing prices, rent prices in your area for at least 2 years (You must note the data source with an accessible link). Data can also be monthly sales of some particular commodity. 1.4 Please do the descriptive analysis, using the method of index number and Exponential Smoothing individually. And try to explain the pattern you find. 1.5 Use two methods you learned to predict the value of your quantity for the next year (12 months). And make a comparison with two results.

Fresh!Now! is a chain of grocery stores in the United States with 1921 grocery stores in total, some of which also sell bakery goods and freshly made food-to-go. Fresh!Now!’s goal is to provide good quality fresh vegetables at affordable prices. However, given the existing market of organic food supplies, Fresh!Now! is facing tremendous competition. They realize that Fresh!Now! has to make their stores more attractive to customers.

In 19 stores across Massachusetts and New York, they have implemented a new concept to present the vegetables in the stores and have collected information of the average daily profit of leafy vegetables (in dollar) per customer per store (see table below). Janine, the head of the analytics department at Fresh!Now!, has tasked you with developing an anlaysis to better understand if the new concept has any effect.

Your first task it to create a 95% confidence interval for the mean of the dataset using the sample collected from Massachusetts and New York.

What is the upper limit of this confidence interval?

What is the lower limit of this confidence interval?

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Part 2

To understand if the new concept has taken effect, you want to conduct a hypothesis test. Average daily profit per customer per store for the leafy vegetables in all other Fresh!Now! grocery stores is 14.

You formulate the following hypothesis test:

H0: Average daily profit at Fresh!Now! in the New York/Massachusetts stores is not higher than the average daily profit of all other Fresh!Now! grocery stores at a confidence level of 95%.

H1: Average daily profit at Fresh!Now! in the New York/Massachusetts stores is higher than the average daily profit of all other Fresh!Now! grocery stores at a confidence level of 95%.

1) Calculate the test-statistic for the hypothesis test above?

2) Please select the result of your hypothesis test:

Choose the correct answer.

Fail to reject H0: You are not 95% confident that the mean profit in the Massachusetts/Boston stores is higher than the population mean.

Accept H0: Profit in the Massachusetts/Boston stores is lower than the population mean at the 95% confidence level.

Reject H0: You are 95% confident that the mean profit in the Massachusetts/Boston      stores is higher than the population mean.

The result of your hypothesis test does not tell you if you can reject H0 or not.

3) Calculate the p-value for the hypothesis test above?

A California grower has a 50-acre farm on which to plant strawberries and tomatoes. The grower has available 300 hours of labor per week and 800 tons of fertilizer, and he has contracted for shipping space for a maximum of 26 acres’ worth of strawberries and 37 acres’ worth of tomatoes. An acre of strawberries requires 10 hours of labor and 8 tons of fertilizer, whereas an acre of tomatoes requires 3 hours of labor and 20 tons of fertilizer. The profit from an acre of strawberries is $400, and the profit from an acre of tomatoes is $300. The farmer wants to know the number of acres of strawberries and tomatoes to plant. Formulate a linear programming model for this problem and solve it using the graphical method. Your file should contain the following information: LP model where decision variables are clearly identified, a graph showing all constraints with feasible region clearly identified and a table showing all extreme corners in the feasible region with optimal solution.

1. The weights of adults (in kg) follows a normal distribution with a mean of 67 and a standard deviation of 11. For a random sample of 64 adults, find the probability that the mean weight of the sample is at most 63 kg.

2. Suppose that 50% of politicians are lawyers. Find the probability that of a random sample of 400 politicians, at least 47% are lawyers.

2.            The proportion of people who wait more than an hour at the Social Security Office is 28%. Use this information to answer the following questions:

A.            If you randomly select 45 people what is the probability that at least 34% of them will wait more than an hour?

B.            If you randomly select 60 people what is the probability that between 25% and 30% of them will wait more than an hour?

C.            If you randomly select 150 people what is the probability that less than 23% of them will wait more than an hour?