A study was conducted to assess the effects that occur when children are exposed to cocaine before birth. Children were tested at age 4 for object assembly​ skill, which was described as​ "a task requiring​ visual-spatial skills related to mathematical​ competence." The 196 children born to cocaine users had a mean of 7.4 and a standard deviation of 2.9. The 183 children not exposed to cocaine had a mean score of 8.3 with a standard deviation of 3.1. Assume that the two samples are independent simple random samples selected from normally distributed​ populations, and do not assume that the population standard deviations are equal. Let population 1 be children born to cocaine users

Identify the null and alternative hypotheses

State the conclusion for the test.

The American Bankers Association reported that, in a sample of 150 consumer purchases in France, 74 were made with cash, compared with 28 in a sample of 60 consumer purchases in the United States.

Construct a 99 percent confidence interval for the difference in proportions. (Round your intermediate value and final answers to 4 decimal places.)

The 99 percent confidence interval is from to _____ . _____

The annual maximum flow data for two different periods of record for Genesee River at Rochester, NY, are given below. Determine whether there is homogeneity in the sequence of data of two periods, at the 2.5% level of significance.

Anystate Auto Insurance Company took a random sample of 368 insurance claims paid out during a 1-year period. The average claim paid was $1585. Assume σ = $242.

Find a 0.90 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

Find a 0.99 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

Suppose that there are two schools in a region. 7% of students will move from school A to school B at the end of each year, while 11% of students will move from school B to school A. Suppose that initially 30% of students attend school A and 70% attend school B.

a) Determine the transition matrix and the initial probability vector which can be used to represent this information.

b) Find the percentage of students attending each school at the end of 3 years ( give answers to four decimal places)

Racism, juries, and interactions: In a study of racism, Nail, Harton, and Decker (2003) had participants read a scenario in which a police officer assaulted a motorist. Half the participants read about an African American officer who assaulted a European American motorist, and half read about a European American officer who assaulted an African American motorist. Participants were categorized based on political orientation: liberal, moderate, or conservative. Participants were told that the officer was acquitted of assault charges in state court but was found guilty of violating the motorist’s rights in federal court. Double jeopardy occurs when an individual is tried twice for the same crime. Participants were asked to rate, on a scale of 1–7, the degree to which the officer had been placed in double jeopardy by the second trial. The researchers reported the interaction as F(2, 58) = 10.93, p < 0.0001. The means for the liberal participants were 3.18 for those who read about the African American officer and 1.91 for those who read about the European American officer. The means for the moderate participants were 3.50 for those who read about the African American officer and 3.33 for those who read about the European American officer. The means for the conservative participants were 1.25 for those who read about the African American officer and 4.62 for those who read about the European American officer. ***This prompt requires certain formatting so that you can draw tables and bar graphs. You can use Microsoft Excel or Microsoft Word, or any other word processing software to create your post/ post it as an attachment in the discussion. Draw a table of cell means that includes the actual means for this study. Do the reported statistics indicate that there is a significant interaction? If yes, describe the interaction in your own words. Draw a bar graph that depicts the interaction. Include lines that connect the tops of the bars and show the pattern of the interaction. Is this a quantitative or qualitative interaction? Explain. Change the cell mean for the conservative participants who read about an African American officer so that this is now a quantitative interaction. Draw a bar graph that depicts the pattern that includes the new cell means. Change the cell means for the moderate and conservative participants who read about an African American officer so that there is now no interaction. Draw a bar graph that depicts the pattern that includes the new cell mean

   5. A new young mother has opened a cloth diaper service. She is interested in simulating the number of diapers required for a one-year- old. She hopes to use this data to show the cost effectiveness of cloth diapers. The table below shows the number of diapers demanded daily and the cumulative probabilities associated with each level of demand.

(a)    Find the missing values x.

(b)   Find the probability of each of daily demands?

(c)    If the random number 96 were generated for a particular day, what would be the simulated demand for that day?

Salmon Weights: Assume that the weights of spawning Chinook salmon in the Columbia river are normally distributed. You randomly catch and weigh 18 such salmon. The mean weight from your sample is 19.2 pounds with a standard deviation of 4.7 pounds. You want to construct a 95% confidence interval for the mean weight of all spawning Chinook salmon in the Columbia River. (a) What is the point estimate for the mean weight of all spawning Chinook salmon in the Columbia River? pounds (b) Construct the 95% confidence interval for the mean weight of all spawning Chinook salmon in the Columbia River. Round your answers to 1 decimal place. < μ < (c) Are you 95% confident that the mean weight of all spawning Chinook salmon in the Columbia River is greater than 15 pounds and why? No, because 15 is above the lower limit of the confidence interval. Yes, because 15 is below the lower limit of the confidence interval. No, because 15 is below the lower limit of the confidence interval. Yes, because 15 is above the lower limit of the confidence interval. (d) Recognizing the sample size is less than 30, why could we use the above method to find the confidence interval? Because we do not know the distribution of the parent population. Because the sample size is greater than 10. Because the parent population is assumed to be normally distributed. Because the sample size is less than 100.

20. A film distribution manager calculates that 8% of the films released are flops. If the manager is right, what is the probability that the proportion of flops in a sample of 409 released films would differ from the population proportion by more than 3%? Round your answer to four decimal places.

1. A soft drink manufacturer wishes to know how many soft drinks adults drink each week. They want to construct a 98% confidence interval with an error of no more than 0.07. A consultant has informed them that a previous study found the mean to be 6.4 soft drinks per week and found the variance to be 0.81. What is the minimum sample size required to create the specified confidence interval? Round your answer up to the next integer.

Researchers watched groups of dolphins off the coast of Ireland in 1998 to determine what activities the dolphins partake in at certain times of the day ("Activities of dolphin," 2013). The numbers in table #4.3.3 represent the number of groups of dolphins that were partaking in an activity at certain times of days. Table #4.3.3: Dolphin Activity Activity Period Morning Noon Afternoon Evening Total Travel 6 6 14 13 39 Feed 28 4 0 56 88 Social 38 5 9 10 62 Total 72 15 23 79 189 a.) What is the probability that a dolphin group is partaking in travel? b.) What is the probability that a dolphin group is around in the morning? c.) What is the probability that a dolphin group is partaking in travel given that it is morning? d.) What is the probability that a dolphin group is around in the morning given that it is partaking in socializing? e.) What is the probability that a dolphin group is around in the afternoon given that it is partaking in feeding? f.) What is the probability that a dolphin group is around in the afternoon and is partaking in feeding? g.) What is the probability that a dolphin group is around in the afternoon or is partaking in feeding? h.) Are the events dolphin group around in the afternoon and dolphin group feeding mutually exclusive events? Why or why not? i.) Are the events dolphin group around in the morning and dolphin group partaking in travel independent events? Why or why not?

Suppose that a pharmaceutical company makes the assertion that Drug A has a stronger effect than Drug B. To test this claim, 1000 randomly selected people were given the two drugs during different treatment periods. Among them, 600 preferred taking Drug A because of the stronger effect they felt; whereas 400 preferred Drug B. Determine whether there is sufficient evidence, at the 5% level of significance, to support the company’s claim that Drug A is stronger and preferred by more than 50% of patients.

Select one:

a. Reject H₀; Drug A is stronger and preferred by less than 50% of patients.

b. Reject H₀; Drug A is stronger and preferred by more than 50% of patients.

c. Do not reject H₀; Drug A is stronger and preferred by less than 50% of patients.

d. Do not reject H₀; Drug A is stronger and preferred by more than 50% of patients.

Campus Barber Shop has one barber. Customers arrive at a rate of 2.2 per hour, and haircuts are given at a rate of 3 per hour. Assume the basic Poisson-Exponential model and answer the following questions.

1. What is the probability that the barber is idle?

2. What is the probability that one customer is getting a haircut and no one is waiting in the line?

3. What is the probability that one customer is receiving a haircut and one customer is in the line waiting?

4. What is the probability that one customer is receiving a haircut and two customers are waiting in the line.

5. On the average, how many customers are in the shop?

6. On the average, how long is the line?

7. What is the average time in the line before service begins.

8. If a customer arrives at 10:00 AM, when should he expect to leave the shop?

Before opening the dataset needed for this problem, you’ll need to call the “car” package:

> library(car)

Now you can import the “Wong” dataset and use it to answer the question below.

Remember to include any code you use along with your answers in your submission!

3. The Wong dataset contains data from a study by Wong, Monette, and Weiner (2001) on patients who fell into comas after sustaining traumatic brain injuries. After waking, Wong and colleagues administered two different intelligence tests (the “piq” and “viq” variables). The “duration” variable indicates how long each patient was in a coma before waking (measured in days).
a. Consider that this dataset represents the population of all patients who fell into comasafter sustaining traumatic brain injuries. Calculate the population mean and standard deviation of the duration variable.

b. Simulate drawing 1,000 random samples of size n =30 and store the sample mean durations in a vector (see the Lab 4 handout and/or video). Create a histogram of your sampling distribution of means for duration.

c. Calculate the mean and standard deviation of your sampling distribution. How do they compare to the population mean and standard deviation?

d. If you decreased your sample size to n=10, how would the shape of your sampling distribution change compared to what you reported above?

Commute times in the U.S. are heavily skewed to the right. We select a random sample of 230 people from the 2000 U.S. Census who reported a non-zero commute time.

In this sample the mean commute time is 28.6 minutes with a standard deviation of 19.3 minutes. Can we conclude from this data that the mean commute time in the U.S. is less than half an hour? Conduct a hypothesis test at the 5% level of significance.

What is the $p$-value for this hypothesis test?

Your answer should be rounded to 4 decimal places

The American Bankers Association reported that, in a sample of 125 consumer purchases in France, 62 were made with cash, compared with 21 in a sample of 40 consumer purchases in the United States.

Construct a 99 percent confidence interval for the difference in proportions. (Round your intermediate value and final answers to 4 decimal places.)

The 99 percent confidence interval is from _____ to _____ .