A social scientist is interested in determining if there is a significant difference in the proportion of people who report working full time between two groups: those with a high school education or less (Group 1) and those with an associates’s degree or higher (Group 2). Using data from the General Social Survey, the researcher obtains the following table:

What is the lower bound of the 95% confidence interval for the difference in the proportion of people working full time with a high-school education or less and those working full time with an associate's degree or higher, to three decimal places?  Take all calculations toward the answer to four (4) decimal places.

Suppose you administer a certain aptitude test to a random sample of 9 students in your high school, and the average score is 105. We want to determine the mean μ of the population of all students in the school. Assume a standard deviation of σ = 15 for the test. Round all answers to 2 decimals.

1.What is the margin of error for a 98% confidence interval?

2.What would be the interval for a 98% confidence interval?

3. Write a sentence explaining the 98% confidence interval in context of the question. (There are only a few ways to do this correctly, so be sure to read the book closely.)

4. Write a few sentences explaining what would happen to the size of the CI if you wanted a 80% confidence interval?

5. Write a few sentences explaining what would happen to the size of the CI if you changed the sample size to be 81 and kept a 98% confidence interval.

1.

A student bikes to school by traveling first dN = 1.00miles north, then dW = 0.500miles west, and finally dS = 0.200miles south.

If a bird were to start out from the origin (where the student starts) and fly directly (in a straight line) to the school, what distance db would the bird cover?

Express your answer in miles.

2.

You will now find the same quantity algebraically, without the need to use much geometry. Take the north direction as the positive y direction and east as positive x. The origin is still where the student starts biking.

Let d? N be the displacement vector corresponding to the first leg of the student's trip. Express d? N in component form.

Express your answer as two numbers separated by a comma (e.g., 1.0,2.0). By convention, the x component is written first.

1. The annual earnings of 25 people with a high school diploma and 16 people with an associate degree are shown below. Can you conclude that there is a difference in the mean annual earnings based on level of education? Assume that population are normally distributed and population variances are not equal.

1. Identify the claim and state the null and alternative hypothesis.

2. What type of statistical test should be used to answer the researcher’s question?

(Note: Is this a z-test or a t-test? One sample, dependent sample or independent sample)

3. Find the standardized test statistic and corresponding critical value(s).

4. At 0.05 significance level, decide whether to reject or fail to reject the null hypothesis.
5. Interpret the decision in the context of the original claim.

a). A student read that a 95% confidence interval for the mean SAT Mathematics score of Texas high school seniors in 2019 is 467 to 489. Asked to explain the meaning of this interval, the student responded, “In 2019, 95% of Texas high school seniors had SAT Mathematics scores between 467 and 489.” Is the student essentially correct? Justify your answer fully.

b). A consumer group chose to study the true population mean salary (??) of “family practice” doctors in the Greater Houston Metroplex. A random sample of one hundred family practice doctors working in this area produced the 95% confidence interval [$241,150, $249,070] for ??. Answer the following:

i). If possible, find the sample average salary for the one hundred family practice doctors involved in this study. If not possible, then state why this statistic cannot be found.

ii). Find the margin of error associated with this confidence interval.

In a survey of 1000 randomly selected adults in the United States, participants were asked what their most favorite and what their least favorite subject was when they were in school (Associated Press, August 17, 2005). In what might seem like a contradiction, math was chosen more often than any other subject in both categories! Math was chosen by 222 of the 1000 as the favorite subject, and it was also chosen by 362 of the 1000 as the least favorite subject.

(a) Construct a 95% confidence interval for the proportion of U.S. adults for whom math was the favorite subject in school. (Give the answers to four decimal places.)
(  ,  )

(b) Construct a 95% confidence interval for the proportion of U.S. adults for whom math was the least favorite subject. (Give the answers to four decimal places.)
(  ,  )

You may need to use the appropriate table in Appendix A to answer this question.

A second grade teacher has a 7-year old boy who has difficulty staying at his desk, in school. The boy came from a nuclear family of a mother, father and a little sister. He plays soccer on the weekends, in a community group, with his friends. The little boy has average grades, in school. He often gets out of his seat during classroom time to play with the class pet hamster and he wants to go outside to play, for recess. The boy often states that he will do his schoolwork later.

You are the second-grade teacher and you will use a behavioral theory to keep this second-grade boy in his seat during class time. Please utilize one of the following behavioral theorists, such as B.F. Skinner, Pavlov, or Watson, to change this boy’s classroom behavior

Jack’s friend plans to buy a boat 45 years from now, when he retires. Today’s price for the boat is $300,000. The price is expected to rise 3% per year. The friend also wants to send his child to BC in 12 years. College is expected to cost $117,000 in the child’s first year, growing at 4% per year while in school. College lasts for 4 years and the first payment is due the first day of school. The friend has $25000 saved now and expects to put a certain fraction of his salary away each year, starting in 1 year with the final payment on the retirement date. His salary will grow by 2% per year. He currently makes $120,000. If Jack can earn 6% per year on the friend’s investments, what fraction of the friend’s salary must be saved?

The Survey of Study Habits and Attitudes (SSHA) is a phychological test that measures the motivation, attitude toward school, and study habits of students. Scores range from 0 to 200. The mean score for U.S. college students is about 115, and the standard deviation is about 30. A teacher who suspects that older students have better attitudes toward school gives that the SSHA to 25 students who are at least 30 years of age. Their mean is ¯x = 127.8.

(a) Assuming that σ = 30 for the population of older students, carry out a test of

H0 : µ = 115

Ha : µ > 115

Report the P-value of your test, and state your conclusion clearly.

(b) Your test in part (a) required two important assumptions in addition to the assumption that the value of σ is known. What are they? Which of these assumptions is most important to the validity of your conclusion in part (a)?

ath & Music (Raw Data, Software Required):
There is a lot of interest in the relationship between studying music and studying math. We will look at some sample data that investigates this relationship. Below are the Math SAT scores from 8 students who studied music through high school and 11 students who did not. Test the claim that students who study music in high school have a higher average Math SAT score than those who do not. Test this claim at the 0.05 significance level.