For each problem students will write out all steps of hypothesis testing including populations, hypotheses, cutoff scores, and all relevant calculations.

A nationwide survey in 1995 revealed that U.S. grade-school children spend an average of µ = 8.4 hours per week doing homework.  The distribution is normal with σ = 3.2.  Last year, a sample of n = 100 grade-school children was given the same survey.  For this sample, the mean number of homework hours was 7.1.   Has there been a significant change in the homework habits of grade-school children?  Test with α = .05.

A researcher estimates the following regression using 1000 observations:

W=-3.13+1.47*EDU

                                                                                                                         (0.93)     (0.07)

Where W is wage, EDU is years of education and the numbers in parentheses are standard errors of the coefficients.

1. Calculate a 95% confidence interval for the coefficient on EDU.

2. A high school graduate is contemplating whether to obtain a 4-year college degree. How much is his/her wage expected to rise?

3. A high school counselor tells a student that college graduates earn a wage $12 per hour higher than high school graduates. Is this statement consistent with the evidence?

Large Sample Proportion Problem. A survey was conducted on high school marijuana use. Of the 2266 high school students surveyed, 970 admitted to smoking marijuana at least once.  A study done 10 years earlier estimated that 45% of the students had tried marijuana. We want to conduct a hypothesis test to see if the true proportion of high school students who tried marijuana is now less than 45%.   Use alpha = .01.
What is the critical value for this test?

Group of answer choices

-1.96

-2.576

-2.33

2.33

SHOW ALL WORK AND WHICH CALC FUNCTIONS WERE USED

In 1994, 52% of parents with children in high school felt it was a serious problem that high school students were not being taught enough math and science. A recent survey found that 374 of 800 parents with children in high school felt it was a serious problem that high school students were not being taught enough math and science. Do parents feel differently today than they did in 1994? Use the α = 0.05 significance level.

a) Determine the null and alternative hypotheses for this scenario.

H0: H1: b) Determine the level of significance.

Answer:
c) Check the assumptions for this problem.

d) Determine the test statistic.

Answer:
e) Determine the p-value.

Answer:
f) Interpret the p-value.

g) What decision do we conclude based on this information? Interpret this in the context of the problem.

1. A high school principal is interested in the amount of time her students spend per week working at an after school job. 37 students are randomly selected and their working hours are recorded. The sample had a mean of 12.3 hours and a standard deviation of 11.2 hours. We would like to construct an 80% confidence interval for the population mean hours worked weekly by high school students.
   1. What critical value will you use for an 80% confidence interval? Give the value and specify whether it comes from the standard normal distribution or the t distribution ( or ).

_______________

1. Calculate the margin of error, E. (You must show the setup to receive credit. You may round to three decimal places, if needed.)

E = _______________

2. Construct the 80% confidence interval for the population mean hours worked weekly by high school students. (Round limits to one decimal place.)

_______________<  < _______________

A survey of a group of college students was done to find out how students get to school for the school year. 15% of those surveyed were from out of state. Of those that were in-state, 56% used a car as their primary form of transport to school, 13% used a train and 18% used a bus. Of those that were from out of state, 29% used an airplane, 31% used a car, and 12% used the train.

1. What is the probability that a respondent uses the train?

2. What is the probability a randomly chosen respondent is from out of state and uses the bus as his primary transport?

3. What is the probability that a respondent is from in state, takes an airplane or both?

4. If a respondent is chosen and that person uses a car, what is the probability the respondent is from out of state?  

5. Are primary form of transportation to school and in state/out of state statistically independent?

The term “reverse discrimination”. Discussed with the Bakke case where in Mr. Bakke had the qualifications needed to get into medical school in California. However, in an attempt to make up for discrimination in education in the 1960’s and earlier (Bakke took place in the late 60’s), the school kept 16 of its 100 seats open for minority applicants only; the other 84 could be competed for by anyone. Bakke sued the school, and the Court ruled that he was the victim of reverse discrimination.

Re: the case of Steelworkers v. Weber. In that case, the Court didn’t exactly define reverse discrimination. Rather, the Court set forth a set of factors to use to determine whether reverse discrimination had been committed, or if the employer, school, etc. was acting properly to make up for past discrimination.

Read the Court’s list of factors and discuss your thoughts on the Court’s opinion.

Calculating Relative Risk and Odds Ratios Your final answers should be rounded to one decimal point. Developed depressive Symptoms Did not develop depressive symptoms Total Experienced Bullying 237 1,715 1,952 Did not experience bullying 22 629 651 Total 259 2,344 2,603 1.What is the relative risk of developing depressive symptoms as an adult if that person was bullied as an adolescent in high school? 2.What is the risk (per 1,000 persons) of developing depressive symptoms that is attributable to bullying? 3.What percent of the risk of developing depressive symptoms as an adult is due to being bullied in high school? 4.How much of the incidence (per 1,000 persons) of developing depressive symptoms among the adult population is due to being bullied in high school? 5. What percentage of the depressive symptomology in the adult population is due to being bullied in high school?

Write a C program that creates a structure and displays its content. • Create a struct that will be used to hold a student's name, age, and year in school (Freshman, Sophomore, Junior, or Senior) • Within function main, dynamically allocate space to hold the structure and assign a pointer to point to the memory space allocated • Read in (from the keyboard) the student's name, age, and year in school • Create a separate function with the prototype: void display (struct student *) that can be used to display the contents of a single structure • Call this function twice - once for the original contents of the structure and again when the structure has been modified (Display year in school as indicated above, not 1, 2, 3, 4) • Increase the student's age by one and upgrade their year in school one level (unless they are already a Senior) • Free up the memory space before exiting