Some additional collected data is presented in the table below:

You are asked to investigate the impact of diabetes on elementary school students’ academic performance. You decide to test whether the mean standardized test performance of students with diabetes is worse than the test performance of the school as a whole. The school has 235 students and the average test score for the school is set at 100 and has a standard deviation of 25. You are given data from 10 diabetic students who have an average score of 80. Please use a significance of 0.01.

a. Identify the assumed sample distribution, the formula for the test statistic, the significance level, the test distribution, and the null & alternative hypotheses

b. Calculate and report the test statistic, the input values for the test statistic, and the p value that results from the test. Also calculate the statistical power.

c. Decide whether you will reject or fail to reject the null hypothesis. Interpret that decision in the context of the problem. Evaluate the statistical power.

For a regression of test score (T) on the endogenous variable student-teacher ratio (R), Hoxby (2000) suggests using as an instrument the deviation of potential enrollment from its long-term trend (P), where "potential enrollment" means how many children of kindergarten age there are (whether or not they attend public school). Which of the following arguments would NOT support P as an instrument for R?

PLEASE PROVIDE EXPLANATION IN ANSWER

2. A researcher wishes to determine whether there is a difference in the average age of elementary school, high school, and community college teachers. Teachers are randomly selected from each group. Their ages are recorded below. Test the claim that at least one mean is different from the others. Use α = 0.01.
Resource: The One-Way ANOVA

EVERY ANSWER POSTED HAD SOME WRONG THINGS

A report says that 82% of British Columbians over the age of 25 are high school graduates. A survey of randomly selected British Columbians included 1290 who were over the age of 25, and 1135 of them were high school graduates. Does the city’s survey result provide sufficient evidence to contradict the reported value, 82%?

Part i) What is the parameter of interest?

A. All British Columbians aged above 25.
B. The proportion of all British Columbians (aged above 25) who are high school graduates.
C. The proportion of 1290 British Columbians (aged above 25) who are high school graduates.
D. Whether a British Columbian is a high school graduate.

Part ii) Let p be the population proportion of British Columbians aged above 25 who are high school graduates. What are the null and alternative hypotheses?

A. Null: p=0.82. Alternative: p=0.88.
B. Null: p=0.88. Alternative: p≠0.88.
C. Null: p=0.82. Alternative: p≠0.82.
D. Null: p=0.88. Alternative: p>0.88.
E. Null: p=0.88. Alternative: p≠0.82.
F. Null: p=0.82. Alternative: p>0.82.

Part iii) The P-value is less than 0.0001. Using all the information available to you, which of the following is/are correct? (check all that apply)

A. The observed proportion of British Columbians who are high school graduates is unusually low if the reported value 82% is incorrect.
B. The observed proportion of British Columbians who are high school graduates is unusually high if the reported value 82% is incorrect.
C. Assuming the reported value 82% is incorrect, it is nearly impossible that in a random sample of 1290 British Columbians aged above 25, 1135 or more are high school graduates.
D. The observed proportion of British Columbians who are high school graduates is unusually low if the reported value 82% is correct.
E. The observed proportion of British Columbians who are high school graduates is unusually high if the reported value 82% is correct.
F. The reported value 82% must be false.
G. Assuming the reported value 82% is correct, it is nearly impossible that in a random sample of 1290 British Columbians aged above 25, 1135 or more are high school graduates.

Part iv) What is an appropriate conclusion for the hypothesis test at the 5% significance level?

A. There is sufficient evidence to contradict the reported value 82%.
B. There is insufficient evidence to contradict the reported value 82%.
C. There is a 5% probability that the reported value 82% is true.
D. Both A. and C.
E. Both B. and C.

Part v) Which of the following scenarios describe the Type II error of the test?

A. The data suggest that reported value is incorrect when in fact the value is incorrect.
B. The data suggest that reported value is correct when in fact the value is incorrect.
C. The data suggest that reported value is incorrect when in fact the value is correct.
D. The data suggest that reported value is correct when in fact the value is correct.

Part vi) Based on the result of the hypothesis test, which of the following types of errors are we in a position of committing?

A. Type I error only.
B. Type II error only.
C. Neither Type I nor Type II errors.
D. Both Type I and Type II errors.

In each scenario below, specify each variable as a response variable, an explanatory variable, or neither. Explain your choices.

a. A climatologist wishes to predict future monthly rainfall in Los Angeles. To inform his predictive model, for each month of the past 30 years, he records the name of the month (Jan.-Dec.), total rainfall (mm), and the Oceanic Niño Index (a measure of sea surface temperature differences, in ºC).

b. A researcher conducts an experiment in a residence for senior citizens to investigate the effect of floor type on the risk of fall-related injury. For each individual in the facility, she records the type of flooring (either standard flooring or a new, rubber flooring that absorbs the impact of falls) in their room, their age, and the number of fall-related injuries that they sustained over the previous two years. my question : are the age and the number of fall related injuries over the previous two year also the explanatory variables?

c. A medical researcher studies a group of boys, recording the age at which they reach puberty (years) and their BMI (kg/m2) at that time. Her goal is to quantify the association between these two variables.

My answer: is this correct?

a. Explanatory variable : records the name of the month (Jan.-Dec.), the Oceanic Niño Index (a measure of sea surface temperature differences, in ºC)

Response variable: total rainfall (mm),

b.Explanatory variable: the type of flooring (either standard flooring or a new, rubber flooring that absorbs the impact of falls) in their room, their age, the number of fall-related injuries that they sustained over the previous two years.

c. Neither: the age at which they reach puberty (years) and their BMI (kg/m2) at that time