If the alternative hypothesis is that the proportion of items in population 1 is larger than the proportion of items in population 2, then the null hypothesis should be _____.

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution _____.

The academic planner of a university thinks that at least 35% of the entire student body attends summer school. The correct set of hypotheses to test their belief is _____.

When developing an interval estimate for the difference between two sample means, with sample sizes of n1 and n2, _____.

If a hypothesis is rejected at a 5% level of significance, it _____.

The risk of an investment is measured in terms of the variance in the return that could be observed. Random samples of 10 yearly returns were obtained from two different portfolios. The data are given below (in thousands of dollars.) Portfolio 1 130  135  135  131  129  135  126  136  127  132 Portfolio 2 154  144  147  150  155  153  149  139  140  141 What is 95% confidence interval on the ratio of the variances of the two portfolios. Interpret your answer.

The Dean of Students at ACME University wants to estimate the proportion of students who cheated on a major exam. Previous studies at other universities indicate this proportion is less than 65.7% How many students does the Dean need to select in the sample in order to be 95% confident that the sample proportion is within two percentage points of the actual proportion who cheated, if the Dean thinks ACME students have more integrity than students at other universities. (Hint: Don’t use 0.657 in your calculations)

Bonus question 1: 3 points (Refer to class diagram 1) Write the code for the getArea method of the Square class that overrides the abstract method named getArea in the Shape class. This method should return the area of the Square object. Write this method as concisely as possible.

(Refer to class diagram 1) Code the abstract method named getArea in the Shape class.  

Suppose the user enters 243.3 at the prompt “Enter quantity: “. What is the output of the following code? int quantity = 0;try {     System.out.print(“Enter quantity: “);     quantity = sc.nextInt();}catch (InputMismatchException e) {     sc.next();     System.out.println(“Error! Invalid quantity. Try again.\n”);     continue;}