In a population of students, 60% study for every homework assignment. A sample of 40 students from this population is taken, and the number who study for every homework assignment from this sample is recorded as the random variable X.

a) (4 pts) Verify that X has a binomial distribution.

b) (4 pts) Find the probability that exactly 25 students from the sample study for the exam.

c) (4 pts) Find the mean for this binomial experiment

10% of all college students volunteer their time. Is the percentage of college students who are volunteers smaller for students receiving financial aid? Of the 322 randomly selected students who receive financial aid, 26 of them volunteered their time. What can be concluded at the αα = 0.05 level of significance?

1. For this study, we should use Select an answer t-test for a population mean z-test for a population proportion
2. The null and alternative hypotheses would be:   

H0:H0:  ? μ p  Select an answer ≤ < ≥ ≠ > =   (please enter a decimal)   

H1:H1:  ? μ p  Select an answer < ≤ ≠ > ≥ =   (Please enter a decimal)

3. The test statistic ? z t  =  (please show your answer to 3 decimal places.)
4. The p-value =  (Please show your answer to 4 decimal places.)
5. The p-value is ? ≤ >  αα
6. Based on this, we should Select an answer fail to reject reject accept  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest the population proportion is not significantly lower than 10% at αα = 0.05, so there is insufficient evidence to conclude that the percentage of financial aid recipients who volunteer is lower than 10%.
   • The data suggest the populaton proportion is significantly lower than 10% at αα = 0.05, so there is sufficient evidence to conclude that the percentage of financial aid recipients who volunteer is lower than 10%.
   • The data suggest the population proportion is not significantly lower than 10% at αα = 0.05, so there is sufficient evidence to conclude that the percentage of financial aid recipients who volunteer is equal to 10%.

At a large university, freshmen students are required to take an introduction to writing class. Students are given a survey on their attitudes towards writing at the beginning and end of class. Each student receives a score between 0 and 100 (the higher the score, the more favorable the attitude toward writing). The scores of nine different students from the beginning and end of class are shown below. Use the Wilcoxon signed-rank test to check at a 5% significance level whether the attitudes toward writing appear to increase by the end of the class?

5. Samples of sizes 100 and 80 of calculus students were acquired. The students in the first sample got into calculus by passing the pre-calculus course. Those in the second sample got in by getting a passing score on a placement test. In the first group, 65 succeeded in calculus. In the second group, 41 succeeded. Without using R find a 95% confidence interval for the difference in the success rates of the two populations.

6. For the same data, find the p-value for a test of the alternative hypothesis that the two success rates are not equal without using R.

7. Repeat problems 5 and 6 using R.

In a survey of MBA students, the following data were obtained on “students’ first reason for application to the school in which they matriculated.” Reason for Application School School cost or Quality Convenience Other Totals Enrollment Status Full Time 421 393 76 890 Part Time 400 593 46 1039 Totals 821 986 122 1929 (a) Develop a joint probability table for these data. (b) Use the marginal probabilities of school quality, school cost or convenience, and other to comment on the most important reason for choosing a school. (c) If a student goes full time, what is the probability that school quality is the first reason for choosing a school? (d) If a student goes part time, what is the probability that school quality is the first reason for choosing a school? (e) Are the enrollment status and the reason for application independent? Explain using probabilities.

A researcher interested in the working habits of students at RCC randomly selects 300 students and

finds that 23% have a full time job.

(a) Did the study use population or sample data? Explain.

(b) If sample data was used, what is the population it was drawn from?

(c) Is the figure 23% a parameter or a statistic? Explain.

(d) Is the variable qualitative or quantitative? Explain.

In an introductory statistics class, there are 18 male and 22 female students. Two students are randomly selected (without replacement).

(a) Find the probability that the first is female

(b) Find the probability that the first is female and the second is male.

(c) Find the probability that at least one is female

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I know that this question has to use the counting method, but i got confuse with how to start because i have to now find the probability of FIRST being a female, etc. Please provide workings with explanations alongside. Thank you in advance!

/*
   * Returns a new array of students containing only those students from the given roster that belong
   * to the given academic program
   * The resulting array must not contain any null entries
   * Returns empty array (length == 0) if no students belong to the program
   */
   public static UStudent[] filterByProgram(String program, UStudent[] roster) {
       //YOUR CODEf
       int counter=0;
       for(int i=0;i<roster.length;i++) {
           if(roster[i].getAcademicProgram().equals(program)) {
               counter++;
               UStudent[] Studentbelongprogram = new UStudent[counter];
               Studentbelongprogram[i]=roster[i];
               roster=Studentbelongprogram;
           }else {
               return new UStudent[0];
           }

       }
       return roster;  
   }

An object of irregular shape has a characteristic length of L = 1 m and is maintained at a uniform surface temperature of T_s = 325 K. It is suspended in an airstream that is at atmospheric pressure (p = 1 atm) and has a velocity of V = 100 m/s and a temperature of T_? = 275 K. The average heat flux from the surface to the air is 12,000 W/m². Referring to the foregoing situation as case 1, consider the following cases and determine whether conditions are analogous to those of case 1. Each case involves an object of the same shape, which is suspended in an airstream in the same manner. Where analogous behavior does exist, determine the corresponding value of the average heat or mass transfer convection coefficient, as appropriate.

(a) The values of T_s, T_?, and p remain the same, but L = 2 m and V = 50 m/s.

(b) The values of T_s and T_? remain the same, but L = 2 m, V = 50 m/s, and p = 0.2 atm.

(c) The surface is coated with a liquid film that evaporates into the air. The entire system is at 300 K, and the diffusion coefficient for the air–vapor mixture is D_AB = 1.12 × 10^?4 m²/s. Also, L = 2 m, V = 50 m/s, and p = 1 atm.

(d) The surface is coated with another liquid film for which D_AB = 1.12 × 10^?4 m²/s, and the system is at 300 K. In this case L = 2 m, V = 250 m/s, and p = 0.2 atm.