Q1: For the Academic Community of Higher Education improving student’s academic performance is not an easy task. A case study was conducted using descriptive Statistics which is the discipline of quantitatively describing the main features of a collection of information. A data of 200 Students marks as population was collected and out of it 25 students marks are being analyzed for the case study by applying some measures that can be used to describe a data set.

            Let us consider the marks obtained from a sample of 25 students listed as follows:

70 80 86 46 56 66 76 86 90 70 50 45

94   65 55 60 90 80 70 71 72 62 64 76 70

1. Construct a frequency distribution & relative frequency distribution for the above data with 5 classes.            (1)                                                                   
2. Construct a Histogram with appropriate scale for the data.   (1)                   
3. Calculate the mean for the data using the frequency distribution table.     (1)

Q2: Three males with an X-linked genetic disorder have one child each. The random variable x is the number of children among the three who inherit the X-linked genetic disorder.

Determine whether it is a probability distribution or not. If it is a probability distribution, find its mean and standard deviation.

Q3: One Market Research company determined that 13% of college students work part-time during the academic year. For a random sample of 5 students, what is the probability that at least 3 students work part-time?

2. Data concerning employment status were collected from a sample of 50 World Campus students. In that sample of 50 students, 33 students reported they were employed full-time.

A. Use Minitab Express to construct a 95% confidence interval to estimate the proportion of all World Campus students who are employed full-time. If assumptions were met, use the normal approximation method. Remember to include all relevant Minitab Express output and to clearly identify your answer. [15 points]

B. What sample size would be necessary to construct a 95% confidence interval to estimate the proportion of all World Campus students who are employed full-time with a margin of error of 2%? You will need to do hand calculations. Show all of your work. [10 points]

C. We want to know if there is evidence that in the population of all World Campus students, more than 60% are employed full-time. Use the five-step hypothesis testing procedure to address this research question. The only hand calculations that you will need to do will be in step 1 to check assumptions; use Minitab Express for steps 2 and 3. Remember to include all relevant Minitab Express output and to clearly identify your test statistic and p value. [25 points]

Step 1: Check assumptions and write hypotheses

Step 2: Calculate the test statistic

Step 3: Determine the p value

Step 4: Decide to reject or fail to reject the null

Step 5: State a “real world” conclusion

Researchers are comparing the proportion of University Park students who are Pennsylvania residents to the proportion of World Campus students who are Pennsylvania residents. Data from a sample are presented in the contingency table below.

1. Construct a 95% confidence interval to estimate the difference between the proportion of all University Park students who are Pennsylvania residents and the proportion of all World Campus students who are Pennsylvania residents. If assumptions are met, use the normal approximation method. Show how you checked assumptions. You should not need to do any hand calculations. Use Minitab Express to construct the confidence interval. Remember to copy+paste all relevant Minitab Express output and always clearly identify your final answer. [15 points]
2. B. Interpret the confidence interval that you computed in part A by completing the following sentence. [5 points]
3. C. Use the five-step hypothesis testing procedure given below to determine if there is evidence of a difference between the proportion of University Park students who are Pennsylvania residents and the proportion of World Campus students who are Pennsylvania residents. If assumptions are met, use the normal approximation method. Use Minitab Express. You should not need to do any hand calculations. Remember to copy+paste all relevant Minitab Express output. [30 points]

Two statistics professors at two rival schools decide to use IQ scores as a measure of how smart the students at their respective schools are. IQ scores are known to be Normally distributed. The two professors will use this knowledge to their advantage. They will randomly select 10 students from their respective schools and determine the students' IQ scores by means of the standard IQ test. The two professors will use the pooled version of the two-sample t test to determine whether the students at the two universities are equally smart. Let m1 and m2 represent the mean IQ scores of the students at the two universities. Let s1 and s2 be the corresponding population standard deviations. The hypotheses they will test are H0: m1 – m2 = 0 versus Ha: m1 –m2 ¹ 0. Based on the two samples of 10 students, the two professors find the following information: = 113, = 122 s1 = 8, and s2 = 12. (Hint: Calculate sp2 first.)

A. In a study comparing four groups with six observations in each group, the MSE = 467 and the MSG = 2345. What is the value of the coefficient of determination? A) 0.484 B) 0.516 C) 0.587 D) 0.939 34.

B. A study compares six groups with five observations in each group. An F statistic of 3.712 is reported. What can we say about the P-value for this F test? A) P-value < 0.001 B) 0.001 < P-value < 0.01 C) P-value > 0.01 D) 0.01 < P-value < 0.05

An analyst believes that incoming GPA, the number of hours spent on Facebook per week, and upperclassman status can predict scores. Data is collected for 260 students. Students’ incoming GPA and the average number of hours spent on Facebook each week is recorded. For Academic Standing, data was included based on the number of years of college already completed  (3 = senior, 2 = junior, 1 = sophomore , 0 = freshmen). A regression is performed, and the results of the regression are in Table 1.
TABLE 1

1.What is the dependent variable?

Intercept

GPA

academic standing

Facebook

The Score

2. From Table 1, what is the t-stat for the Academic Standing coefficient ?

Enter your answer with two decimals.

3.According to Table 1, the coefficients are:

Not statistically significant.

All statistically significant

All statistically significant except for Academic Standing.

All statistically significant except for GPA.

All statistically significant except for Facebook.

4.According to the sign on the Academic Standing coefficient from Table 1,

If the Academic Standing coefficient is bigger than the Facebook coefficient, students grades will increase.

If students been at college longer, then the score is lower.

If students been at college longer, then the score is higher.

If students been at college longer, then the Facebook use is higher.

An instructor gave students the option to purchase an interactive program that allows them to answer questions during class and receive credit for participating. Alternatively, students could work an extra problem during weekly homework assignments. The instructor randomly selected 10 students, then randomly divided them into two groups of five each. One group was provided the interactive tool, the other group was asked to work the extra problem. The instructor knew from prior experience that the interactive tool increases attendance. The table displayed contains the final exam scores for the 10 students, on a scale from 0 to 100. Interactive 65 78 84 88 96 Extra problem 56 61 70 75 82 The instructor wishes to test whether increased attendance throughout the semester leads to improved exam scores. Let μ I = mean score that would be observed if all students used the interactive tool and μ E = mean score if all students worked an extra problem. For testing H 0 : μ I = μ E , it has been suggested in the past to use a version of the t test that calculates a pooled variance estimate. Such an assumption requires that:

the population standard deviations σ 1 and σ 2 be equal. the sample means ¯ x 1 x ¯ 1 and ¯ x 2 x ¯ 2 be equal.

the sample standard deviations s 1 s 1 and s 2 s 2 be equal.

the population means μ 1 μ 1 and μ 2 μ 2 be equal.

Question 3

In a study conducted on 335 primary school students in a small district in Malaysia, students at primary levels 4-6 were asked which goal in terms of good grades, athletic ability or popularity (being popular in school) was most important to them. A two-way table (Table 3.1) separating the students by their educational levels and goals is shown below:

Table 3.1

1. To investigate possible differences among the students' goals by educational levels, a researcher suggested that it is useful to compute the column percentages. You are required to compute the column percentages and explain the meaning of these percentages. Do the results suggest that there is much of a variation in goals across the three educational levels?   
2. The dataset from the same study now divides the students' responses into "Urban," "Suburban," and "Rural" school areas as shown in Table 3.2. You are required to conduct a Chi-Squared test to investigate whether there is an association between school area and the students' goals of getting good grades, athletic ability or popularity as most important to them?

Table 3.2

An IAB study on the state of original digital video showed that original digital video is becoming increasingly popular. Original digital video is defined as professionally produced video intended only for ad-supported online distribution and viewing. According to IAB data, 30% of American adults 18 or older watch original digital videos each month. Suppose that you take a sample of 1.100 U.S. adults, what is the probability that fewer than 25 in your sample will watch original digital videos?

NEXT QUESTION

Use the following information to answer the next questions:
Sally Soooie believes University of Arkansas students are more generous than students at other SEC schools and believes that this generosity will lead them to sign up to be organ donors more frequently. She takes a random survey of 100 U of A students (Sample 1) and finds that 78 of them have signed the form to be organ donors. A random sample of students from Vanderbilt (Sample 2) found 62 out of 100 are registered organ donors.
  
1.What is the 90% confidence interval for the proportion of Vanderbilt students that are organ donors based on this sample?

2.What would happen to the confidence interval if the professor sampled an additional 100 students to the sample?

apply statistical methods and analysis. Unless otherwise stated, use 5% (.05) as your alpha level (cutoff for statistical significance).


#1.  For each example, state whether the one-sample, two-independent-sample, or related-samples t test is most appropriate. If it is a related-samples t test, indicate whether the test is a repeated-measures design or a matched-pairs design.     

A professor tests whether students sitting in the front row score higher on an exam than students sitting in the back row.

A graduate student selects a sample of 25 participants to test whether the average time students attend to a task is greater than 30 minutes.

A researcher matches right-handed and left-handed siblings to test whether right-handed siblings express greater emotional intelligence than left-handed siblings.

A principal at a local school wants to know how much students gain from being in an honors class. He gives students in an honors English class a test prior to the school year and again at the end of the school year to measure how much students learned during the year.

#2.

A random sample of 25 professional basketball players shows a mean height of 6 feet, 5 inches with a 95% confidence interval of 0.4 inches. Explain what this indicates.

If the sample were smaller, would the confidence interval become smaller or larger? Explain.

If you wanted a higher level of confidence (99%) would the confidence interval become smaller or larger? Explain.

1. A pump lifts 1000 (liters) of water from ground to a tank on the roof of a building 100 (m) high. What is the potential energy in the water? [ 1 (liter) = 1000 cm3 ]. Show all your steps to the solution.

2. A skier is coming downhill. At one point she is 50 (m) above the bottom of the hill and moving at 20 (m/s). What is her speed as she reaches the bottom of the hill?

1. 22.3 (m/s) b. 37.5 (m/s) c. 44.8 (m/s) d. Cannot say without her mass

3. A car of mass 1000 (kg) and moving at 60 (mph) collides with a barrier and comes to a stop in

0.5 (s). Ignoring friction, what is the value of the force that acts on the car?

1. 0 b. 20,000 (N) c. 450, 000 (N) d. 900,000 (N)

4. A coil spring has an elastic constant of 200 (N/m). If it is compressed by 20 (cm), what is the energy stored in the spring?

1. 4 (J) b. 10 (J) c. 20 (J) d. 40 (J)

5. A 60 (kg) sprinter starts from rest and reaches a speed of 12 (m/s) in 6 (s). What is the power that she must have to reach this speed?

1. 720 (J) b. 720 (W) c. 1440 (W) d. 4320 (J)

15. In the gym a weight-lifter lifts a 50 kg barbell straight up a distance of 50 cm in 0.5 s. What is the work done by the weight-lifter?

1. 25 (W) b. 250 (J) c. 250 (W) d. 500 (J)

16.In the above question, what is Power of the weight-lifter?

1. 25 (W) b. 250 (J) c. 250 (W) d. 500 (W)

17.Consider the following situations.

1. A ball moving at a speed “v” is brought to rest

2. The same ball is thrown from rests o that it moves at speed “v”

3. The same ball is moving at speed “v” is brought to rest and reversed in direction to move at speed “v”

In which case does the ball undergo the largest change in momentum?

1. I b. I and ii c. i, ii and iii d. ii and iii e. iii

18. A cart moving at a velocity “v” collides with an identical stationary cart on air track. The two carts stick together after collision. What is their combined velocity after the collision?

1. v b. 0.5 v c. 0 d. – 0.5 v f. Need more information

19. Two cars, one twice the mass of the other, are stationary on a horizontal road. A person pushes each car separately with the same with the same force for 5 (s). One can say that the momentum of the lighter car compared to the momentum of the heavier car after 5 (s) is

1. Smaller b. Larger c. Same

20. A simple pendulum is pulled up in an arc and let go from a stationary position. As it swings back and forth

1. Its kinetic energy (KE) converts to potential energy (PE) b. Its PE converts to KE

c. Its Potential Energy Converts to Elastic Energy (EE) d. Its EE converts to KE   

e. Its EE converts to PE