A study was conducted to determine if the students from the public universities
take longer to graduate than the students from the private universities. 100
students from both the public universities and private universities were
surveyed. Suppose that from the years of research, it was known that the
population standard deviations were 1.58 years and 1 year respectively. The
following data were collected. The public and private universities students took
an average of 4.5 and 4.1 years respectively with a standard deviation of 0.3.
Use a 0.01 level of significance to test the claim.
(i) State the null and alternative hypotheses.

(ii) Is there any evidence to support the claim at α =0.01?

MANUAL CALCULATION

A student researcher compares the ages of cars owned by students and cars owned by faculty at a local state college. A sample of 78 cars owned by students had an average age of 5.04 years. A sample of 118 cars owned by faculty had an average age of 8 years. Assume that the population standard deviation for cars owned by students is 3.06 years, while the population standard deviation for cars owned by faculty is 3.24 years. Determine the 98% confidence interval for the difference between the true mean ages for cars owned by students and faculty.

Step 3 of 3: Construct the 98% confidence interval. Round your answers to two decimal places.

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

What percentage of your campus student body is female? Let p be the proportion of women students on your campus.

(a) If no preliminary study is made to estimate p, how large a sample is needed to be 99% sure that a point estimate p̂ will be within a distance of 0.03 from p? (Round your answer up to the nearest whole number.)
_____ students

(b) A report indicates that approximately 54% of college students are females. Answer part (a) using this estimate for p. (Round your answer up to the nearest whole number.)
______ students

The college bookstore tells prospective students that the average cost of its textbooks is $108 with a standard deviation of $4.50. A group of smart statistics students thinks that the average cost is higher. In order to test the bookstore’s claim against their alternative, the students will select a random sample of size 100. Assume that the mean from their random sample is $112.80.

1. Perform a hypothesis test (using R) at the 5% level of significance and state your decision. Also construct a 90% confidence interval (using R) for the average cost of textbook.
2. Perform the above task under the assumption that the students selected a random sample of size 10.
3. Write the difference between your findings of (1) and (2).

A researcher compares the effectiveness of two different instructional methods for teaching electronics. A sample of 138 students using Method 1 produces a testing average of 61 . A sample of 156 students using Method 2 produces a testing average of 64.6 . Assume that the population standard deviation for Method 1 is 18.53 , while the population standard deviation for Method 2 is 13.43 . Determine the 98% confidence interval for the true difference between testing averages for students using Method 1 and students using Method 2. Step 2 of 3 : Calculate the margin of error of a confidence interval for the difference between the two population means. Round your answer to six decimal places.

The table below contains various grades for three students obtained over the course of the year. Assuming that all grades are equally weighted, generate a new table that displays the name of the student, their average grade, and the number of grades they had in their record.

import numpy as np

np.random.seed(seed=0)

Students = ['Samir','Mark','Zoe','Andrew','Rupert']

Grades_Data = []

for i in range(100): 

    Student_Index = np.random.randint(0,len(Students))

    Student = Students[Student_Index]

    Grade = round(np.random.normal(loc=75,scale=15),1)

    Grades_Data.append([Student,Grade])

import pandas as pd

Grades_df = pd.DataFrame(data=Grades_Data,columns=['Student','Grade'])

Grades_df.iloc[0:10]

Mr. Grade’s was a new teacher whose students loved to chew gum, but it wasn’t allowed at school. To motivate his students, Mr. Grade created a classroom procedure that stated that students could chew gum during independent work. His students behaved well during independent work time, and their rate of work completion increased. One day, Mr. Grade was observed by the principal. After the observation, the principal asked Mr. Grade to see her during his planning period. From the following what is the best reason do you think the principal asked for this meeting? A minimum of 3 paragraphs are required and please justify your position with scientific evidence.

QUESTION 5

From a sample of 500 college students it was found that 300 of them had taken a statistics course.

Construct a 95% confidence interval for the proportion of college students who have taken a statistics course. What is the LOWER BOUND on the interval? Round your answer to three decimal places (i.e. 0.123).

4 points   

QUESTION 6

From a sample of 500 college students it was found that 300 of them had taken a statistics course.

Construct a 95% confidence interval for the proportion of college students who have taken a statistics course. What is the UPPER BOUND on the interval? Round your answer to three decimal places (i.e. 0.123).

1. Do male and female college students have the same distribution of living arrangements? Use a level of significance of 0.05. Suppose that 113 randomly selected male college students and 84 randomly selected female college students were asked about their living arrangements: dormitory, apartment, or other. The results are shown in Table. Do male and female college students have the same distribution of living arrangements?

What is the chi-square test-statistic for this data?
χ2=χ2=

Report all answers accurate to three decimal places.

2. Do male and female college students have the same distribution of living arrangements? Use a level of significance of 0.05. Suppose that 113 randomly selected male college students and 84 randomly selected female college students were asked about their living arrangements: dormitory, apartment, or other. The results are shown in Table. Do male and female college students have the same distribution of living arrangements?

What is the chi-square test-statistic for this data?
χ2=χ2=

Report all answers accurate to three decimal places.

3.You are conducting a test of homogeneity for the claim that two different populations have the same proportions of the following two characteristics. Here is the sample data.

What is the chi-square test-statistic for this data?
χ2=χ2=

Report all answers accurate to three decimal places.

   Question No.1

ABC Company makes bicycles. It produces 500 bicycles. It buys the tires for bicycles from a supplier at a cost of 15 RO per tire.

The company inventory carrying cost is estimated to be 20% of cost and the ordering cost is 45 RO per order.

(a) Determine the economic order quantity (EOQ).

(b) How many orders will be placed per year using the EOQ?

(c) What is the length of an order cycle?

(d) What is the total annual cost if the EOQ quantity is ordered?


Question No.2:

The computer lab at BUC has a help desk to help the students working on computer spreadsheet assignments. The students patiently from a single line in front of the desk to wait for help. Students are served based on a first-come, first-served priority rule. On average, 15 students per hour arrive at the help desk. Student arrivals are best described using a Poisson distribution. The help desk server can help an average of 21 students per hour, with the service rate being described by an Exponential distribution. Calculate the following operating characteristics of the service system.

1. Rate of arrivals

2. Rate of service

3. The average utilization of the help desk server

4. The average number of students in the system

5. The average number of students waiting in queue

6. The average time a student spends waiting in line

7. The average time a student spends in the system

8. The probability of having more than 4 students in the system

Question No.3:

Solve the following assignment Problem by complete enumeration method.