statistic

(insert name of Program)

(FC301 Statistics)

(Mid Module Progress Test Assignment)

Question Book

Time: 90 Minutes

Instructions to students:

Your FC301- Statistics module assessment is an online timed open book exam.

You will have to complete the exam paper and upload your answers in order to complete this assessment and get a grade for the module. 

This examination is ‘open-book’, meaning you can access module learning resources, including your textbooks and notes, whilst you are answering the examination questions. The questions will not ask you to copy any specific information from your learning materials, rather you will be asked to use the information and apply it in a thoughtful way. This does not mean you will be summarising the information from a textbook; it means you will be asked to interpret or use the information in relation to the specific examination questions and/or problems/case studies/scenarios.

You are expected to work on this assessment on your own. Please note that you may be required to attend an online meeting with your teacher to confirm that it is your own work.

You should type your answers into a document. For answers that require equations, formulae, graphs or diagrams you should write your answers clearly on paper and take a photograph of each page. You must upload your answers to the VLE.

In order to complete this assessment, you must:  

· read all instructions very carefully

· read the question paper carefully before you begin to answer

· type or write your answers clearly

· upload your answers to the VLE

Question1. (6 marks)

A study was done to compare the high-risk people from Covid-19 of city workers to farm workers.

The researcher studied a random sample of 100 workers from her city and another random sample of 100 workers from the nearby farms. Other factors that might affect the risk are smoking habits, number of working hours, and exercise habits. The smoking habits of the two worker types are similar, but city workers generally exercise less than the farm workers.

A. Which of the following is the explanatory variable in this study? (1 mark)

1) Exercise

2) Number of working hours

3) Smoking or not

4) Number of workers

5) Occupation

B. Which of the following are qualitative variable(s) is this study? (1 mark)

1) Exercise

2) Number of working hours

3) Smoking or not

4) Number of workers

5) Occupation

C. Which of the following variable(s) are continues? (1 mark)

1) Exercise.

2) Number of working hours

3) Smoking or not

4) Number of workers

5) Occupation

D. Write down one advantage and one disadvantage in this method of choosing her sample. (2 marks)

Advantage:…………………………………………………………………. .

……………………………………………………………………..

Disadvantage: ……………………………………………………………….

………………………………………………………………….

E. What type of data can be defined as ‘describing position’ [Equation]<m:oMath xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><m:r><m:rPr><m:sty m:val="bi" /></m:rPr><w:rPr xmlns:w="http://schemas.openxmlformats.org/wordprocessingml/2006/main"><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math" w:cs="Arial" /><w:lang w:eastAsia="x-none" /></w:rPr><m:t xml:space="preserve">m = </m:t></m:r><m:f><m:fPr><m:ctrlPr><w:rPr xmlns:w="http://schemas.openxmlformats.org/wordprocessingml/2006/main"><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math" w:cs="Arial" /><w:b /><w:i /><w:lang w:eastAsia="x-none" /></w:rPr></m:ctrlPr></m:fPr><m:num><m:r><m:rPr><m:sty m:val="bi" /></m:rPr><w:rPr xmlns:w="http://schemas.openxmlformats.org/wordprocessingml/2006/main"><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math" w:cs="Arial" /><w:lang w:eastAsia="x-none" /></w:rPr><m:t>3</m:t></m:r></m:num><m:den><m:r><m:rPr><m:sty m:val="bi" /></m:rPr><w:rPr xmlns:w="http://schemas.openxmlformats.org/wordprocessingml/2006/main"><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math" w:cs="Arial" /><w:lang w:eastAsia="x-none" /></w:rPr><m:t>2</m:t></m:r></m:den></m:f></m:oMath>?[Equation]<m:oMath xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><m:d><m:dPr><m:ctrlPr><w:rPr xmlns:w="http://schemas.openxmlformats.org/wordprocessingml/2006/main"><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math" w:cs="Arial" /><w:b /><w:i /><w:lang w:eastAsia="x-none" /></w:rPr></m:ctrlPr></m:dPr><m:e><m:r><m:rPr><m:sty m:val="bi" /></m:rPr><w:rPr xmlns:w="http://schemas.openxmlformats.org/wordprocessingml/2006/main"><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math" w:cs="Arial" /><w:lang w:eastAsia="x-none" /></w:rPr><m:t>6,8</m:t></m:r></m:e></m:d></m:oMath>  (1 mark)

Question 2: (4 marks)

Choose the right answer for the following questions:

A. What is one of the distinctions between a population parameter and a sample statistic? (1 mark)

1) A population parameter is only based on conceptual measurements, but a sample statistic is based on a combination of real and conceptual measurements.

2) A sample statistic changes each time you try to measure it, but a population parameter remains fixed.

3) A population parameter changes each time you try to measure it, but a sample statistic remains fixed across samples.

4) The true value of a sample statistic can never be known but the true value of a population parameter can be known.

B. Which of the following would be most likely to produce selection bias in a survey? (1 mark)

1) Using questions with biased wording.

2) Only receiving responses from half of the people in the sample.

3) Conducting interviews by telephone instead of in person.

4) Using a random sample of students at a university to estimate the proportion of people who think the legal drinking age should be lowered.

C. Which one of the following variables is not categorical? (1 mark)

1) Age of a person.

2) Gender of a person: male or female.

3) Choice on a test item: true or false.

4) Marital status of a person (single, married, divorced, other)

D. One use of a regression line is: (1 mark)

1) To determine if any x-values are outliers.

2) To determine if any y-values are outliers.

3) To determine if a change in x causes a change in y.

4) To estimate the change in y for a one-unit change in x

A. The number of people visited a local library each day, for 11 days, is listed below.

104 131 120 115 109 124 128 118 116 120 125

1) Complete an ordered stem and leaf diagram for this information. A key has included (4 marks)

Key 10 | 4 means 104

2) Write down the mode. (1 mark)

3) Write down the median (1 mark)

4) Write down the range. (1 mark)

B. The stem and leaf diagram below shows the ages, in years, of males and females at a tennis club.

Key: 1 | 1 | 0 = 11 years for males and 10 years for females

1) What was the range, the mode and the mean age (to the nearest year) for males? (3 marks)

2) What was the range, the median and the mean age (to the nearest year) for females? (3 marks)

A. A teacher asks the students in Foundation year what type of transport they use to get to Kaplan college. The dual bar chart shows some of the results.

1)   What is the most popular type of transport used by the boys? (1 mark)

2) 7 girls walk to college. Show this information on the dual bar chart. (1 mark)

3) More of the students get to college by car than by bus. How many more? (1 mark)

4) The number of students in the Language department is the same as the number of Foundation course students. What is the total number of students in Language course and Foundation?

(2 marks)

B. The table shows some information about the weights, in kg, of some boxes.

Yusuf uses this information to draw the box plot below.

1) Write down two things wrong with this box plot. (2 Marks)

Question 5 (8 marks)

The frequency polygon shows the time taken for 100 male students to solve a statistics question.

A. The table shows the times taken by 100 female students to answer the same question.

(6 marks)

1) Work out the mid-point and the cumulative frequency.

2) Draw a frequency polygon to show this information on the diagram above.

B. Write two sentences comparing the times taken by the 100 female students and 100 male students. (2 marks)

Question 6 (10 marks)

pie charts show information about the first-choice university of each student at College A and of each student at College B

A. Work out the number of students from College A have City University as their first choice (4 marks)

B. Tong says, "The same number of students at each College have Birmingham University as their first-choice university”. Is Tong correct? You must show how you get your answer? (6 marks)

Question 7 (9 marks)

A shop sells desktop computers, laptops and tablets.

The composite bar chart shows information about sales over the last three years.

A.  Write down the number of desktop computers sold in 2015 (1 mark)

B. Work out the total number of laptops sold in the 3 years. (4 marks)

C.  State the item that had the greatest increase in sales over the 3 years.

Give a reason for your answer. (2 marks)

D. Alex says, “In 2017, more tablets were sold than desktop computers. This means the shop makes more profit from the sale of tablets than from the sale of desktop computers.”

Is Alex correct? You must justify your answer. (1 mark)

E. Which was the most popular device? (1 mark)

Question 8 (10 marks)

The waiting times, t hours, for 40 patients at an accident and emergency department in one evening is shown below.

A. Calculate the Frequency Density (5 marks)

B. Draw a histogram to show this information. (5 marks)

The table shows data on the number of visitors to the UK in a month, v (1000s), and the amount of money they spent, m (£ millions), for each of 8 months

A. Find the product moment correlation coefficient between m and v. (3 marks)

B. Give a reason to support fitting a regression model of the form to these data

(1 mark)

C. Find the value of b to 3 decimal places. (3 marks)

D. Interpret the value of b (1 mark)

E. Find the equation of the regression line of m in v (9 marks)

F. Using the answer to part (d) to estimate the amount of money spent when the number of visitors to the UK in a month is 2 500 000 (4 marks)

Question 10 (12 marks)

A. If you deposit £250 in a bank account which is paying 5% interest per year. How much simple interest will be earnt over 5 years? (2 marks)

B. If you deposit £1,000 in a bank account which is paying 3% compound interest per year. How much interest would be earnt over 3 years? (6 marks)

C. The value of a mobile was £600 on 1st March 2019. Every four months, the value of the mobile decreased by 8% of its value at the start of that four months.

What was the value of the mobile on 1st March 2020? (4 marks)

***********************This is the end of the examination paper *************************

FC301 Statistics Mid of Module Exam