Question 1

A researcher attempts to study the relationship between income increment and number of years in service of a random company S. Out of the 1644 employees, 127 male and 98 female employees participated in the study. It was found that, on average, a worker who works with the company will receive an annual bonus of RM150. This information was then used as a rebuttal against the company who claimed that every employee had been receiving a yearly increment of RM250. Some workers even exclaimed that they only received a meager RM50 per year. Dissatisfaction roses and an employee strike seems inevitable.

a)Identify the population of interest.

b)Identify the sample.

c)Identify the parameter of the study.

d)Identify the statistic of the study.

Question 2

During a one-day blood drive300people donated blood at a mobile donation center. The blood types of these300donors are summarized below.

Blood TypeOABAB

Frequency1361203212

Identify the blood type that has the highest relativefrequency for these300people. Can you conclude that the blood type you identified is also most common for all people in the population at large? Explain.

Question 3

Cordelia records her daily commute time to work each day, to the nearest minute, for two months, and obtains the following data.

Time (X)26 272829303132

Frequency 34 16 12621

a.Based on the frequencies, do you expect the mean and the median to be about the same or markedly different, and why?

b.Compute the mean, the median, and the mode.

c.Compute therange and sample standard deviation.

d.Cordelia is supposed to be at work at8:00a.m but refuses to leave her house before7:30.

i.Find thepercentile rank of30, the time she has to get to work.

ii.Assuming that thesample accurately reflects the population ofallof Cordelia's commute times, use your answer to part (a) to predict the proportion of the work days she is late for work.

Question 4

The following table list the joint probabilities of achieving grades of Aand not achieving A's in two MBA courses.

Achieves a Grade of A

In Marketing

Doe not achieves a Grade of A

In Marketing

Achieve a Grade of A in

Statistics

0.053

0.130

Does not achieve a Grade of A in Statistics

0.237

0.580

a.What is the probability that a student achieves a grade A in marketing?

b.What is the probability that a student achieves a grade A in marketing , given that he or she does not achieve a grade of A in Statistics?

c.Are achieving grades of A in marketing and statistics independent event? Explain.

Question 5

After watching a number of children playing games at a video archade, a statistics practitioner estimated the following probability distribution of X, the number of games played.

X

1

2

3

4

5

6

7

Total

P(X)

0.05

0.15

0.15

0.25

0.2

0.1

0.1

1

a.What is the probability that a child will play more than four games?

b.What is the probability that a child will play at least two games?

c.Determine the mean and variance of the number of games played.

d.Suppose that each game costs the player 25 cents. Determine the expected value and variance of the amount of money the arcade takes in.

e.Use the laws of expected value and variance to determine the expected value and variance of the amount of money the arcade takes in.

Question 6

Before January semester 2021, Student's distance from home to a random university follows strictly a normal distribution with mean of 15km and a variance of 5km.

a)Are the listed variables above a parameter or statistic?

b)In January semester 2021, the average travelling distance for 48 students from home to campus is 12.8km. Can we conclude that these new students stayed much nearer compared to students from previous semesters? Perform a hypothesis test at 99% confidence.

Question 7

Researchers studying the effects of a new diet found that the weight loss over a one-month period by those on the diet was normally distributed with a mean of 10 pounds and a standard deviation of 5 pounds.

a)Calculate the proportion of the dieters lost more than 12 pounds.

b)Calculate the proportion of the dieters gained weight.

c)What is the cutoff for the bottom 5% of the weight?

d)If five dieter is selected at random, what is the probability that the dieter lost more than 7.5 pounds?

Question 8

A tool and die maker operates out of a small shop making specialized tools.He is considering increasing the size of his business and needs to know more about his costs. One such cost is electricity, which he needs to operate his machines and lights. (Some jobs require that he turn an extra bright lights to illuminate his work.) He keeps track on his daily electricity costs and the number of too;ls that he madethat day. These data are listed next.

Day

12345678910

Number of tools

732581151536

Electricity cost

23.80 11.8915.9826.1131.7939.9312.2740.0621.3818.65

a.Draw a scatter diagram of the data and plot the least squares regression line on it

[4 marks]

b.Determine the fixed and variable electricity cost.

[6 marks]

c.Calculate the standard error of estimate and describe what this statistic tells you about the regression line.

[4 marks]

d.Calculate the coefficient of determination and describe what this statistic tells you about the relationship between the two variables.