Assignment help-Unit: TSTA101 – INTRODUCTORY STATISTICS

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Individual Assignment
Unit: TSTA101 – INTRODUCTORY STATISTICS
Due Date: Thursday, 28/09/2017 (16:00pm)
Number of Questions: Six (6) Questions
Total Marks: Twenty (20) marks
Instructions: All questions should be attempted.
The marks of each question would be awarded based on your understanding of the questions, concepts and procedures; hence you should demonstrate your answers step by step.
Question 1 [3 marks]
Part a)
Find the following probabilities by checking the z table
i) P((Z>-0.8)
ii) P (-1.3<Z<-0.7)
iii) Z0.2
Part b)
A new car has recently hit the market. The distance travelled on 1 gallon of fuel is normally distributed with a mean of 65 miles and a standard deviation of 4 miles. Find the probability of the following events.
i) The car travels more than 70 miles per gallon.
ii) The car travels less than 60 miles per gallon.
iii) The car travels between 55 and 70 miles per gallon.
Question 2 [3 marks]
Part a)
A sample of n=25 observations is drawn from a normal population with μ=100 and σ=20. Find the following.
i) P(<96)
ii) P(96<<105)
Part b)
The amount of time the university professors devote to their jobs per week is normally distributed with a mean of 52 hours and a standard deviation of 6 hours.
i) What is the probability that a professor works for more than 60 hours per weeks?
ii) Find the probability that the mean amount of work per week for three randomly selected professors is more than 60 hours?
Question 3 [2 marks]
Part a)
Given the following information =500, σ=12, n=50
i) Determine the 95% confidence interval estimate of population mean.
ii) Determine the 99% confidence interval estimate of population mean.
Part b)
A statistics practitioner calculated the mean and standard deviation from a sample of 51. They are =120 and s=15.
(i) Estimate the population mean with 95% confidence level.
(ii) Estimate the population mean with 99% confidence level.
X
X
X
X
Question 4 [4 marks]
Part a)
Calculate the statistic, set up the rejection region, interpret the result, and draw the sampling distribution.
H0: μ=10
H1: μ≠10
Given that: σ=10, n=100, =10, α=0.05.
Part b)
A statistics practitioner is in the process of testing to determine whether is enough evidence to infer that the population mean is different from 180. She calculated the mean and standard deviation of a sample of 200 observations as =175 and s=22. Calculate the value of the test statistic of the test required to determine whether there is enough evidence to infer at the 5% significance level that the population mean is different from 180.
Question 5 (2 marks)
Suppose you are using a completely randomized design to study some phenomenon.
There are five treatment levels and a total of 55 people in the study. Each treatment
level has the same sample size. Complete the following ANOVA. Use α=0.05 to find the table F value and use the data to test the null hypothesis.
Source of Variance
SS
df
MS
F
Treatment
583.39
Error
972.18
Total
1555.57
Question 6 (6marks)
There is a simple linear regression model given by:
where price = used car price in dollars and
age = age of the car in years.
The EXCEL results obtained using Ordinary Least Squares are presented below:
Regression Statistics
R2
0.077
Standard Error
42069
Observations
117
Coefficients
Standard Error
t Stat
Intercept
A
6748
7.035
Age
-2658
856
B
Use the above output for answering the following questions:
a) Calculate the missing values from the summary output: A and B
b) Interpret the slope of the regression line.
c) Write down the estimated linear regression line.
d) What is the value of the coefficient of determination? Interpret this value
e) What is the value of the coefficient of correlation? Interpret this value.
f) Test whether the estimated coefficient of Age is significantly less than zero at the 5% level of significance.
g) Predict price if the car has driven 3 years. X