Question 1082059: Question 1(a)
Suppose that the amount of time teenagers spend on the Internet is normally distributed, with a standard deviation of 1.5 hours. A sample of 100 teenagers is selected at random, and the sample mean is computed as 6.5 hours.
(i) Determine the 99% confidence interval estimate of the population mean.
(ii) Determine the 95% confidence interval estimate of the population mean, changing the sample size to 300.
(iii) Comment on how the confidence interval and changes to sample size will impact on the interval estimates.
Question 1(b)
The amount of time spent by Australian adults playing sports per day is normally distributed, with a mean of 4 hours and standard deviation of 1.25 hours. Use this information to answer the following question(s).
(i) Find the probability that a randomly selected Australian adult plays sport for more than 5 hours per day.
(ii) That if four Australian adults are randomly selected, their average number of hours spent playing sport is more than 5 hours per day.
(iii) Find the probability that if four Australian adults are randomly selected, all four play sport for more than 5 hours per day.
Question 2(a)
At present, many universities in Australia are adopting the practice of having lecture recordings automatically available to students. A university lecturer is trying to investigate whether having lecture recordings available to students has significantly decreased the proportion of students passing her course. When lecture recordings were not provided to students, the proportion of students that passed her course was 80%. The lecturer takes a random sample of 25 students, when lecture recordings are offered to students, and finds that 11 students have passed the course. Is there significant evidence to support this university lecturer’s claim? Use α = 0.01
Question 2(b)
A drug company is interested in the effectiveness of a new sleeping pill. A random sample of 50 people try the new sleeping pill and the number of additional hours of sleep (compared with the nights without any sleeping pill), X, are recorded. The sample mean of additional hours of sleep is 2.2 hours and the sample standard deviation of X is 3 hours.
Test the claim that the new drug increases the number of hours of sleep at least by 2 hours on average at the 5% level of significance.
Question 3(a)
In 2003, computers of Brand A controlled 25% of the market, Brand B 20%, Brand C 10% and Brand D 45%. In 2004, sample data were collected from many randomly selected stores throughout the country. Of the 1200 computers sold, 280 were Brand A, 270 were Brand B, 90 were Brand C and 560 were Brand D. Has the market changed since 2003? Test at the 1% significance level
Question 3(b)
A major insurance firm interviewed a random sample of 1500 college students to find out the type of life insurance preferred, if any. The results follow:
Insurance Preference
Gender Term Whole life No insurance
Female 170 110 470
Male 195 75 480
Is there evidence that the life insurance preference of male students is different to that of female students? Test using the 5% level of significance.
Question 3(c)
The following data are believed to have come from a normal probability distribution.
26 21 25 20 21 29 26 23 22 24
24 30 23 32 26 24 32 16 36 26
21 31 26 23 32 35 40 30 14 26
46 27 33 25 27 21 26 18 29 36
The mean of this sample equals 26.80, and the standard deviation equals 6.378.
Investigate at the 5% significance level to test this claim.
Question 4:
Pop-up coffee vendors have been popular in most campuses world-wide. A potential vendor is interested in exploring the possibility of operating a pop-coffee in Darwin. People she spoke to are trying to discourage her as they claim that the median temperature of 38 degrees Celsius is too hot for people to consume coffee through an open transportable vending facility. You have been appointed to offer assistance in knowing how temperature (in degrees Celsius) impacts daily hot coffee sales revenue (in $00’s).
The potential vendor has collected using a random sample for 6 days to generate a link between the daily hot coffee sales revenue and the corresponding temperature of that day noted.
Coffee sales revenue Temperature
6.50 25
10.00 17
5.50 30
4.50 35
3.50 40
28.00 9
An Excel regression output was obtained on this data which is given below.
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.8644
R Square 0.7472
Adjusted R Square 0.6840
Standard Error 5.2027
Observations 6
ANOVA
df SS MS F Significance F
Regression 1 320.0617 320.0617 11.8244 0.0263
Residual 4 108.2716 27.0679
Total 5 428.3333
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 27.7179 5.6629 4.8946 0.0081 11.9952 43.4406
Temperature -0.6943 0.2019 -3.4387 0.0263 -1.2549 -0.1337
(a) Estimate daily hot coffee sales revenue on a day of 38 degrees Celsius. (2 marks)
(b) State with reasons why your prediction in part (a) is reasonable or not? (2 marks)
(c) Test the significance of the slope, against a two-tailed alternative, at the 5% level of significance.
(d) Prepare a short report to the potential vendor of your analysis including your recommended decisions.
Question 5:
A statistics course at a large university is taught in each semester. A student has noticed that the students in semester 1 and semester 2 are enrolled in different degrees. The student believes that the cohort of students in semester 1 do better than in Semester 2. To investigate, the student takes a random sample of 25 students from semester 1 and 25 students from semester 2 and records their final marks (%) provided in the table below. Excel was used to generate descriptive statistics on each sample. Based on past experience we know that final marks in statistics course have a normal distribution.
Sample of semester 1 final marks Sample of semester 2 final marks
65 45 53 76 53 45 40 53 58 75
85 55 63 85 77 46 82 54 75 59
45 57 55 60 83 45 54 87 77 63
56 83 55 52 67 81 60 56 53 65
82 64 62 88 71 52 65 60 65 54
Semester 1 Semester 2
Mean 65.48 Mean 60.96
Standard Error 2.679 Standard Error 2.5136
Median 63 Median 59
Mode 55 Mode 54
Standard Deviation 13.395 Standard Deviation 12.568
Sample Variance 179.43 Sample Variance 157.96
Range 43 Range 47
Minimum 45 Minimum 40
Maximum 88 Maximum 87
Sum 1637 Sum 1524
Count 25 Count 25
Comment on the two semester grades detailing the steps you would take (based on session 1 to 11 discussions in this unit) and investigate if student’s in different semesters do produce different grades.
Answer by ikleyn(52772)   (Show Source):
You can put this solution on YOUR website! .
1. The rules of this site are:
One problem per post and one question per post.
Your post violates these rules.
2. In this site we, the tutors, help students solve their problems.
It is the aim and the goal of this site.
We do not serve for INDUSRIALISTS who post series of problems.
3. What I see in this post is the series of problems, which AUTOMATICALLY puts the post out of the tasks we are working on.
|
|
|
