I drive to school and am currently looking for a parking spot so I can walk to Jacob's. If I turn into a parking lot to look for a spot to park in that specific lot, the process of looking for a spot takes 1 minute of time whether I find a spot or not.  

Parking lot A is closest to Jacobs. If I get a spot here, it takes me 1 minute to walk into my class at the business school, however there is only a 10% chance I'll find a spot if I look.

Parking lot B is a 4-minute walk; if I pull in to look for a spot, there is a 30% chance I'll find a spot.

Parking lot C is an 8-minute walk; if I pull in to look for a spot, there is a 100% chance I will find a spot.  

Which strategy to find a parking spot is best for me (ie. which order should I check the parking lots for spots to park), assuming we are risk-neutral, and simply want to have the earliest expected arrival time to Jacob’s as possible? (Another way to say this is we want the smallest expected value of time spent getting to Hall).

Now, assume I am risk averse (let’s say that in this second case, my class starts in 10 minutes, and there is a large decrease in my utility if I am late for class). Is the best strategy the same as when I am risk-neutral, or has it changed?

ou are going to calculate a 95% confidence interval for a one-sample proportion. Which of the following would be your critical value (z*)?

(a) Briefly discuss the binomial probability distribution.

(b) A coin is flipped 12 times: what is the probability of getting:

i. no heads; and)

ii. no more than 3 heads?

Over the past 10 years two golfers have had an ongoing battle as to who the better golfer is. Curtley Weird has won 120 of their 200 matches, while Dave Chilly has won 70 with 10 of them ending in ties. Because Dave is going overseas they decide to play a tournament of five matches to establish once and for all who the better player is.

Find the probabilities that:

(a) Dave wins at least three of the matches;

(b) Curtley wins no more than two games; and

(c) all of the games end in a tie.

(a) Discuss probability, independence and mutual exclusivity, giving examples to illustrate your answer.

i. How many ways are there of choosing a committee of three people from a club of ten?

ii. How many ways are there of selecting from those three people a president, secretary and treasurer?

iii. Illustrate your answer to the second part of the question with a tree diagram.

An ice-cream vendor on the beachfront knows from long experience that the average rate of ice-cream sales is 12 per hour. If, with two hours to go at work, she finds herself with only five ice-creams in stock, what are the probabilities that

(a) she runs out before the end of the day;

(b) she sells exactly what she has in stock by the end of the day without any excess demand after she sells the last one; and

(c) she doesn't sell any?

A company applying for medical aid cover counts that 70 of its 140 male employees smoke. Of the 100 female employees, 20 smoke. What is the probability that an employee chosen at random

(a) is female and smokes; (2)

b) does not smoke; and

(c) is male or smokes?

In a true or false assignment of six questions you are obliged to get at least four correct to pass. If you guess the answers to the questions, what are the probabilities that:

a) you pass; (4)

(b) you get at least 50% of the answers correct; and

(c) you get no more than two correct? (3)

onist claims that he gets 10 calls every five minutes. To demonstrate this to his boss he makes a tape lasting five minutes. What are the probabilities that he gets:

(a) no calls in the five minutes; (2)

(b) less than three calls; and (5)

(c) exactly 10 calls? (

Assume that matric marks are standardised to have a mean of 52% and a standard deviation of 16% (and assume that they have a normal distribution). In a class of 100 students estimate how many of them:

(a) pass (in other words get more than 33,3%);

(b) get A's (more than 80%); and

(c) get B's (between 70% and 80%).

As manager of a company you know that the distribution of completion times for an assembly operation is a normal distribution with a mean of 120 seconds and a standard deviation of 20 seconds. If you have to award bonuses to the top 10% of your workers what time would you use as a cut-off time? [6]

20. Jogger A can run laps at the rate of 2 minutes per lap. Jogger B can run laps on the same track at the rate of 150 seconds per lap. If they start at the same place and time and run in the same direction, how long (in time) will it be before they are at the starting place again at the same time?

A) 5 minutes

B) 300 seconds

C) 10 minutes

The average length of time customers spent on waiting at ABC Store’s check-out counter before a new P.O.S. system was installed was 4.3 minutes. A sample of 40 customers randomly selected at the check-out counter after the new P.O.S. system was installed showed that the average waiting time was 3.5 minutes with a sample standard deviation of 2.8 minutes. We wish to determine if the average waiting time after the P.O.S. system was installed is less than 4.3 minutes.

1.   State the null and alternative hypotheses to be tested. (2 Points)

2.   Compute the test statistic. (2 Points)

3.   Determine the critical value for this test at the 0.05 level of significance. (2 Points)

4.   What do you conclude at the 0.05 level of significance? (2 Points)

5.   Construct a 95% confidence interval for the average waiting time after the new P.O.S. system was installed.

(1 point) A poll is taken in which 388 out of 600 randomly selected voters indicated their preference for a certain candidate.

(a) Find a 99% confidence interval for p (....... ≤p≤........)

(b) Find the margin of error for this 99% confidence interval for p.

Scenario 3:

To determine the effectiveness of a new diuretic drug, urine output was measured in 20 men and compared to 20 men that received placebo control. The data are summarized in Table 2 below. The null hypothesis is: H₀: μ _Placebo= μ  _drug.

Table2.  Effectiveness of New Diuretic Drug

What is the null hypothesis equation for this experiment?

What statistical test would you use?

t-test

ANOVA

Relative Risk

POWER

What is the 95% confidence intervals for this 2 sample t-test?

4.                          Based on the statistical test that you chose, do you accept or reject the null hypothesis at P=0.05? Please paste your data output file in the area below.

5.                          What is the Power of this test?Please paste your data output file in the area below.

How many samples are needed to achieve a power of 0.80?  Please paste your data output file in the area below.   

Find the level of a two-sided confidence interval that is based on the given value of t and the given sample size.
6. t = 1.943, sample size n = 7. (Multiple choice)

Choices: 80%, 90%, 95%, 98%

7. t = 2.093, sample size n = 20.

Choices: 90%, 98%, 95%, 99%

10. t = 1.753, n = 16

Choices: 80%, 90%, 95%, 99%

Q1: A transport company wants to compare the fuel efficiencies of the two types of lorry it operates. It obtains data from samples of the two types of lorry, with the following results:

At 90% confidence level, test the hypothesis that lorries of type B are more efficient than type A. Use critical value approach and assume unequal variation in mpg of two types.

The National Sleep Foundation (NSF) recommends that college students get between 8 and 9 hours of sleep per night. Not believing this is happening at a local college, a random sample of 20 students resulted in a mean of 6.94 hours, with a standard deviation of 1.1 hours.

Part 1 of 3

If it is assumed that hours of sleep for college students is approximately normally distributed, construct and interpret a 95% confidence interval statement as well as a confidence level statement. Do the students at this local college meet the NSF recommendation? (Round your answers to two decimal places. Use a table or technology.

(R code needed) Lifetimes of electronic components manufactured by an electronic company are assumed to follow an Exp(λ) distribution with mean 1/λ. A random sample of 30 lifetimes in years was obtained and shown below: 5.1888 3.6757 4.5091 7.1320 1.3711 1.6454 2.1979 3.8805 0.5290 2.3796 3.2840 3.6678 0.6836 7.9914 12.9922 2.6192 0.3593 5.0234 0.2240 7.5862 0.1172 0.0618 2.6203 16.2319 17.2107 0.8101 8.9368 2.0752 0.9925 1.0187

The data can also be found in life2018.csv.

(a) Find the moment estimate of λ. [4 points]

(b) Find the MLE of λ. Does the MLE match the moment estimate? [4 points]

(c) Let Sλ(2) = exp(−2λ) denote the survival function at time y = 2. Find the MLE of Sλ(2). [4 points]

(d) Find the moment estimate of Sλ(2). [4 points]

A recent national survey found that high school students watched an average of 6.8 DVDs per month with a population standard deviation of 0.5 DVDs. The distribution follows the normal distribution. A random sample of 36 college students revealed that the mean number of DVDs watch last month was 6.2. At the .05 significance level, can we conclude that college students watch fewer DVDs a month than high school students?

a. What is the null and alternative hypotheses?

b. Is this a two-tailed or one-tailed test?

c. Which distribution should we use? Normal or Student t

d. What is the critical value(s)? (the line in the sand values)

e. What is your test statistic value?

f. What is the p-value

g. What is your decision regarding the null hypothesis?

Using the data provided:

1. Plot the data. What does the plot tell you about the appropriateness of using a trend and seasonally adjusted model for your data?
2. Develop a forecast model that incorporates both a trend and seasonal adjustment (even if its not necessarily there).
3. Develop a forecast for the four periods beyond your data.
4. Calculate a MAD and Bias based on the last 12 periods of known data. What do the MAD and bias indicate about your model?
5. Overall, are you satisfied with your model? If so, why? If not, suggest some things that could be done to improve your model.

data: