My commute to university, follows a NORMAL distribution with a 35.5 minutes as mean and a standard deviation of 2.5 min. If my commute starts at 8:20 am and ideally I must be at university by 9am.

Define two random variables and formulate two questions, one involving binomial distribution and the other involving geometric distribution.

Suppose a professor splits their class into two groups: students whose last names begin with A-K and students whose last names begin with L-Z. If p1 and p2 represent the proportion of students who have an iPhone by last name, would you be surprised if p1 did not exactly equal p2? If we conclude that the first initial of a student's last name is NOT related to whether the person owns an iPhone, what assumption are we making about the relationship between these two variables?

Suppose we have two thermometers. One thermometer is very precise but is delicate and heavy (X). We have another thermometer that is much cheaper and lighter, but of unknown precision (Y). We would like to know if we can (reliably) bring the lighter thermometer with us into the field. So, we set up an experiment where we expose both thermometers to 31 different temperatures and measure the temperature with each. We get the following observations
x = 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120
y = 0.02, 3.99, 7.91, 12.03, 16.09, 20.00, 23.98, 28.09, 31.94, 36.03, 40.00, 44.05, 47.95, 52.00, 55.87, 59.90, 63.91, 67.95, 72.11, 76.02, 80.01, 84.10, 88.06, 91.74, 96.02, 99.95, 103.87, 108.01, 111.99, 116.04, 120.03
We want to test if these thermometers seem to be measuring the same temperatures. Let's use the threshold . Answer all questions up to 3 decimals

(a) Write down the appropriate hypothesis tests for . H₀:   ---Select--- ≠ = > <  and H_a:   ---Select--- ≤ = > ≠ ≥ <

(b) The test statistic is  (Use 2 decimal places)

(c) The p-value is  (Use 4 decimal places)

(d) Therefore, we can conclude that

The data provides evidence at the 0.1 significance level that these thermometers are not consistentThe data provides no evidence at the 0.1 significance level that these thermometers are not consistentThe probability that the null hypothesis is true is equal to the p-valueThe probability that we have made a mistake is equal to 0.1

Rob is 84 years old, and his wife of 60 years recently died from a long-term illness. Rob has been experiencing some health concerns and is finding managing on his own difficult. Donna is meeting with Rob to plan for the provision of home and community care services.

Donna notes that Rob is articulate and neatly dressed. His home is a little dusty, but well organised. Rob is a little thin and admits that he is not a very good cook. He says he is happy to have help, as he wants to stay in his own home for as long as possible.

1. What are the physical and psychological factors Donna should take into account when planning service delivery? (Approx. 30 words).

2. How could Donna explain the purpose of the planning process to Rob? (Approx. 20 words).

3. What are two different service options that Donna could discuss with Rob? (Approx. 30 words).

4. Does Rob seem ready for the development of an individualised plan? Why or why not? (Approx. 50 words).

5. How can Donna help Rob select the most appropriate service option? (Approx. 30 words).

6.Who should be included in the planning process for Rob’s individualised plan? (Approx. 50 words).

7.What are two things Donna and Rob need to organise for the planning session on Rob’s goals? (Approx. 50 words).

8.Who does Donna need to inform about Rob’s individualised plan? (Approx. 15 words).

9.Does Donna need to liaise with Rob’s assessor about his requirements prior to the planning sessions? Why or why not? (Approx. 35 words).

A statistical program is recommended.

Consider the following data for a dependent variable y and two independent variables,

x₁

and

x₂.

(a)

Develop an estimated regression equation relating y to

x₁.

(Round your numerical values to one decimal place.)ŷ =

  Predict y if

x₁ = 43.

(Round your answer to one decimal place.)

(b)

Develop an estimated regression equation relating y to

x₂.

(Round your numerical values to one decimal place.)ŷ =

  Predict y if

x₂ = 19.

(Round your answer to one decimal place.)

(c)

Develop an estimated regression equation relating y to

x₁ and x₂.

(Round your numerical values to one decimal place.)ŷ =

  Predict y if

x₁ = 43

and

x₂ = 19.

(Round your answer to one decimal place.)

1. A fund had the following annual prices and dividends (beginning of the year): 2002 2003 2004 2005* 2006 2007 $50 $55 $63 $20 $24 $23 $1 $1 $.40 $.40 $.40 * Price reflects a three for one split.

a. Compute each year return.

b. Compute the four years holding period return.

c. Compute the annualized rate of return

Bradley-Link’s December 31, 2018, balance sheet included the following items: Long-Term Liabilities ($ in millions) 8.0% convertible bonds, callable at 102 beginning in 2019, due 2022 (net of unamortized discount of $4) [note 8] $146 11.0% registered bonds callable at 105 beginning in 2028, due 2032 (net of unamortized discount of $1) [note 8] 54 Shareholders’ Equity 5 Equity—stock warrants

Note 8: Bonds (in part) The 8.0% bonds were issued in 2005 at 96.0 to yield 10%. Interest is paid semiannually on June 30 and December 31. Each $1,000 bond is convertible into 50 shares of the Company’s no par common stock. The 11.0% bonds were issued in 2009 at 103 to yield 10%. Interest is paid semiannually on June 30 and December 31. Each $1,000 bond was issued with 50 detachable stock warrants, each of which entitles the holder to purchase one share of the Company’s no par common stock for $30, beginning 2019. On January 3, 2019, when Bradley-Link’s common stock had a market price of $37 per share, Bradley-Link called the convertible bonds to force conversion. 90% were converted; the remainder were acquired at the call price. When the common stock price reached an all-time high of $42 in December of 2019, 40% of the warrants were exercised.

Required: 1. Prepare the journal entries that were recorded when each of the two bond issues was originally sold in 2005 and 2009. 2. Prepare the journal entry to record (book value method) the conversion of 90% of the convertible bonds in January 2019 and the retirement of the remainder. 3. Assume Bradley-Link induced conversion by offering $140 cash for each bond converted. Prepare the journal entry to record (book value method) the conversion of 90% of the convertible bonds in January 2019. 4. Assume Bradley-Link induced conversion by modifying the conversion ratio to exchange 55 shares for each bond rather than the 50 shares provided in the contract. Prepare the journal entry to record (book value method) the conversion of 90% of the convertible bonds in January 2019. 5. Prepare the journal entry to record the exercise of the warrants in December 2019.  

Bradley-Link’s December 31, 2018, balance sheet included the following items: Long-Term Liabilities ($ in millions) 9.0% convertible bonds, callable at 104 beginning in 2019, due 2022 (net of unamortized discount of $3) [note 8] $197 11.0% registered bonds callable at 107 beginning in 2028, due 2032 (net of unamortized discount of $1) [note 8] 66 Shareholders’ Equity 6 Equity—stock warrants Note 8: Bonds (in part) The 9.0% bonds were issued in 2005 at 97.5 to yield 10%. Interest is paid semiannually on June 30 and December 31. Each $1,000 bond is convertible into 50 shares of the Company’s no par common stock. The 11.0% bonds were issued in 2009 at 105 to yield 10%. Interest is paid semiannually on June 30 and December 31. Each $1,000 bond was issued with 50 detachable stock warrants, each of which entitles the holder to purchase one share of the Company’s no par common stock for $30, beginning 2019. On January 3, 2019, when Bradley-Link’s common stock had a market price of $37 per share, Bradley-Link called the convertible bonds to force conversion. 90% were converted; the remainder were acquired at the call price. When the common stock price reached an all-time high of $42 in December of 2019, 40% of the warrants were exercised. Required: 1. Prepare the journal entries that were recorded when each of the two bond issues was originally sold in 2005 and 2009. 2. Prepare the journal entry to record (book value method) the conversion of 90% of the convertible bonds in January 2019 and the retirement of the remainder. 3. Assume Bradley-Link induced conversion by offering $160 cash for each bond converted. Prepare the journal entry to record (book value method) the conversion of 90% of the convertible bonds in January 2019. 4. Assume Bradley-Link induced conversion by modifying the conversion ratio to exchange 55 shares for each bond rather than the 50 shares provided in the contract. Prepare the journal entry to record (book value method) the conversion of 90% of the convertible bonds in January 2019. 5. Prepare the journal entry to record the exercise of the warrants in December 2019.

Bradley-Link’s December 31, 2018, balance sheet included the following items:

Note 8: Bonds (in part)
The 11.0% bonds were issued in 2005 at 98.0 to yield 10%. Interest is paid semiannually on June 30 and December 31. Each $1,000 bond is convertible into 50 shares of the Company’s no par common stock.

The 11.0% bonds were issued in 2009 at 103 to yield 10%. Interest is paid semiannually on June 30 and December 31. Each $1,000 bond was issued with 50 detachable stock warrants, each of which entitles the holder to purchase one share of the Company’s no par common stock for $30, beginning 2019.

On January 3, 2019, when Bradley-Link’s common stock had a market price of $37 per share, Bradley-Link called the convertible bonds to force conversion. 90% were converted; the remainder were acquired at the call price. When the common stock price reached an all-time high of $42 in December of 2019, 40% of the warrants were exercised.

Required:
1. Prepare the journal entries that were recorded when each of the two bond issues was originally sold in 2005 and 2009.
2. Prepare the journal entry to record (book value method) the conversion of 90% of the convertible bonds in January 2019 and the retirement of the remainder.
3. Assume Bradley-Link induced conversion by offering $170 cash for each bond converted. Prepare the journal entry to record (book value method) the conversion of 90% of the convertible bonds in January 2019.
4. Assume Bradley-Link induced conversion by modifying the conversion ratio to exchange 55 shares for each bond rather than the 50 shares provided in the contract. Prepare the journal entry to record (book value method) the conversion of 90% of the convertible bonds in January 2019.
5. Prepare the journal entry to record the exercise of the warrants in December 2019.