Assuming that the population is normally​ distributed, construct a 99% confidence interval for the population mean for each of the samples below. Explain why these two samples produce different confidence intervals even though they have the same mean and range.

SAMPLE A: 1 1 4 4 5 5 8 8

SAMPLE B: 1 2 3 4 5 6 7 8

1.Construct a 99% confidence interval for the population mean for sample A. ( type integers or decimals rounded to two decimal places)

2. Construct a 99% confidence interval for the population mean for sample B.  ( type integers or decimals rounded to two decimal places)

3. Explain why these two samples produce different confidence intervals even though they have the same mean and range.

a. The samples produce different confidence intervals because their standard deviations are different

b.The samples produce different confidence intervals because their sample sizes are different

c.The samples produce different confidence intervals because their critical values are different

d. The samples produce different confidence intervals because their medians are different

To test the effect of a physical fitness course on one's physical ability, the number of sit-ups that a person could do in one minute, both before and after the course, was recorded. Ten individuals are randomly selected to participate in the course. The results are displayed in the following table. Using this data, find the 99%

confidence interval for the true difference in the number of sit-ups each person can do before and after the course. Assume that the numbers of sit-ups are normally distributed for the population both before and after completing the course.

Step 1 of 4:Find the point estimate for the population mean of the paired differences. Let x1

be the number of sit-ups before taking the course and x2 be the number of sit-ups after taking the course and use the formula d=x2−x1 to calculate the paired differences. Round your answer to one decimal place.

Step 2 of 4:Calculate the sample standard deviation of the paired differences. Round your answer to six decimal places.

Step 3 of 4:Calculate the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.

Step 4 of 4:Construct the 99%

confidence interval. Round your answers to one decimal place.

Q1. Using the data provided for your group assignment estimate the simple regression

Y= Final_exam and X= assignment_grade. Each part of question is worth 2 marks.

1. Prior to estimating the regression what are your a priori expectations about the sign of β1? Explain.
2. Write down the regression results in traditional form, with t statistics below each of the estimated coefficients and anything else that should be included.
3. Test the null hypothesis that β1=0 against the two sided alternative hypothesis at the 5% level of significance. Interpret your results.
4. Now estimate the multiple regression model including assignment_grade (X1) and Tutorial_attend (X2). Write down the regression results in traditional form, with t statistics below each of the estimated coefficients and anything else that should be included.
5. Within the multiple regression model- test the null hypothesis that β1=0 against the two sided alternative hypothesis at the 5% level of significance. Interpret your results.

5-8

Oslo Company prepared the following contribution format income statement based on a sales volume of 1,000 units (the relevant range of production is 500 units to 1,500 units):

5.If sales decline to 900 units, what would be the net operating income?

6 If the selling price increases by $2 per unit and the sales volume decreases by 100 units, what would be the net operating income?

7.  If the variable cost per unit increases by $1, spending on advertising increases by $1,150, and unit sales increase by 130 units, what would be the net operating income?

8. What is the break-even point in unit sales?

Mary-Lou is a 75-year-old widow, who lost her husband to cancer over a year ago. Her family and friends have noticed that she has been very teary, has low self-esteem and has lost interest in the things she used to love such as going to bingo with her friends and gardening. Her family initially put this down to the loss of her husband and thought it would pass with time. However, they are now getting really concerned as they have noticed that her mood is not improving still. When asked by her daughter if she is sleeping well, she says she has been drinking wine every night to help her go to sleep. It makes her feel happy and relaxed. What started as one glass a night has now increased to two or three glasses a night, and she has also started drinking during the day. Her daughter has noticed that her mum’s face always appears flushed and that she has had quite a few colds lately. Mary-Lou is also losing her balance and experiencing mood swings. Her daughter is worried that she is relying too heavily on alcohol and fears that she is starting to get short-term memory loss from the alcohol consumption. She has been forgetting things such as where she put her keys, whether she turned on the washing machine, why she opened the fridge and forgetting the topic of conversation when talking with her daughter on the phone. Mary-Lou has also been getting disorientated and getting lost when she goes out on her daily walks. A neighbor rang her daughter one day to tell her that she found Mary-Lou wandering around aimlessly, and when questioned what she was doing Mary-Lou snapped and said she was trying to get home. Her daughter decided it was time to take Mary-Lou to the local GP to work out what was going on with her. After listening to the signs and symptoms Mary-Lou was experiencing, the GP diagnosed her with depression and prescribed 50 mg of Fluoxetine/Prozac daily. Based on the results of clinical and radiological assessments, the GP determined that she had early onset Alzheimer’s disease. He prescribed a cholinesterase inhibitor and gave them information on support groups and tips on what to do from here on in. He also prescribed 10 mg of Diazepam daily to help with the withdrawals from alcohol abuse.

Explain the mechanism of action of two drug types Mary-Lou is prescribed with and describe how these drug actions help mitigate some of her symptoms. In your answer, make references to the pathophysiology of the relevant diseases. Explain how these drug help to mitigate her symptoms.

0. Mary-Lou is a 75-year-old widow, who lost her husband to cancer over a year ago. Her family and friends have noticed that she has been very teary, has low self-esteem and has lost interest in the things she used to love such as going to bingo with her friends and gardening. Her family initially put this down to the loss of her husband and thought it would pass with time. However, they are now getting really concerned as they have noticed that her mood is not improving still. When asked by her daughter if she is sleeping well, she says she has been drinking wine every night to help her go to sleep. It makes her feel happy and relaxed. What started as one glass a night has now increased to two or three glasses a night, and she has also started drinking during the day. Her daughter has noticed that her mum’s face always appears flushed and that she has had quite a few colds lately. Mary-Lou is also losing her balance and experiencing mood swings. Her daughter is worried that she is relying too heavily on alcohol and fears that she is starting to get short-term memory loss from the alcohol consumption. She has been forgetting things such as where she put her keys, whether she turned on the washing machine, why she opened the fridge and forgetting the topic of conversation when talking with her daughter on the phone. Mary-Lou has also been getting disorientated and getting lost when she goes out on her daily walks. A neighbor rang her daughter one day to tell her that she found Mary-Lou wandering around aimlessly, and when questioned what she was doing Mary-Lou snapped and said she was trying to get home. Her daughter decided it was time to take Mary-Lou to the local GP to work out what was going on with her.

   After listening to the signs and symptoms Mary-Lou was experiencing, the GP diagnosed her with depression and prescribed 50 mg of Fluoxetine/Prozac daily. Based on the results of clinical and radiological assessments, the GP determined that she had early-onset Alzheimer’s disease. He prescribed a cholinesterase inhibitor and gave them information on support groups and tips on what to do from here on in. He also prescribed 10 mg of Diazepam daily to help with the withdrawals from alcohol abuse.

1. Explain the mechanism of action of two drug types Mary-Lou is prescribed with and describe how these drug actions help mitigate some of her symptoms. In you answer, make references to the pathophysiology of the relevant diseases.

Consider two genes with different expected mutation rates due to size. Gene 1 has a mutation rate of 1 x 10-6 in the population, while gene 2 has a mutation rate of 3 x 10-6 in the population. Assume that the probability for an individual to have two mutations in one gene is 0. Also, the number of bases, n, in a gene is large.

1. State the probability for gene 1 and for gene 2 that there is exactly one person with a mutation in the gene in a random sample of 1000 people.

2. State the probability for gene 1 and for gene 2 that there is exactly one person with a mutation in either of the two genes in your sample.

3. State the probability for each gene separately that they are exactly two people with mutations in your sample.

4. State the probability that there is either zero or at least one person with a mutation in a gene in your sample.

5. State the probability that there are more than two people with mutations total between the two genes in your sample.

6. Consider the case that gene 2 controls the potential for mutation of gene 1. If gene 2 is mutated, gene 1 has a probability of 50% of being mutated, while if gene 2 is not mutated, gene 1 has a probability of 10% of being mutated. What is the probability that gene 1 is mutated in an individual.

A crystal composed of atoms of one unknown species has experimentally determined values of molar heat capacity at
constant pressure and two different temperatures:

Cp (200 K) = 21.573 J.K^-1.mol^-1
Cp (100 K) = 13.360 J K^-1.mol^-1

Determine the approximate molar heat capacity at a constant volume of this crystal as a function of temperature over the interval from
50-300 K and plot it with the two experimental points.

Suppose that you have inherited an annuity that will pay $1000 for 50 years.

A) Assuming that the first payment occurs exactly one year from now and that the annual opportunity cost of capital is 10% , what is the value of this annuity today? Round your final answer to two decimals.

B) Assuming that the first payment occurs immediately and that the annual opportunity cost of capital is 10%, What is the value of this annuity today? Round your final answer to two decimals.