Category: Mathematics

What does the value in cell A33 tell you about the hypothesis. Do we reject the null hypothesis? Why? Put your explanation in cell A36.

State the null hypothesis from this example in cell A35.

What does the value in cell A33 tell you about the hypothesis. Do we reject the null hypothesis? Why? Put your explanation in cell A36.

Instead of using Excel, we can look at the t chart. Find the critical value for the t distribution from that table. You may find it on page 335. Put that value in cell A37.

Compare the t value in cell A29 to the table t value in cell A37. What is this comparison telling you about rejecting or not rejecting the null hypothesis. Put your explanation in cell A38.

In nursing, when might you want to know the mean differences between two or more groups? describe the situation (what groups, what measurements) including how and why it would be used.

Now, without calculating a mean or margin of error or a confidence level, provide an example from your current (or your future) professional or personal life that describes a measurement that is normal—and how much wiggle room on either side would be appropriate. When would you want a 95% confidence interval and when would you be interested in a 99% confidence level (a little more wiggle room—so a wider range)?

Topic 2

Two or more samples are often compared when we suspect that there are differences between the groups—for example, are cancer rates higher in one town than another, or are test scores higher in one class than another? In nursing, when might you want to know the mean differences between two or more groups? describe the situation (what groups, what measurements) including how and why it would be used.

If John can drink one barrel of water in 6 days, and Mary can drink one barrel of water in 12 days, how long would it take them to drink one barrel of water together in days?

Quantitative Report

A bat and a ball cost £1.10 in total.  The bat costs £1.00 more than the ball.  How much does the ball cost in pence?

If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets in minutes?

In a lake, there is a patch of lily pads.  Every day, the patch doubles in size.  If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake in days?

If John can drink one barrel of water in 6 days, and Mary can drink one barrel of water in 12 days, how long would it take them to drink one barrel of water together in days?

Jerry received both the 15th highest and the 15th lowest mark in the class.  How many students are in the class?

A man buys a pig for £60, sells it for £70, buys it back for £80 and sells it finally for £90. How much money has he made in pounds?

Simon decided to invest £8000 on the stock market one day early in 2008.  Six months after he invested, on July 17, the stocks he had purchased were down 50%.  Fortunately for Simon, from July 17, to October 17, the stocks he purchased went up by 75%.  At this point, Simon
has broken even on the stock market (1)
is ahead of where he began (2)
has lost money (3)

Mary’s mother had four children.  The youngest three are named: Spring, Summer, and Autumn.  What is the oldest child’s name?

 Find the slope of the indifference curve. Does the marginal rate of substitution (MRS) diminish along the indifference curve when X increases? Prove your answer.

An indifference curve is given by X0.4Y0.7 = 100, where X and Y are quantities of goods X and Y consumed, with Y is on the vertical axis and X is on the horizontal axis.

Find the slope of the indifference curve.

Does the marginal rate of substitution (MRS) diminish along the indifference curve when X increases? Prove your answer.

A generalized production function Q=f(K,L) is defined implicitly from the following equation, f(Q, K, L) = QerQ-AKaLb = 0. Find the marginal product of L and K, and the MRTS.

A demand function for good X is given by X=APx

PyβIγ, where A>0, Px and Py are prices of good X and the other good Y, I is the income, α, β, and γ are parameters. Find the own-price elasticity, cross-price elasticity, and income elasticity. Show your work. Discuss signs of α, β, and γ.

Given A=2 3 14 1 25 3 4 and B=2 7 05 8 16 7 0 .
a) Find AB and BA, showing AB

BA.
b) Show that det(AB) = det(BA) = (detA)*(detB).
c) Find A+B and show that det(A+B)  det(A)+det(B).

Is a savings account a good way to earn interest? When looking at opening a savings account, what should you look for: higher interest rate or more frequent compounding?

Financial

Use exponents to calculate the amount of interest earned on an investment.
Evaluate formulas with exponents.
Convert interest rates to decimals.
Apply the order of operations.

Is a savings account a good way to earn interest? When looking at opening a savings account, what should you look for: higher interest rate or more frequent compounding?

What amount of the risk of developing a disease is attributable to a particular exposure?By what percent would the risk of developing disease be reduced if the exposure were eliminated?

Measures of Risk
Measures of Attributable Risk answer the following questions:

What amount of the risk of developing a disease is attributable to a particular exposure?

By what percent would the risk of developing disease be reduced if the exposure were eliminated?

For public health decision-making purposes, it is valuable to be able to answer these questions from two perspectives: the impact of eliminating the exposure on only those who are exposed and impact of eliminating the exposure on the entire population.

Question 1:

The preventive advantages of eating fish have been reported in numerous studies. A cohort study reported that never or rarely eating fish increased the risk for stroke. The table below shows the results of this study:

Calculate the incidence of stroke in persons who eat fish 0-1 times per week.

Calculate the incidence of stroke in persons who eat fish 2+ times per week.

Calculate and interpret the Relative Risk for the association between eating fish and stroke.

Calculate and interpret the attributable risk among persons who never or rarely eat fish.

Calculate and interpret the attributable risk percent among persons who never or rarely eat fish.

Calculate and interpret the population attributable risk.

Calculate and interpret the population attributable risk percent.

Question 2:

In a cohort study of smoking and lung cancer, the incidence of lung cancer among current smokers was 9/1,000 and 45% of the total population were current smokers. The incidence among current nonsmokers was 1/1,000.

The incidence of lung cancer attributable to smoking in the total population is:

The proportion attributable risk in the total population that is attributable to smoking is:

What information would you need to see if there is an association between Gilbert being on duty and code/death rates?What are your null hypotheses and alternative hypotheses?

What information would you need to see if there is an association between Gilbert being on duty and code/death rates?

What other explanations might there be for why Gilbert had more deaths on her shifts?

What type of statistical test would you use for this case to see if there is an association?

What are your null hypotheses and alternative hypotheses?

The following is an analysis of 1641 eight-hour shifts. Use this data to decide if there is enough statically support for an arrest warrant. (Use 95% confidence interval)
Deaths during shift?
Gilbert present Yes No
Yes 40 217
No 34 1350