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Mat201 case 5 | Mathematics homework help

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By submitting this assignment, you affirm that it contains all original work, and that you are familiar with Trident University’s Academic Integrity policy in the Trident Policy Handbook. You affirm that you have not engaged in direct duplication, copy/pasting, sharing assignments, collaboration with others, contract cheating and/or obtaining answers online, paraphrasing, or submitting/facilitating the submission of prior work. Work found to be unoriginal and in violation of this policy is subject to consequences such as a failing grade on the assignment, a failing grade in the course, and/or elevated academic sanctions. You affirm that the assignment was completed individually, and all work presented is your own.

Problems need to include all required steps and answer(s) for full credit. All answers need to be reduced to lowest terms where possible.

Answer the following problems showing your work and explaining (or analyzing) your results.

  1. Explain Type I and Type II errors. Use an example if needed.
  2. Explain a one-tailed and two-tailed test. Use an example if needed.
  3. Define the following terms in your own words.
  • Null hypothesis
  • P-value
  • Critical value
  • Statistically significant
  • A homeowner is getting carpet installed. The installer is charging her for 250 square feet. She thinks this is more than the actual space being carpeted. She asks a second installer to measure the space to confirm her doubt. Write the null hypothesis Ho and the alternative hypothesis Ha.
  • Drug A is the usual treatment for depression in graduate students. Pfizer has a new drug, Drug B, that it thinks may be more effective. You have been hired to design the test program. As part of your project briefing, you decide to explain the logic of statistical testing to the people who are going to be working for you. 
    • Write the research hypothesis and the null hypothesis.
    • Then construct a table like the one below, displaying the outcomes that would constitute Type I and Type II error.  
    • Write a paragraph explaining which error would be more severe, and why. 

    1. Cough-a-Lot children’s cough syrup is supposed to contain 6 ounces of medicine per bottle. However since the filling machine is not always precise, there can be variation from bottle to bottle. The amounts in the bottles are normally distributed with σ = 0.3 ounces.  A quality assurance inspector measures 10 bottles and finds the following (in ounces):
    5.95 6.10 5.98 6.01 6.25 5.85 5.91 6.05 5.88 5.91

    Are the results enough evidence to conclude that the bottles are not filled adequately at the labeled amount of 6 ounces per bottle?

    1. State the hypothesis you will test.
    2. Calculate the test statistic.
    3. Find the P-value.
    4. What is the conclusion?
    1. Calculate a Z score when X = 20, μ = 17, and σ = 3.4.
    2. Using a standard normal probabilities table, interpret the results for the Z score in Problem 7.
    3. Your babysitter claims that she is underpaid given the current market. Her hourly wage is $12 per hour. You do some research and discover that the average wage in your area is $14 per hour with a standard deviation of 1.9. Calculate the Z score and use the table to find the standard normal probability. Based on your findings, should you give her a raise? Explain your reasoning as to why or why not.
    4. Tutor O-Rama claims that their services will raise student SAT math scores at least 50 points. The average score on the math portion of the SAT is μ=350 and σ=35. The 100 students who completed the tutoring program had an average score of 385 points. 
      1. Is the students’ average score of 385 points significant at the 5% and 1% levels to support Tutor O-Rama’s claim of at least a 50-point increase in the SAT score?
      2. Is the Tutor O-Rama students’ average score of 385 points significantly different at the 5% and 1% levels from the average score of 350 points on the math portion of the SAT?  What conclusion can you make, based on your results, about the effectiveness of Tutor O-Rama’s tutoring?
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    Approximate price: $22

    July 1, 2023
        

     

     

    51) In the short run, a decrease in aggregate demand will lead to

    A) a decrease in the price level and an increase in real GDP.

    B) an increase in the price level and a decrease in real GDP.

    C) a decrease in the price level and an increase in the unemployment rate.

    D) an increase in the price level and an increase in real GDP.

    E) no change in the price level and a decrease in real GDP.

     

    52) If the economy moves upward along its short-run Phillips curve, in the AS-AD diagram, this movement is shown by a

    A) movement upward along the AS curve as a result of a rightward shift of the AD curve.

    B) rightward shift of potential GDP.

    C) movement downward along the AS curve as a result of a leftward shift of the AD curve.

    D) rightward shift of the AS curve and a movement along the AD curve.

    E) leftward shift of the AS curve and a movement along the AD curve.

     

    53) If aggregate demand increases, thereby leading to an increase in real GDP and inflation, there is

    A) a movement downward along the short-run Phillips curve.

    B) a movement upward along the short-run Phillips curve.

    C) a rightward shift in the short-run Phillips curve.

    D) a leftward shift in the short-run Phillips curve.

    E) neither a movement along nor a shift in the short-run Phillips curve.

    54) The relationship between the AS-AD model and the Phillips curve points out that as aggregate demand increases, the unemployment rate

    A) decreases and the inflation rate rises.

    B) increases and the inflation rate falls.

    C) decreases and the price level falls.

    D) increases and the inflation rate rises.

    E) decreases and the inflation rate does not change, only the price level rises.

     

    55) Data from the United States and the United Kingdom show that the short-run Phillips curve exhibits

    A) a great deal of shifting.

    B) stability with shifts occurring only when external forces are strong.

    C) stability with shifts occurring only when there is an internal change of government.

    D) shifts that occur every five years or so.

    E) positive slopes in both nations.

     

    56) Changes in which of the following shift the short-run Phillips curve?

    i.changes in the natural unemployment rate

    ii.changes in the expected inflation rate

    iii.changes in the inflation rate

    A) i only

    B) ii only

    C) iii only

    D) i and ii

    E) i, ii, and iii

    57) The short-run Phillips curve shows a relationship between the

    A) inflation rate and the interest rate.

    B) inflation rate and real GDP.

    C) unemployment rate and the interest rate.

    D) inflation rate and the unemployment rate.

    E) price level and real GDP.

     

    58) The short-run Phillips curve is

    A) vertical at the natural unemployment rate.

    B) upward sloping.

    C) downward sloping.

    D) horizontal at the expected inflation rate.

    E) U-shaped.

     

    59) Moving along the short-run Phillips curve, as the unemployment rate increases the inflation rate

    A) decreases.

    B) increases.

    C) remains unchanged.

    D) initially decreases and then increases.

    E) initially increases and then decreases.

     

    60) When a movement up along the aggregate supply curve occurs, there is also

    A) a movement down along the short-run Phillips curve.

    B) a movement up along the short-run Phillips curve.

    C) a rightward shift of the short-run Phillips curve.

    D) a leftward shift of the short-run Phillips curve.

    E) no movement along nor a shift in the short-run Phillips curve.

    61) If real GDP exceeds potential GDP, then employment is ________ full employment and the unemployment rate is ________ the natural unemployment rate.

    A) below; above

    B) equal to; below

    C) above; below

    D) above; above

    E) equal to; equal to

     

    62) According to Okun's Law, if the natural unemployment rate is 5 percent, the actual unemployment rate is 4 percent, and potential GDP is $15 trillion, then actual real GDP is

    A) $12.0 trillion.

    B) $15.0 trillion.

    C) $14.7 trillion.

    D) $15.4 trillion.

    E) $15.3 trillion.

     

    63) When aggregate demand increases, there is a movement ________ along the AS curve and ________.

    A) up; a movement up along the short-run Phillips curve

    B) up; a movement down along the short-run Phillips curve

    C) up; an upward shift of the short-run Phillips curve

    D) down; a downward shift of the short-run Phillips curve

    E) down; a movement down along the short-run Phillips curve

     

     

    default image
    July 1, 2023
        

     

     

    51) In the short run, a decrease in aggregate demand will lead to

    A) a decrease in the price level and an increase in real GDP.

    B) an increase in the price level and a decrease in real GDP.

    C) a decrease in the price level and an increase in the unemployment rate.

    D) an increase in the price level and an increase in real GDP.

    E) no change in the price level and a decrease in real GDP.

     

    52) If the economy moves upward along its short-run Phillips curve, in the AS-AD diagram, this movement is shown by a

    A) movement upward along the AS curve as a result of a rightward shift of the AD curve.

    B) rightward shift of potential GDP.

    C) movement downward along the AS curve as a result of a leftward shift of the AD curve.

    D) rightward shift of the AS curve and a movement along the AD curve.

    E) leftward shift of the AS curve and a movement along the AD curve.

     

    53) If aggregate demand increases, thereby leading to an increase in real GDP and inflation, there is

    A) a movement downward along the short-run Phillips curve.

    B) a movement upward along the short-run Phillips curve.

    C) a rightward shift in the short-run Phillips curve.

    D) a leftward shift in the short-run Phillips curve.

    E) neither a movement along nor a shift in the short-run Phillips curve.

    54) The relationship between the AS-AD model and the Phillips curve points out that as aggregate demand increases, the unemployment rate

    A) decreases and the inflation rate rises.

    B) increases and the inflation rate falls.

    C) decreases and the price level falls.

    D) increases and the inflation rate rises.

    E) decreases and the inflation rate does not change, only the price level rises.

     

    55) Data from the United States and the United Kingdom show that the short-run Phillips curve exhibits

    A) a great deal of shifting.

    B) stability with shifts occurring only when external forces are strong.

    C) stability with shifts occurring only when there is an internal change of government.

    D) shifts that occur every five years or so.

    E) positive slopes in both nations.

     

    56) Changes in which of the following shift the short-run Phillips curve?

    i.changes in the natural unemployment rate

    ii.changes in the expected inflation rate

    iii.changes in the inflation rate

    A) i only

    B) ii only

    C) iii only

    D) i and ii

    E) i, ii, and iii

    57) The short-run Phillips curve shows a relationship between the

    A) inflation rate and the interest rate.

    B) inflation rate and real GDP.

    C) unemployment rate and the interest rate.

    D) inflation rate and the unemployment rate.

    E) price level and real GDP.

     

    58) The short-run Phillips curve is

    A) vertical at the natural unemployment rate.

    B) upward sloping.

    C) downward sloping.

    D) horizontal at the expected inflation rate.

    E) U-shaped.

     

    59) Moving along the short-run Phillips curve, as the unemployment rate increases the inflation rate

    A) decreases.

    B) increases.

    C) remains unchanged.

    D) initially decreases and then increases.

    E) initially increases and then decreases.

     

    60) When a movement up along the aggregate supply curve occurs, there is also

    A) a movement down along the short-run Phillips curve.

    B) a movement up along the short-run Phillips curve.

    C) a rightward shift of the short-run Phillips curve.

    D) a leftward shift of the short-run Phillips curve.

    E) no movement along nor a shift in the short-run Phillips curve.

    61) If real GDP exceeds potential GDP, then employment is ________ full employment and the unemployment rate is ________ the natural unemployment rate.

    A) below; above

    B) equal to; below

    C) above; below

    D) above; above

    E) equal to; equal to

     

    62) According to Okun's Law, if the natural unemployment rate is 5 percent, the actual unemployment rate is 4 percent, and potential GDP is $15 trillion, then actual real GDP is

    A) $12.0 trillion.

    B) $15.0 trillion.

    C) $14.7 trillion.

    D) $15.4 trillion.

    E) $15.3 trillion.

     

    63) When aggregate demand increases, there is a movement ________ along the AS curve and ________.

    A) up; a movement up along the short-run Phillips curve

    B) up; a movement down along the short-run Phillips curve

    C) up; an upward shift of the short-run Phillips curve

    D) down; a downward shift of the short-run Phillips curve

    E) down; a movement down along the short-run Phillips curve

     

     

    default image
    July 1, 2023
        

     

     

    51) In the short run, a decrease in aggregate demand will lead to

    A) a decrease in the price level and an increase in real GDP.

    B) an increase in the price level and a decrease in real GDP.

    C) a decrease in the price level and an increase in the unemployment rate.

    D) an increase in the price level and an increase in real GDP.

    E) no change in the price level and a decrease in real GDP.

     

    52) If the economy moves upward along its short-run Phillips curve, in the AS-AD diagram, this movement is shown by a

    A) movement upward along the AS curve as a result of a rightward shift of the AD curve.

    B) rightward shift of potential GDP.

    C) movement downward along the AS curve as a result of a leftward shift of the AD curve.

    D) rightward shift of the AS curve and a movement along the AD curve.

    E) leftward shift of the AS curve and a movement along the AD curve.

     

    53) If aggregate demand increases, thereby leading to an increase in real GDP and inflation, there is

    A) a movement downward along the short-run Phillips curve.

    B) a movement upward along the short-run Phillips curve.

    C) a rightward shift in the short-run Phillips curve.

    D) a leftward shift in the short-run Phillips curve.

    E) neither a movement along nor a shift in the short-run Phillips curve.

    54) The relationship between the AS-AD model and the Phillips curve points out that as aggregate demand increases, the unemployment rate

    A) decreases and the inflation rate rises.

    B) increases and the inflation rate falls.

    C) decreases and the price level falls.

    D) increases and the inflation rate rises.

    E) decreases and the inflation rate does not change, only the price level rises.

     

    55) Data from the United States and the United Kingdom show that the short-run Phillips curve exhibits

    A) a great deal of shifting.

    B) stability with shifts occurring only when external forces are strong.

    C) stability with shifts occurring only when there is an internal change of government.

    D) shifts that occur every five years or so.

    E) positive slopes in both nations.

     

    56) Changes in which of the following shift the short-run Phillips curve?

    i.changes in the natural unemployment rate

    ii.changes in the expected inflation rate

    iii.changes in the inflation rate

    A) i only

    B) ii only

    C) iii only

    D) i and ii

    E) i, ii, and iii

    57) The short-run Phillips curve shows a relationship between the

    A) inflation rate and the interest rate.

    B) inflation rate and real GDP.

    C) unemployment rate and the interest rate.

    D) inflation rate and the unemployment rate.

    E) price level and real GDP.

     

    58) The short-run Phillips curve is

    A) vertical at the natural unemployment rate.

    B) upward sloping.

    C) downward sloping.

    D) horizontal at the expected inflation rate.

    E) U-shaped.

     

    59) Moving along the short-run Phillips curve, as the unemployment rate increases the inflation rate

    A) decreases.

    B) increases.

    C) remains unchanged.

    D) initially decreases and then increases.

    E) initially increases and then decreases.

     

    60) When a movement up along the aggregate supply curve occurs, there is also

    A) a movement down along the short-run Phillips curve.

    B) a movement up along the short-run Phillips curve.

    C) a rightward shift of the short-run Phillips curve.

    D) a leftward shift of the short-run Phillips curve.

    E) no movement along nor a shift in the short-run Phillips curve.

    61) If real GDP exceeds potential GDP, then employment is ________ full employment and the unemployment rate is ________ the natural unemployment rate.

    A) below; above

    B) equal to; below

    C) above; below

    D) above; above

    E) equal to; equal to

     

    62) According to Okun's Law, if the natural unemployment rate is 5 percent, the actual unemployment rate is 4 percent, and potential GDP is $15 trillion, then actual real GDP is

    A) $12.0 trillion.

    B) $15.0 trillion.

    C) $14.7 trillion.

    D) $15.4 trillion.

    E) $15.3 trillion.

     

    63) When aggregate demand increases, there is a movement ________ along the AS curve and ________.

    A) up; a movement up along the short-run Phillips curve

    B) up; a movement down along the short-run Phillips curve

    C) up; an upward shift of the short-run Phillips curve

    D) down; a downward shift of the short-run Phillips curve

    E) down; a movement down along the short-run Phillips curve

     

     

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