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Each member of a random sample of 20 business economists was asked to

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Question 1[20 points, 5 marks each]

  1. Each member of a random sample of 20 business economists was asked to predict the rate of inflation for the coming year. Assume that the predictions for the whole population of business economists follow a normal distribution with a standard deviation of 2%.

 

  1. The probability is 0.01 that the sample standard deviation is larger than what value?

 

  1. The probability is 0.025 that the sample standard deviation is smaller than what value?

 

  1. Monthly rates of return on the shares of a particular common stock are independent of one another and normally distributed with a standard deviation of 1.8. A sample of 15 months is taken.

  1. Find the probability that the sample standard deviation is less than 2.6.

 

  1. Find the probability that the sample standard deviation is more than 1.2.

 

Question 2[20 points]

  1. [10 points]To calculate a required sample size to estimate a population proportion, given a desired confidence interval and margin of error, the sample proportion is required but often unknown before the sample is collected. How is this predicament resolved?

  2. [5 points]How large a sample is needed to estimate the population proportion if ME = 0.09, = 0.05?

 

  1. [5 points]A fast food company wants to determine the average number of times that fast food eaters visit fast food restaurants per week. They have decided that their estimate needs to be accurate to within plus or minus one-tenth of a visit, and they want to be 90% sure of this. Previous research has shown that the standard deviation is 0.7 visits. What is the required sample size?

 

Question 3 [25 points]

A company selling licenses for new e-commerce computer software advertises that firms using this software obtain, on average during the first year, a yield of 10% on their initial investments. A random sample of 10 of these franchises produced the following yields for the first year of operation:

6.1 9.2 11.5 8.6 12.1 3.9 8.4 10.1 9.4 8.9

 

  1. [4 marks] Calculate the sample mean and sample standard deviation.

 

  1. [4 marks] Assuming that the population distribution is normal, construct a 95% confidence interval for the true standard deviation of the yield on initial investment during the first year.

 

  1. [2 marks] Assuming that the population distribution is normal, formulate a suitable null and alternative hypothesis to test the company’s claim at the 5% level of significance.

 

  1. [2 marks] What is the test’s decision rule?

 

  1. [2 marks] Calculate the test statistic.

 

  1. [1 mark] Based on the test statistic calculated in (d) above, what is your conclusion about the company’s claim?

 

  1. [2 marks] Calculate the p-value for the test statistic computed in (d) above.

 

  1. [1 mark] Using the p-value found in (f) above, what is your conclusion about the company’s claim?

 

  1. [3 marks] Construct a 95% confidence interval for the average yield on initial investment during the first year for all firms using the company’s software.

 

  1. [3 marks] Does the confidence interval in (h) above support your conclusion from the hypothesis test? Explain.

 

Question 4[16 points, 8 points each]

  1. A music industry professional claims that the average amount of money that an average teenager spends per month on music is at least $50. Based upon previous research, the population standard deviation is estimated to be $12.42. The music professional surveys 20 students and finds that the mean spending is $47.77. Is there evidence that the average amount spent by students is less than $50? Using the p-value approach, test at the 10% significance level.

 

  1. The manufacturer of a new chewing gum claims that at least eight out of ten dentists surveyed prefer their type of gum and recommend it for their patients who chew gum. An independent consumer research firm decides to test their claim. The findings in a sample of 400 doctors indicate that 76% do actually prefer the manufacturer’s gum. Is this evidence sufficient to cast doubt on the manufacturer’s claim? Use α = 0.05.

 

 

 

 

 

 

Question 5: EXCEL Question[20 points]

 

Step1 Draw 500 N(0,1) random numbers for each of ten variables. This will show up in EXCEL as 10 columns of 500 rows.

Step 2 View each row as a sample of length 10. For each of the 500 samples, calculate the sample mean and sample standard deviation. These computations lead to two new columns of length 500.

Step 3 Calculate a z-stat (assuming known σ = 1) and a t-stat (σ unknown) for each sample.

Step 4 Determine critical values z.025 and t9,025 (from Tables).

Step 5 Fill in the following Table.

Step 6 Interpret the results in language using the null and alternative hypotheses presented in class.

 

Percentage Tail Draws Based on N(0,1) Samples

500 samples; size n = 10

 

 

z-left tail

z-right tail

total z-tails

t-left tail

t-right tail

total t-tails

t-crit9,025

 

z-crit025

 

 

 

 

 

 

 

 

Percentage tail values

 

 

 

 

 

 
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July 1, 2023
    

 

71) Suppose the change in the government's debt-to-GDP ratio in a given year is 0.026. This figure tells us that the government's debt-to-GDP ratio has

A) fallen by 0.026%.

B) risen by 0.026%.

C) risen by 2.6 percentage points.

D) fallen by 2.6 percentage points.

E) risen by 0.026 percentage points.

72) Suppose the government's debt-to-GDP ratio on January 1 of Year 1 is 32%. The change in the debt-to-GDP ratio during Year 1 is -0.037. On January 1 of Year 2 the government's debt-to-GDP ratio is

A) 31.963%.

B) 32. 037%.

C) 28.3%.

D) 35.7%.

E) Not enough information to determine.

73) Consider the following data about government debt and deficit in a given year:

A) remained unchanged.

B) risen by 50%.

C) fallen by 50%.

D) risen by 0.5 percentage points.

E) fallen by 0.5 percentage points.

74) Consider the following data about government debt and deficit in a given year:

A) 82 percentage points.

B) 8.2 percentage points.

C) 0.82 percentage points.

D) 2.8 percentage points.

E) 0.28 percentage points.

75) Consider the following data about government debt and deficit in a given year:

A) remained unchanged.

B) risen by 0.2 percentage points.

C) fallen by 0.2 percentage points.

D) risen by 2 percentage points.

E) fallen by 2 percentage points.

76) Suppose that the real rate of interest on government bonds is 4% and the growth rate of real GDP is 2%. If the government has a positive stock of outstanding debt and its policy objective is to hold the debt-to-GDP ratio constant at its current level, it must

A) eliminate the overall deficit.

B) run an annually balanced budget.

C) run a cyclically balanced budget.

D) run a primary budget deficit.

E) run a primary budget surplus.

77) Suppose the government's objective is to hold its debt-to-GDP ratio constant at its current level of 30%. If the real interest rate on government bonds is 4% and the growth rate of real GDP is 2%, the government must

A) run a primary budget deficit of 0.6% of GDP.

B) run an overall budget deficit of 6.0% of GDP.

C) run an overall budget surplus of 6.0% of GDP.

D) run a primary budget surplus of 0.6% of GDP.

E) balance the overall budget.

78) Suppose that the real rate of interest is 3% and the growth rate of real GDP is 1%. If the government has a positive stock of outstanding debt and its goal is to hold the debt-to-GDP ratio constant at its current level, then it

A) must run a cyclically balanced budget.

B) must run an annually balanced budget.

C) must run a primary budget deficit.

D) must run a primary budget surplus.

E) must eliminate the overall deficit.

79) Consider a government with an outstanding stock of public debt. If, in any given year, the government has a primary budget surplus and the real interest rate on government bonds is less than the growth rate of real GDP, then

A) debt-service payments will be eliminated.

B) the debt-to-GDP ratio is certainly negative.

C) the debt-to-GDP ratio will certainly rise.

D) the debt-to-GDP ratio will certainly fall.

E) real GDP will certainly rise.

80) Consider a government with an outstanding stock of public debt. If, in any given year, the government has a primary budget surplus and the real interest rate on government bonds is more than the growth rate of real GDP, then

A) the debt-to-GDP ratio will certainly fall.

B) debt-service payments will be eliminated.

C) the debt-to-GDP ratio is certainly negative.

D) the debt-to-GDP ratio will certainly rise.

E) the effect on the debt-to-GDP ratio is uncertain.

 

 

default image
July 1, 2023
    

 

71) Suppose the change in the government's debt-to-GDP ratio in a given year is 0.026. This figure tells us that the government's debt-to-GDP ratio has

A) fallen by 0.026%.

B) risen by 0.026%.

C) risen by 2.6 percentage points.

D) fallen by 2.6 percentage points.

E) risen by 0.026 percentage points.

72) Suppose the government's debt-to-GDP ratio on January 1 of Year 1 is 32%. The change in the debt-to-GDP ratio during Year 1 is -0.037. On January 1 of Year 2 the government's debt-to-GDP ratio is

A) 31.963%.

B) 32. 037%.

C) 28.3%.

D) 35.7%.

E) Not enough information to determine.

73) Consider the following data about government debt and deficit in a given year:

A) remained unchanged.

B) risen by 50%.

C) fallen by 50%.

D) risen by 0.5 percentage points.

E) fallen by 0.5 percentage points.

74) Consider the following data about government debt and deficit in a given year:

A) 82 percentage points.

B) 8.2 percentage points.

C) 0.82 percentage points.

D) 2.8 percentage points.

E) 0.28 percentage points.

75) Consider the following data about government debt and deficit in a given year:

A) remained unchanged.

B) risen by 0.2 percentage points.

C) fallen by 0.2 percentage points.

D) risen by 2 percentage points.

E) fallen by 2 percentage points.

76) Suppose that the real rate of interest on government bonds is 4% and the growth rate of real GDP is 2%. If the government has a positive stock of outstanding debt and its policy objective is to hold the debt-to-GDP ratio constant at its current level, it must

A) eliminate the overall deficit.

B) run an annually balanced budget.

C) run a cyclically balanced budget.

D) run a primary budget deficit.

E) run a primary budget surplus.

77) Suppose the government's objective is to hold its debt-to-GDP ratio constant at its current level of 30%. If the real interest rate on government bonds is 4% and the growth rate of real GDP is 2%, the government must

A) run a primary budget deficit of 0.6% of GDP.

B) run an overall budget deficit of 6.0% of GDP.

C) run an overall budget surplus of 6.0% of GDP.

D) run a primary budget surplus of 0.6% of GDP.

E) balance the overall budget.

78) Suppose that the real rate of interest is 3% and the growth rate of real GDP is 1%. If the government has a positive stock of outstanding debt and its goal is to hold the debt-to-GDP ratio constant at its current level, then it

A) must run a cyclically balanced budget.

B) must run an annually balanced budget.

C) must run a primary budget deficit.

D) must run a primary budget surplus.

E) must eliminate the overall deficit.

79) Consider a government with an outstanding stock of public debt. If, in any given year, the government has a primary budget surplus and the real interest rate on government bonds is less than the growth rate of real GDP, then

A) debt-service payments will be eliminated.

B) the debt-to-GDP ratio is certainly negative.

C) the debt-to-GDP ratio will certainly rise.

D) the debt-to-GDP ratio will certainly fall.

E) real GDP will certainly rise.

80) Consider a government with an outstanding stock of public debt. If, in any given year, the government has a primary budget surplus and the real interest rate on government bonds is more than the growth rate of real GDP, then

A) the debt-to-GDP ratio will certainly fall.

B) debt-service payments will be eliminated.

C) the debt-to-GDP ratio is certainly negative.

D) the debt-to-GDP ratio will certainly rise.

E) the effect on the debt-to-GDP ratio is uncertain.

 

 

default image
July 1, 2023
    

 

71) Suppose the change in the government's debt-to-GDP ratio in a given year is 0.026. This figure tells us that the government's debt-to-GDP ratio has

A) fallen by 0.026%.

B) risen by 0.026%.

C) risen by 2.6 percentage points.

D) fallen by 2.6 percentage points.

E) risen by 0.026 percentage points.

72) Suppose the government's debt-to-GDP ratio on January 1 of Year 1 is 32%. The change in the debt-to-GDP ratio during Year 1 is -0.037. On January 1 of Year 2 the government's debt-to-GDP ratio is

A) 31.963%.

B) 32. 037%.

C) 28.3%.

D) 35.7%.

E) Not enough information to determine.

73) Consider the following data about government debt and deficit in a given year:

A) remained unchanged.

B) risen by 50%.

C) fallen by 50%.

D) risen by 0.5 percentage points.

E) fallen by 0.5 percentage points.

74) Consider the following data about government debt and deficit in a given year:

A) 82 percentage points.

B) 8.2 percentage points.

C) 0.82 percentage points.

D) 2.8 percentage points.

E) 0.28 percentage points.

75) Consider the following data about government debt and deficit in a given year:

A) remained unchanged.

B) risen by 0.2 percentage points.

C) fallen by 0.2 percentage points.

D) risen by 2 percentage points.

E) fallen by 2 percentage points.

76) Suppose that the real rate of interest on government bonds is 4% and the growth rate of real GDP is 2%. If the government has a positive stock of outstanding debt and its policy objective is to hold the debt-to-GDP ratio constant at its current level, it must

A) eliminate the overall deficit.

B) run an annually balanced budget.

C) run a cyclically balanced budget.

D) run a primary budget deficit.

E) run a primary budget surplus.

77) Suppose the government's objective is to hold its debt-to-GDP ratio constant at its current level of 30%. If the real interest rate on government bonds is 4% and the growth rate of real GDP is 2%, the government must

A) run a primary budget deficit of 0.6% of GDP.

B) run an overall budget deficit of 6.0% of GDP.

C) run an overall budget surplus of 6.0% of GDP.

D) run a primary budget surplus of 0.6% of GDP.

E) balance the overall budget.

78) Suppose that the real rate of interest is 3% and the growth rate of real GDP is 1%. If the government has a positive stock of outstanding debt and its goal is to hold the debt-to-GDP ratio constant at its current level, then it

A) must run a cyclically balanced budget.

B) must run an annually balanced budget.

C) must run a primary budget deficit.

D) must run a primary budget surplus.

E) must eliminate the overall deficit.

79) Consider a government with an outstanding stock of public debt. If, in any given year, the government has a primary budget surplus and the real interest rate on government bonds is less than the growth rate of real GDP, then

A) debt-service payments will be eliminated.

B) the debt-to-GDP ratio is certainly negative.

C) the debt-to-GDP ratio will certainly rise.

D) the debt-to-GDP ratio will certainly fall.

E) real GDP will certainly rise.

80) Consider a government with an outstanding stock of public debt. If, in any given year, the government has a primary budget surplus and the real interest rate on government bonds is more than the growth rate of real GDP, then

A) the debt-to-GDP ratio will certainly fall.

B) debt-service payments will be eliminated.

C) the debt-to-GDP ratio is certainly negative.

D) the debt-to-GDP ratio will certainly rise.

E) the effect on the debt-to-GDP ratio is uncertain.

 

 

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