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MSIN 0010 Significance Level and Hypothesis Testing Questions

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MSIN0010 Data Analytics I
Homework 3
Due: Tuesday 27 November
1. (5 points) According to a financial planner, individuals should save 10% of their
income over their working life to secure a comfortable retirement. An agency wants
to test whether this actually happens with people in the UK, suspecting the overall
savings rate may be lower. A random sample of 40 individuals revealed an average
savings rate of 8%. Further assume that the standard deviation of savings rates in the
population is known to be 3%. Carry out a hypothesis test to determine if the savings
rate is actually lower than 10%. Use a 5% significance level and be sure to follow the
five steps of hypothesis testing.
n=40, ,  , =3
 
 
one-sample z-test, 

 
  

 
 
- 






0.00000122
As 0.00000122 is smaller than 0.05, we reject null hypothesis and can conclude that
the savings rate is actually lower than 10%
2. (5 points) According to BusinessWeek, the average market value of a biotech
company is $250 million. A sample of 50 firms reveals an average of $235 million and
a sample standard deviation of $85 million. Using this sample, test whether the
average value in the population is actually $250 million. Use a 1% significance level
and be sure to follow the five steps of hypothesis testing.
n=50, ,  , 
 
 
one-sample t-test, 

 
 


  
- 










0.21796
As the 0.217 is greater than 0.01, we fail to reject the null hypothesis and can
conclude that the average market value of a biotech company is $250 million

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