Need clear and simple solutions to help me to study for stats test. Document Preview: ECMT1010...

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Need clear and simple solutions to help me to study for stats test.

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ECMT1010 – Workshop 8 Problems 1. (Chapter 9, problem 9.2) Use the data given to test the following hypotheses. Assume the data are normally distributed in the population. 2. (Chapter 9, problem 9.6) According to a study several years ago, the average BMW driver earns $82 600 per year. Suppose a researcher believes that the average annual earnings of a BMW driver are lower now, and he sets up a study in an attempt to prove his theory. He randomly samples 18 BMW drivers and finds out that the average annual salary for this sample is $78 974, with a population standard deviation of $7810. Use a = .01 to test the researcher's theory. Assume annual salaries are normally distributed. 3. (Chapter 9, problem 9.10) A random sample of size 20 is taken, resulting in a sample mean of 16.45 and a sample standard deviation of 3.59. Assume x is normally distributed and use this information and a = .05 to test the following hypotheses. 4. (Chapter 9, problem 9.16) Suppose that in past years the average price per square metre for warehouses has been $322.80. A national real estate investor wants to determine whether that figure has changed now. The investor hires a researcher who randomly samples 19 warehouses that are for sale and finds that the mean price per square metre is $316.70, with a standard deviation of $12.90. If the researcher uses a 5% level of significance, what statistical conclusion can be reached? What are the hypotheses? 5. (Chapter 9, problem 9.20) Suppose you are testing H : p = .29 versus H : p ? .29. A random sample of 740 items shows 0 a that 207 have this characteristic. With a .05 probability of committing a Type I error, test the hypothesis. For the p-value method, what is the probability of the calculated z value for this problem? If you had used the critical value method, what would the two critical values be? How do the sample results compare with the critical values? 6. (Chapter 9,...

005_z2lo8pk-c1fhczqx.pdf

Robert · Accepted Answer

A1) We will construct the test statistic first using the given information. The test statistic is given by: 
  
n
x
Z
/

  
 Using the given values , we compute Z under H0 . Thus, Z=-2.3078 
 Now the critical value at 1% and one sided is 2.32635 (Using standard normal tables) 
 The modulus Z is less than the critical value, therefore we do not reject the null hypothesis 
that 48.7 . 
A2) Null hypothesis,H0: 82600  
Alternative hypothesis,H1: 82600  
Where  is the average income of BMW driver  
Test statistic: 
n
x
Z
/

  
 7810,18,78974  nx  
 Thus Under H0,Z=-1.969 
 The critical value at 1% and one sided is 2.32635  
 Since the modulus value of Z is less than 2.32635, we do not reject the null hypothesis at 1% 
level of significance and conclude that there is insufficient evidence to reject that average income of 
BMW driver is equal to 82600. 
A3)In this question, since we do not know the population standard deviation we would use the t test 
instead of Z. 
 The test statistic is given by: 
ns
x
t
/

 , where s is the sample standard deviation. 
 From the values given in the question, we have 59.3,20,45.16  snx  
 Thus t=0.5605 
 The critical value for t with n-1 degrees of freedom is :2.093. 
Again since the observed is less than tabulated value , we do not reject the null hypothesis at 5% , 
two tailed test. 
A4)Setting up the null and alternative hypothesis first. 
 H0: 80.322  
 H1: 80.322  
 Where  is the average price per sq metre.  
Test statistic: 
ns
x
t
/

  
 From the information given , 90.12,19,70.316  snx  
 Thus , t=-2.061184 
 From the t tables, critical value is 2.1, (18 d.f) 
 Since the calculated value of modulus t is less than 2.1, we do not reject the null hypothesis  
at 5 % level . 
A5)We first compute the test statistic for this proportion problem. 
 The test statistic is 
n
pp
pp
Z
)1(
ˆ


  
 Where 28.0740/207ˆ p  is the sample proportion and n=740 
 Thus Under H0, Z=-0.599 
 The critical values at 5% two sided are: -1.96 and 1.96.

Need clear and simple solutions to help me to study for stats test. Document Preview: ECMT1010 – Workshop 8 Problems 1. (Chapter 9, problem 9.2) Use the data given to test the following hypotheses....

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