Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations. (You may find it useful to reference the appropriate table: z table...

Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations.(You may find it useful to reference the appropriate table:
z tableor t table)



H₀
:μ₁
 −μ₂
 ≥ 0

H_A
:μ₁
 −μ₂
 <>

a-1. Calculate the value of the test statistic under the assumption that the population variances are equal.(Negative values should be indicated by a minus sign. Round all intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

a-2. Find thep-value.

multiple choice 1

• 
  
  
  

  
  p-value <>

  
  
  
  


• 
  
  
  

  0.01 ≤p-value <>

  
  
  
  


• 
  
  
  

  0.025 ≤p-value <>

  
  
  
  


• 
  
  
  

  0.05 ≤p-value <>

  
  
  
  


• 
  
  
  

  
  p-value ≥ 0.10

  
  
  
  

a-3. Do you reject the null hypothesis at the 5% level?

multiple choice 2

• 
  
  
  

  Yes, since the value of thep-value is less than the significance level.

  
  
  
  


• 
  
  
  

  No, since the value of thep-value is less than the significance level.

  
  
  
  


• 
  
  
  

  Yes, since the value of thep-value is greater than the significance level.

  
  
  
  


• 
  
  
  

  No, since the value of thep-value is greater than the significance level.

  
  
  
  

a-4.Interpret the results at

= 0.05.

multiple choice 3

• 
  
  
  

  We conclude that the population means differ.

  
  
  
  


• 
  
  
  

  We cannot conclude that the population means differ.

  
  
  
  


• 
  
  
  

  We conclude that population mean 1 is less than population mean 2.

  
  
  
  


• 
  
  
  

  We cannot conclude that population mean 1 is less than population mean 2.

  
  
  
  

b-1. Calculate the value of the test statistic under the assumption that the population variances are not equal.(Negative values should be indicated by a minus sign. Round all intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

b-2. Find thep-value.

multiple choice 4

• 
  
  
  

  
  p-value <>

  
  
  
  


• 
  
  
  

  0.01 ≤p-value <>

  
  
  
  


• 
  
  
  

  0.025 ≤p-value <>

  
  
  
  


• 
  
  
  

  0.05 ≤p-value <>

  
  
  
  


• 
  
  
  

  
  p-value ≥ 0.10

  
  
  
  

b-3. Do you reject the null hypothesis at the 5% level?

multiple choice 5

• 
  
  
  

  Yes, since the value of thep-value is less than the significance level.

  
  
  
  


• 
  
  
  

  No, since the value of thep-value is less than the significance level.

  
  
  
  


• 
  
  
  

  Yes, since the value of thep-value is greater than the significance level.

  
  
  
  


• 
  
  
  

  No, since the value of thep-value is greater than the significance level.

  
  
  
  

b-4.Interpret the results at

= 0.05.


multiple choice 6

• 
  
  
  

  We conclude that the population means differ.

  
  
  
  


• 
  
  
  

  We cannot conclude that the population means differ.

  
  
  
  


• 
  
  
  

  We conclude that population mean 1 is less than population mean 2.

  
  
  
  


• 
  
  
  

  We cannot conclude that population mean 1 is less than population mean 2