nsider 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 or t table)

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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 or t table)
 
H0μ1 − μ2 ≥ 0
HAμ1 − μ2 < 0
 

x⎯⎯1x¯1
= 249
x−2x−2
= 262
s1 = 35 s2 = 23
n1 = 10 n2 = 10


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 the p-value.
 
multiple choice 1

  • p-value < 0.01
  • 0.01 ≤ p-value < 0.025
  • 0.025 ≤ p-value < 0.05
  • 0.05 ≤ p-value < 0.10
  • p-value ≥ 0.10


 
a-3. Do you reject the null hypothesis at the 5% level?
 
multiple choice 2

  • Yes, since the value of the p-value is less than the significance level.
  • No, since the value of the p-value is less than the significance level.
  • Yes, since the value of the p-value is greater than the significance level.
  • No, since the value of the p-value is greater than the significance level.



a-4. Interpret the results at

αα

= 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 the p-value.
 
multiple choice 4

  • p-value < 0.01
  • 0.01 ≤ p-value < 0.025
  • 0.025 ≤ p-value < 0.05
  • 0.05 ≤ p-value < 0.10
  • p-value ≥ 0.10


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

  • Yes, since the value of the p-value is less than the significance level.
  • No, since the value of the p-value is less than the significance level.
  • Yes, since the value of the p-value is greater than the significance level.
  • No, since the value of the p-value is greater than the significance level.

 


b-4. Interpret the results at

αα

= 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

 

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