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:ztableorttable) H₀:₁₂ 0 H_A:₁₂< 0

x1x1= 261	x2x2= 267
s1= 30	s2= 18
n1= 12	n2= 12

Calculate the value of the test statistic under the assumption that the population variances are equal.(Negative value should be indicated by a minus sign. Round final answer to 3 decimal places.)

Find thep-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

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

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.

Calculate the value of the test statistic under the assumption that the population variances are unknown and are not equal.(Negative value should be indicated by a minus sign. Round final answer to 3 decimal places.) Find thep-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

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 greater 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 less than the significance level.

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.