Question

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)
 
H₀: μ₁ − μ₂ ≥ 0
H_A: μ₁ − μ₂ < 0
 

x¯1${\overline{x}}_1$ = 249	x−2${\stackrel{-}{x}}_2$ = 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

α$\alpha$

= 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 greater than the significance level.

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

• 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.

b-4. Interpret the results at

α$\alpha$

= 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.

Answer 1

The statistical software output for this problem is:

From above output:

P - value = 0.1592