Question

10) (1 point) A psychologist has developed a new treatment for acrophobia (the extreme fear of heights) and wants to compare the results of this new treatment to the results of the standard treatment. A study is conducted where a random sample of 12 patients undergo the new treatment and their improvement scores on a diagnostic test are compared to a control sample of 13 patients who received the standard treatment. Summary scores for both groups are shown in the table below.

Treatment	Mean	Standard Deviation
New	x¯1=52.9x¯1=52.9	s1=11.2s1=11.2
Standard	x¯2=45.4x¯2=45.4	s2=11.1s2=11.1

1. Select the hypotheses that should be used to assess if the new treatment results in higher average improvement scores than the standard treatment.
A. H0:μ1=μ2H0:μ1=μ2 vs. Ha:μ1≠μ2Ha:μ1≠μ2
B. H0:μ1=μ2H0:μ1=μ2 vs. Ha:μ1>μ2Ha:μ1>μ2
C. H0:μ1=μ2H0:μ1=μ2 vs. Ha:μ1<μ2Ha:μ1<μ2

2. Calculate the test statistic: ? z t X^2 F  =

3. Calculate the p-value:

4. What is the correct interpretation of your p-value?
A. The p-value is the probability the null hypothesis is true.
B. The p-value is the probability of making a Type II error.
C. The p-value is the probability of obtaining a sample result at least as or more in favor of the alternative hypothesis if the null hypothesis is true.
D. The p-value is the proportion of times in repeated sampling that the alternate hypothesis is true.

Answer 1

For Sample 1 :

x̅1 = 52.9

s1 = 11.2

n1 = 12

For Sample 2 :  

x̅2 = 45.4

s2 = 11.1

n2 = 13

α = 0.05

1.

Null and Alternative hypothesis: Answer B.

Ho : µ1 ≤ µ2

H1 : µ1 > µ2

2.

Pooled variance :

S²p = ((n1-1)*s1² + (n2-1)*s2² )/(n1+n2-2) = ((12-1)*11.2² + (13-1)*11.1²) / (12+13-2) = 124.2765

Test statistic:

t = (x̅1 - x̅2) / √(s²p(1/n1 + 1/n2 ) = (52.9 - 45.4) / √(124.2765*(1/12 + 1/13)) = 1.6806

3.

df = n1+n2-2 = 23

p-value = T.DIST.RT(1.6806, 23) = 0.0532

4. Correct interpretation of your p-value:

C. The p-value is the probability of obtaining a sample result at least as or more in favor of the alternative hypothesis if the null hypothesis is true.