Answer:
Step-by-step explanation:
a) The formula for determining the confidence interval for the difference of two population means is expressed as
Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
Where
x1 = sample mean of group 1
x2 = sample mean of group 2
s1 = sample standard deviation for data 1
s2 = sample standard deviation for data 2
For a 90% confidence interval, the z score is 1.645
From the information given,
x1 = 24.5
s1 = 4.3
n1 = 200
x2 = 16.3
s2 = 3.1
n2 = 200
x1 - x2 = 24.5 - 16.3 = 8.2
z√(s1²/n1 + s2²/n2) = 1.645√(4.3²/200 + 3.1²/200) = 1.645√0.1405
z = 0.62
Therefore, the 90% confidence interval is 8.2 ± 0.62
Interpretation:
B.The researchers are 90% confident that the difference of the means is in the interval.
b) B.Since the 90% confidence interval does not contain zero, the results suggest that priming does have an effect on scores.
