0133% asearch performed. Let xi be a random varlable that represents the score o

Question

0133% asearch performed. Let xi be a random varlable that represents the score of a mother on an empathy test (as regards her baby). Let x2 be the empathy score of a father. A random sample of 34 mothers gave a sample mean of x1 67.00. Another random sample of 26 fathers gave X2 60.53. Assume that .-11.27 and 2-11.48. (a) Let 1 be the population mean of xi and let 2 be the population mean of X2. Find a 90% confidence interval for #1-12-(Use 2 decimal places.) lower limit upper limit (b) Examine the confidence interval and explain what it means in the context of this problem. Does the confidence interval contain all positive, all negative, or both positive and negative numbers? What does this tell you about the relationship between average empathy scores for mothers compared with those for fathers at the 90% confidence level? O Because the interval contalns only positive numbers, we can say that the mothers have a higher mean empathy score. O Because the interval contains both positive and negative numbers, we can not say that the mothers have a higher mean empathy score. O We can not make any conclusions using this confidence interval. o Because the interval contains only negative numbers, we can say that the fathers have a higher mean empathy score. 10.32 PM 3/24/2018

Explanation / Answer

a)
Step 1: Find /2
Level of Confidence = 90%
= 100% - (Level of Confidence) = 10%
/2 = 5% = 0.05


Step 2: Find degrees of freedom and t/2
Degrees of freedom = smaller of (n1 - 1 , n2 - 1 ) = smaller of (33 , 25) = 25

Calculate t/2 by using t-distribution with degrees of freedom (DF) = 25 and /2 = 0.05 as right-tailed area and left-tailed area.

Step 3: Calculate Confidence Interval

t/2 = 1.70812

Standard Error = (s)²/n + (s)²/n = 8.804535067873303 = 2.967243681916486

Lower Bound = (x - x) - t/2•( (s)²/n + (s)²/n ) = (67 - 60.53) - (1.70812)(2.967243681916486) = 1.401591722

Upper Bound = (x + x) + t/2•( (s)²/n + (s)²/n ) = (67 - 60.53) + (1.70812)(2.967243681916486) = 11.538408278

Confidence Interval = (1.401591722, 11.538408278)



Interpretation of a confidence interval:
Since we do not know if the confidence interval (1.401591722, 11.538408278) contains ( - ) or not, we are only 90% confident that (1.401591722, 11.538408278) contains ( - ).

b) The correct option is B

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