Question

A study of parental empathy for sensitivity cues and baby temperament was performed. Let x1 be a random variable that represents the score of a mother on an empathy test (as regards to her baby). Let x2 be the empathy score of a father. A random sample of 31 mothers gave a sample mean of x1= 69.55. Another random sample of 36 fathers gave x2= 59.00. Assume that SD1= 10.71 and SD2= 10.57.

(a) Let u1 be the population mean of x1 and let u2 be the population mean of x2. Find a 95% confidence interval for u1- u2.

lower limit=

upper limit=

Answer 1

Answer:

Given that,

A study of parental empathy for sensitivity cues and baby temperament was performed.

Let x₁ be a random variable that represents the score of a mother on an empathy test (as regards to her baby).

Let x₂ be the empathy score of a father.

Score of mother:

Sample size (n₁)=31

Sample mean()=69.55

Standard deviation ()=10.71

Score of father:

Sample size (n₂)=36

Sample mean()=59.00

Standard deviation ()=10.57

(a).

Here,

C.I=95% , =0.95, 1-=1-0.95=0.05

The sample sizes(n₁ and n₂)>30 and population standard deviations are known then we have use Z-table.

We get,

Z/2=Z_0.05=1.960(from C.I table)

Thus 95% confidence interval is,

[-1,22.1]

The 95% confidnce interval for is, [-1,22.1]

Lower limit=-1

Upper limit=22.1