Arandom sample of 100 students at a high school was asked whether they would ask their father or mother for with a homework assignment in science. a second sample of 100 different students was asked the same question for an assignment in history. forty-three students in the first sample and 47 students in the second sample replied that they turned to their mother rather than their father for . construct a 98% confidence interval for p 1 - p 2.

98% confidence interval is given as [-0.204, 0.124]

Step-by-step explanation:

In this question we have given

number of student in sample-1,

number of student in sample-2,

43 students in the first sample and 47 students in the second sample replied that they turned to their mother rather than their father for help

Therefore,

and

and we can determine p by using following formula,

..............(1)

put values of and in equation (1)

Now we can determine q by using following formula

................(2)

put value of p in equation 2

Now we can determine Standard Error of the difference between population proportions  by using following formula

Standard error

= .............(3)

Standard error

=

Standard error

=

standard error=0.07035

standard error=0.0704

z- score for 98% confidence is 2.3263

Now we can determine  lower limit of confidence interval by using following formula

= standard error

lower limit of confidence interval =

lower limit of confidence interval = lower limit of confidence interval=-0.2038

Similarly we can determine  upper limit of confidence interval by using following formula

= standard error

Therefore,

Upper limit of confidence interval =

Upper limit of confidence interval =

Upper limit of confidence interval= 0.1238

Therefore,

98% confidence interval is given as [-0.204, 0.124]

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step-by-step explanation:

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