Answer:
98% confidence interval for the proportion of all American females who support the death penalty for convicted murders is [0.59 , 0.64].
Step-by-step explanation:
We are given that the results of the most recent survey; in a sample of 3100 females, 62% said that they were in favor of the death penalty for convicted murders.
Firstly, the pivotal quantity for 98% confidence interval for the population proportion is given by;
                                  P.Q. =   ~ N(0,1)
  ~ N(0,1)
where,  = sample proportion of females who were in favor of the death penalty for convicted murders = 62%
 = sample proportion of females who were in favor of the death penalty for convicted murders = 62%
n = sample of females = 3100
p = population proportion of all American females who support the death penalty
<em>Here for constructing 98% confidence interval we have used One-sample z proportion statistics.</em>
<u>So, 98% confidence interval for the population proportion, p is ;</u>
P(-2.33 < N(0,1) < 2.33) = 0.98  {As the critical value of z at 1% level
                                                    of significance are -2.33 & 2.33}  
P(-2.33 <  < 2.33) = 0.98
 < 2.33) = 0.98
P(  <
 <  <
 <  ) = 0.98
 ) = 0.98
P(  < p <
 < p <  ) = 0.98
 ) = 0.98
<u>98% confidence interval for p</u> = [  ,
 ,  ]
 ]
 = [  ,
 ,  ]
 ]
 = [0.59 , 0.64]
Therefore, 98% confidence interval for the proportion of all American females who support the death penalty for convicted murders is [0.59 , 0.64].