Question

a pew survey asked a pannel of experts whether or not they thought that networked, automated, artificial intelligence and robotic devices will have displaced more jobs than they have created by 2025. the samole size is the number if experts who responded to the pew survery question n=1896. the report on the survey tells us that 48% of the respondents said they believe net jobs will decrease by 2025 dur to net worked, automated, artificail intelligence and robotic devices. thus the sample proportion is phat=0.48. we can calculate the count x from the info given it is sample size times the proportion responding yes x=nphat=1896(0.48)=910.

a) find SEphat the standard error of phat

b) give the 95% ci for p in the form of estimate plus ir minus the margin of error.

c) give the ci as an interval of percents

d) state your conclusion and interpret the meaning of the confidence interval in part c

Answer 1

A)

N = 1896

P = 0.48

standard error = √{p*(1-p)}/√n = 0.01147369032

B)

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 910

N*(1-p) = 976

Both the conditions are met so we can use standard normal z table to estimate the interval

Critical value z from z table for 95% confidence level is 1.96

Margin of error (MOE) = Z*STANDARD ERROR = 0.02248843303

Confidence interval is given by

P + or - MOE

0.48 + or - 0.02248843303

C)

(P-MOE, P+MOE)

(45.75%, 50.25%)

D)

We are 95% confident that true population proportion lies in between 0.4575 and 0.5025