A recent study reports that women trust recommendations from Linkedin more than recommendations from any other social network platform. The

Question

A recent study reports that women trust recommendations from Linkedin more than recommendations from any other social network platform. The question that arises is that whether trust in Linkedin recomendations differ by gender? The data on this worksheet shows the number of women and men who expressed that they trust recommendations made on LinkedIn in a recent survey.
Provide a 95% confidence interval estimate of the difference between the proportion of women and men who trust recommendations made on LinkedIn.
Women Men
Sample size 150 170

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1 week 2021-09-10T13:04:25+00:00 1 Answer 0

95% confidence interval estimate of the difference between the proportion of women and men who trust recommendations made on LinkedIn is [0.081 , 0.279].

Step-by-step explanation:

We are given the data that shows the number of women and men who expressed that they trust recommendations made on LinkedIn in a recent survey;

Gender       Women      Men

Sample size   150           170

Firstly, the pivotal quantity for 95% confidence interval for the difference between population proportions is given by;

P.Q. =    ~ N(0,1)

where, = sample proportion of women who trust recommendations made on LinkedIn = = 0.78

= sample proportion of men who trust recommendations made on LinkedIn = = 0.60

= sample of women = 150

= sample of men = 170

Here for constructing 95% confidence interval we have used Two-sample z proportion statistics.

So, 95% confidence interval for the difference between population proportions, () is ;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level

of significance are -1.96 & 1.96}

P(-1.96 < < 1.96) = 0.95

P( < < ) = 0.95

P( < () < ) = 0.95

95% confidence interval for () =

[,]

= [ , ]

= [0.081 , 0.279]

Therefore, 95% confidence interval estimate of the difference between the proportion of women and men who trust recommendations made on LinkedIn is [0.081 , 0.279].