In 2014, Facebook reported reported that 23% of it users were ages 18-24. a decr

Question

In 2014, Facebook reported reported that 23% of it users were ages 18-24. a decrease from the 2011 level of 30%. (Though this is partly due to more older people joining Facebook. there was nevertheless a loss of over 3 millions users in this age group ) . A survey of 500 randomly selected Facebook users in March 2016 showed that 100 of them were ages 18--24. Test , using a significance level of alpha =0.10 whether the proportion Facebook users who are ages 18--24 has decreased from the 2014 level of 23
(a) state the claim and the null and alternate hypotheses. Specify which hypothesis is the claim.

(b) Find the p-value of getting the sample data given and use it to reject Ho or fail to reject H0.
(c) Conclude the result of the test in a statement that is understandable to any reader.

Explanation / Answer

a)

Ho : p = 0.23

Ha : p < 0.23

p = 100 / 500 = 0.2

Z = ( 0.2 - 0.23 ) * ( srqt 0.23*0.77 / 500 )

Z = -1.59

p value : 0.0559

for alpha = 0.10

since p value is lwoer than lapha we reject Ho

conclusion : there is evidence to conclude that the proportion Facebook users who are ages 18--24 has decreased from the 2014 level of 23

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