In March 2016, it was reported that key American brands had increased their dail

Question

In March 2016, it was reported that key American brands had increased their daily Instagram posts from 0.89 per day at the end of 2014 to 1.04 posts per day by the end of 2015. With consistent samples sizes of 10,000 each for December 2014 and December 2015, the sample standard deviation for 2014 was 6.5 posts per day and 5 posts per day in 2015. Julian Gottke, writing for Quintly, seemed to indicate that the increase from 0.89 posts per day to 1.04 posts per day was significant. To test whether this change was statistically significant, a two-sample hypothesis test using the t statistic was ordered.

At a level of significance of 0.05, was this increase in daily posts statistically significant using a one-tail hypothesis test (comparing the means of two independent populations)?

Please show a full set of 5- or 6-steps for your hypothesis testing.

Explanation / Answer

H0: 1 – 2 = 0

H1: 1 – 2 > 0

Sp^2= (n1-1)S1^2+(n2-1)S2^2/(n1-1)+(n2-1)

         = (10000-1)*5^2+(10000-1)*6.5^2/9999+9999

         = 33.625

tSTAT=(X1-X2)-(µ1-µ2)/Sp^2(1/n1+1/n2)

       =(1.04-0.89)-0/33.625(1/10000+1/10000)

       =-0.15/0.082

       =1.829

Critical value would be 1.96 and since 1.829 is less than 1.96, we cannot reject the null hypothesis (no increase in daily posts).

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