Question

Some social scientists have collected data on smartphone ownership among teenagers. In 2016, 84% of 12-17 year olds sampled owned at least one smartphone. In 2018, that number increased to 92%. For the purpose of this problem, you can assume that these values were from independent samples of 12-17 year olds taken in 2016 and 2018, each of size 120. We will test the null hypothesis that the population percentage of teenagers owning at least one smartphone was the same between 2016 and 2018, versus the alternative hypothesis that these percentages were different.

(a) Under the null hypothesis, the difference in the sample percentages is expected to be ___________%. The standard error for the difference is estimated to be ___________%.

(b) The appropriate test statistic to use is (circle one) one-sample z-test two-sample z-test one-sample t-test chi-squared test for proportions chi-squared test of independence none of these

(c) The value of the test statistic is _________________.

(d) The p-value is _________________________. (Give a percentage for a z-test or a range of percentages for a t-test or chi-squared test.)

(e) Our conclusion is (circle one) reject the null hypothesis OR don't reject the null hypothesis.

Answer 1

z-test

.........

Ho:   p1 - p2 =   0          
Ha:   p1 - p2 ╪   0          
                  
sample #1   ----->   experimental          
first sample size,     n1=   120          
proportion success of sample 1 , p̂1= 0.8400          
                  
sample #2   ----->   standard          
second sample size,     n2 =    120          
proportion success of sample 1 , p̂ 2= 0.920          
                  
difference in sample proportions, p̂1 - p̂2 =     0.8400   -   0.9200   =   -0.0800
                  
pooled proportion , p =   (x1+x2)/(n1+n2)=   0.8800          
                  
std error ,SE =    =SQRT(p*(1-p)*(1/n1+ 1/n2)=   0.0420          

Z-statistic = (p̂1 - p̂2)/SE = (   -0.080   /   0.0420   ) =   -1.9069
                  
p-value =        0.0565   [excel formula =2*NORMSDIST(z)]  

   
decision :    p-value>α,Don't reject null hypothesis               

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THANKS

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