Question

Suppose you wanted to test a hypothesis that when people pick a number 1 through 10, they pick the number 7 more often than if they were to choose each number with equal probability. You polled 100 people and 15 of them chose the number 7. after finding and labeling the correct test statistic, find and interpret an approximate p value in context, as well as a short conclusion on your findings. also state any assumptions or concerns

Answer 1

null hypothesis: probability of choosing number 7 is 1/10

alternate hypothesis: probability of choosing number 7 is greater than1/10

Ho :   p =    0.1
H1 :   p >   0.1

Number of Items of Interest,   x =   15
Sample Size,   n =    100
      
Sample Proportion ,    p̂ = x/n =    0.15
      
Standard Error ,    SE = √( p(1-p)/n ) =    0.0300
      
Z Test Statistic =    Z = ( p̂-p)/SE =    1.6667

p-Value   =   0.0478

interpretation of p value - the probability of observing that p is greater than 0.1 , when null hypothesis is true is 0.0478.

since, p-value <α=0.05, reject Ho

hence, there is enough evidence that people pick number 7 more often at α=0.05