Question

Think about a population proportion that you may be interested in and propose a hypothesis test problem for this parameter. Gather appropriate data and post your problem. Include the null and alternative hypothesis, alpha value, p-value, and a conclusion. Make sure that you use appropriate terminology, specify whether you are using the classical method or the p-value method, and fully explain your solution.

I went to a local dog park and counted the number of dogs entering the park around from 5-7 a Friday evening. While there I counted 50 dogs, out of the 50 there were 19 small dogs that arrived at the park that evening. assume a random sample. test this at a 0.25 significance level.

H0: is that there is no statistical significance

H1: there is a statistical significance and it is over 0.05

Answer 1

First, your hypotheses are incorrect, and the level of significance used is usually 0.10, 0.05 or 0.01

Ho: The proportion of small dogs on walk is 40% (p = 0.40)

Ha: The proportion of small dogs on walk is less than 40% (p < 0.40)

n = 50, p = 0.4, p' = 19/50 = 0.38

We will use α = 0.05, and use the p- value method

SE = √{p (1 - p)/n} = √(0.4 * (1 - 0.4)/50) = 0.0693   

z = (p' - p)/SE =   (0.38 - 0.4)/0.0693 =    -0.2887

p- value = 0.3864

Since the p- value > 0.05, we do not reject Ho

We conclude that there is not enough statistical evidence that the proportion of small dogs on walk is less than 40%