how do u do hypothesis testing for statistics

Question

For the following hypothesis testing questions, be sure to include the claim, null and alternative hypothese, test statistics, graph, critical values or P-value, reject or fail to reject null hypothesis, and a summary statement of the conclusion in non-technical terms. Assume all samples come from populations that are normailly distributed.

 

9) An article in a national journal reports that 34% of American fathers take no responsibility for child care. A statistics student doesnt agree with this percentage, and claims the tru percentage is less than 34%. She decides to conduct a test and samples 285 fathers from her hometown of Waconia. She discovers that 80 do not take responsibility for child care. Using 0.01 level of significance, test the students claim.

Answer 1

We only have the mean proportion of 34%, and no standard deviation has been given. Let's assume that the standard deviation is 0.5%, implying that the proportion is 34±0.5%. In the test sample the proportion is 80/285=28% approx. 

H₀: μ=34%; H_a: μ<34%, so we do a 1-tailed test (one-sided test). Z=(28-34)/0.5=-12, corresponding to p=0 or thereabouts, which is well in excess of the critical value for 1% significance (Z=2.58). It's clear that without a given standard deviation we conclude that H₀ must be rejected so it's more likely that the proportion is, in fact, lower than 34%. If 6/σ>2.58, that is, only if the population standard deviation, σ<6/2.58, σ<2.3%, can H₀ be rejected. In this case the journal should have stated the proportion as 34±2.3%, that is, between 31.7% and 36.3%. If σ>2.3%, H_a is more likely to be true.