Question

The website Data USA stated that in 2016, Texas had the lowest number of adults with a serious mental illness with an average of M=3.26% of the population affected. The state of Texas wants to test if they have a significantly decreased number of mental illness patients compared with the states with the (n=8) highest level of mental illness found. In 2016 the following states had the highest level of adult patients with mental illness: Arkansas= 5.45%, Montana=5.34%, Vermont=5.32%, Oregon=5.19%, Utah=5.2%, Ohio=5.13, Kentucky=5.25% West Virginia=5.18%. The alpha level for the study was set to α=.05 for the criteria.

a. State the hypotheses of the study.
b. Find the critical t value for this study
c. Compute the one sample t test
d. Compute the Cohen's d for the data
e. State the results in APA format (numbers and words) and don’t forget to include all parts in the sentence and the direction of the results.

Answer 1

a) Ho: Mu texas = Mu other

Ha: Mu texas < Mu other

So here we want to test the alternative hypothesis which has the claim given

b) Here we have total n=8 sample sates hence degrees of freedom= n-1=8-1=7

And we have to test the hypothesis at 95% conf interval and hence we need to check for 5% area under the t-table for t value pertaining to df=7

From t table we get t critical = -1.894579

c,d,e)

Performed the above analysis in R and found the

t=53.539

And from the analysis we have found the p value of the test is 1.039*10^-10 which is very very less than 0.05 and hence we need to Reject the Ho

Hence we can say that the claim of Texas had significantly lowest number of adults with a serious mental illness as compared to other states is true.

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