According to a recent study, the mean cost of a 3 bedroom home costs less in Ohi

Question

According to a recent study, the mean cost of a 3 bedroom home costs less in Ohio than in Alabama. You think this information is incorrect. You randomly select 35 homes in each state. In Ohio, the mean cost is $137,400. In Alabama, the mean cost is $135,900. From past studies, the population standard deviation for 3 bedroom homes in Ohio is $3200 and in Alabama is $2800. Is there enough evidence to support your claim at = 0.05?

A medical research team conducted a study to test whether a drug lowers the chance of getting diabetes. In the study, 2623 people took the drug and 17.1% got diabetes. Also, 2646 people took a placebo and 18.5% got diabetes. At = 0.05, can you support the claim that the drug lowers the chance of getting diabetes?

According to a recent study, the mean cost of a 3 bedroom home costs less in Ohio than in Alabama. You think this information is incorrect. You randomly select 35 homes in each state. In Ohio, the mean cost is $137,400 and the standard deviation is $3200. In Alabama, the mean cost is $135,900 and the standard deviation is $2800. Is there enough evidence to support your claim at = 0.05?

A scientist claims that a new diet pill causes weight loss in men. The table shows the weights (in pounds) of six men before taking the diet pill and then one week after taking the diet pill. Is there enough evidence to reject the claim at = 0.05?

Man 1 2 3 4 5 6

Weight (before) 198 236 217 205 211 228

Weight (after) 195 235 215 202 209 223

Explanation / Answer

According to a recent study, the mean cost of a 3 bedroom home costs less in Ohio than in Alabama. You think this information is incorrect. You randomly select 35 homes in each state. In Ohio, the mean cost is $137,400. In Alabama, the mean cost is $135,900. From past studies, the population standard deviation for 3 bedroom homes in Ohio is $3200 and in Alabama is $2800. Is there enough evidence to support your claim at = 0.05?

Let

u1 = mean cost in Ohio
u2 = mean cost in Alabama

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   <=   0  
Ha:   u1 - u2   >   0  

At level of significance =    0.05          

As we can see, this is a    right   tailed test.      
Calculating the means of each group,              
              
X1 =    137400          
X2 =    135900          
              
Calculating the standard deviations of each group,              
              
s1 =    3200          
s2 =    2800          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    35          
n2 = sample size of group 2 =    35          

Also, sD =    718.729037          
              
Thus, the t statistic will be              
              
z = [X1 - X2 - uD]/sD =    2.087017392          
              
where uD = hypothesized difference =    0          
              
Now, the critical value for z is              
              
zcrit = 1.645

Also, using p values,              
              
p = 0.018443281

              
Thus, as z > 1.645, and P < 0.05, WE REJECT THE NULL HYPOTHESIS.          
              
Hence, there is significant evidence at 0.05 level that the true mean price of 3 bedroom home costs more in Ohio than in Alabama.

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