Hey guys please I need help with problem 987 Thank you 986 P

Hey guys please I need help with problem 9.87

Thank you,

9.86 Public Policy and Political Science Residential mail boxes in Des Moines, Iowa, should be installed such that the bottom of the mailbox is 42 inches above the ground. This rule is designed for safety and to accommodate short mail carriers. A random sample of 75 mailboxes in the city was selected. The height of each was carefully measured, and the sample mean was 43.22 inches. Assume o- = 7.6 inches and use a = 0.05. Is there any evidence to suggest the true mean height of mailboxes in Des Moines is different from 42 inches? 9.87 Public Health and Nutrition Iodine is an important nutri ent for the human body, especially in hormone development. Milk is a natural source of iodine, and the mean amount in cow?s milk is 88 ,Mug/250ml^24 Milk from organic farms is reported to have a lower concentration of elements such as zinc, iodine, and selenium. A random sample of 35 gallons of organic milk from Humboldt County, California, was obtained and the iodine concentration was measured in each. The sample mean was 86.5. Assume sigma = 3.4. Is there any evidence to suggest that the mean iodine concentration in organic milk is less than 88? Use a = 0.01.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   88  
Ha:    u   <   88  
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical z, as alpha =    0.01   ,      
alpha =    0.01          
zcrit =    -   2.326347874      
              
Getting the test statistic, as              
              
X = sample mean =    86.5          
uo = hypothesized mean =    88          
n = sample size =    35          
s = standard deviation =    3.4          
              
Thus, z = (X - uo) * sqrt(n) / s =    -2.610035198          
              
Also, the p value is              
              
p =    0.004526645          
              
As |z| > 2.326, and P < 0.01, we   REJECT THE NULL HYPOTHESIS.          
              
Thus, there is significant evidence that the mean iodine concentration in organic milk is less than 88. [CONCLUSION]