Hello I have some questions about STAT that I want to someon

Hello, I have some questions about STAT that I want to someone can help me. Please give me detailed solutions. Thank you!!

The credit manager of a large department store claims that the average account balance of the store\'s credit customers is $125, with a standard deviation of $50. An auditor from Haskin and Anderson selects 100 accounts at random and observes that the sample mean is $132. Using a 0.05 level of significance, can the credit manager\'s claim be justified? A machine produces twine with an average breaking strength of 40 After the machine has been in use for several working days, a sample of 64 pieces is examined. The sample mean is found to be 38 pounds and the sample standard deviation 5 pounds. Advise the supervisor on whether a change has occurred in the mean breaking strength. whether a change has occurred in the mearn

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.6
Ha:   p   =/=   0.6
As we see, the hypothesized po =   0.6      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.5      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.040824829      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -2.449489743      
          
As this is a    2   tailed test, then, getting the p value,  
          
p =    0.014305878      
significance level =    0.05      

As P < 0.05, we REJECT THE NULL HYPOTHESIS.  

Thus, there is significant evidence that the proportion of all homeowners that move to another house within 5 years from the time they purchased their first house is not 60%. [CONCLUSION]