Adv Stats & Analytics

The director of manufacturing at a cookies needs to determine whether a new machine is production a particular type of cookies according to the manufacturer's specifications, which indicate that cookies should have a mean of 70 and standard deviation of 3.5 pounds. A sample pf 49 of cookies reveals a sample mean breaking strength of 69.1 pounds. A.  State the null and alternative hypothesis   Ho = u>=  70  and alt hypo. Ho = u<70 B.  Is there evidence that the machine is nor meeting the manufacturer's specifications for average strength? Use a 0.05 level of significance .  since the data is random sample size the data seem almost approximate normal.  C.  Compute the p value and interpret its meaning?  (xbar - mu) / (stdsqrt(n)) = (69.1 - 70)/(3.5/sqrt(49)) =  -1.80 this indicted it does not fall under the region and it is rejected.  D.   What would be your answer in (B) if the standard deviation were specified...

1. x̄ = 85 and σ = 8, and n = 64, set up a 95% confidence interval estimate of the population mean μ.  Z= 1-(0.05/2) = 1.96 Sample mean= x-bar = 85 Z*s/sqrt(n) = (1.96*8)/sqrt(64) = 1.96 CI= 85 – 1.96= 83.04 CI= 85- 1.96= 86.96 (83.04, 86.96) 2. If  x̄ = 125, σ = 24 and n = 36, set up a 99% confidence interval estimate of the population mean μ.  Z= 1- (0.01/2) = 0.995= 2.57 Z*s/sqrt(n) = 125 - (2.57*8/sqrt(36) = 3.42-125= 121.58 Z*s/sqrt(n) = 125 + (2.57*8/sqrt(36) = 3.42+125= 128.42 3. The manager of a supply store wants to estimate the actual amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer. It is known from the manufacturer's specification sheet that standard deviation of the amount of paint is equal to 0.02 gallon. A Random sample of 50 cans is selected and the sample mean amount of paint per 1 gallon is 0.99 gallon.  3a. Set up a 99% confidence inter...