Question

A small dairy wants to make sure that their butter mill is producing bricks of butter that do not differ from the labelled weight by too much. The machine produces 30 bricks of butter per minute and runs for 4 hours Monday, Tuesday, and Wednesday mornings. If the weights of the bricks of butter are deemed to be too high or too low then that afternoon will be dedicated to recalibrating the machines.

Question 1.

Use a hypothesis test to determine if Monday's sample indicates we should recalibrate the butter mill.

• a. What are my hypotheses? State them in both words and as equations.
• b. Every hundredth brick is weighed and the weight difference recorded.
  • Suppose we know the sample values are normally distributed.
  • On Monday the sample yielded an average of weight differences of -2.5 g and a sample standard deviation of 10.25 g.
  • Let ? be a random variable representing the difference between the actual weight of a brick of butter and the desired weight of the brick of butter.
  • Write the short hand for the distribution of ?¯ (the sampling distribution for the sample means).
• c. Draw the sampling distribution.
• d. Complete the hypothesis test using ?=0.03α=0.03.
  • Shade the region for the p-value
  • Compute the p-value.
  • Compare the p-value to the critical value.
• e. Write the conclusion in terms of what the dairy owner should plan to do Monday afternoon

Question 2.

On Tuesday the sample yielded an average of weight differences of -2.71 g and a sample standard deviation of 9.87 g. Use a hypothesis test to determine if Tuesday's sample indicates we should recalibrate the butter mill.

• a. Write the short hand for the distribution of ?¯X¯ (the sampling distribution for the sample means).
• b. Draw the sampling distribution.
• c. Complete the hypothesis test using ?=0.03α=0.03.
  • Shade the region for the p-value
  • Compute the p-value.
  • Compare the p-value to the critical value.
• d. Write the conclusion in terms of what the dairy owner should plan to do Tuesday afternoon.

Need Codes for R program

This was the code block given

normalplot<-function(m,sd,region=0){
x<-seq(m-3.5*sd,m+3.5*sd,length=1000)
y<-dnorm(x,m,sd)
plot(x,y,type="l",xlab="",ylab="")
z<-x[x>region[1]]
z<- z[z<region[2]]
polygon(c(region[1],z,region[2]),c(0,dnorm(z,m,sd),0),col="gray")
}

Answer 1