Download 1 - BrainMass

1. The American Sugar Producers Association wants to estimate the
mean yearly sugar consumption. A sample of 16 people reveals the
mean yearly consumption to be 60 pounds with a standard deviation of
20 pounds.
1. What is the value of the population mean? What is the best
estimate of this value?
2. Explain why we need to use the t distribution. What
assumption do you need to make?
3. For a 90 percent confidence interval, what is the value of t?
4. Develop the 90 percent confidence interval for the
population mean.
5. Would it be reasonable to conclude that the population
mean is 63 pounds?
a. population mean is equal to sample mean, that is 60 pounds and best estimator of
population mean is sample mean since sample mean is unbiased estimator for
population mean.
b. since its sample size is smaller than 30.
assume that underlying distribution is normal and population deviation is unknown.
c. its degree is 16-1=15 and t(15, (1-0.9)/2)=1.753
d.90% confidence interval is:
(60-1.753*20/sqrt(16), 60+1.753*20/sqrt(16))
=(51.235, 68.765)
e. since statistc t=(63-60)/(20/sqrt(16))=0.75 < 1.753 => we accept the population
mean is 63 pounds
2. A processor of carrots cuts the green top off each carrot, washes
the carrots, and inserts six to a package. Twenty packages are
inserted in a box for shipment. To test the weight of the boxes, a
few were checked. The mean weight was 20.4 pounds, the
standard deviation 0.5 pounds. How many boxes must the
processor sample to be 95 percent confident that the sample
mean does not differ from the population mean by more than
0.2 pounds?
za
n (

1.96*0.5 2
)2  (
)  24.01  25
E
0.2
2
3. The MacBurger restaurant chain claims that the waiting time of
customers for service is normally distributed, with a mean of 3
minutes and a standard deviation of 1 minute. The qualityassurance department found in a sample of 50 customers at the
Warren Road MacBurger that the mean waiting time was 2.75
minutes. At the .05 significance level, can we conclude that the
mean waiting time is less than 3 minutes?
H0: μ>=3, H1: μ<3
n=50, large sample size
σ assumed to be the same = 1
sample mean: x  2.75
Use Z-test:
α=0.05, Z0.05=1.645, rejection region is z<-1.645.
z 
x 

n

2.75  3
 1.77  1.645
1
50
So reject H0, and conclude that mean is less than 3.