Question

A machine that is programmed to package 4.35 pounds of cereal is being tested for its accuracy. In a sample of 81 cereal boxes, the sample mean filling weight is calculated as 4.35 pounds. The population standard deviation is known to be 0.09 pound. Use Table 1.

  

a-1.	Identify the relevant parameter of interest for these quantitative data.
	The parameter of interest is the average filling weight of all cereal packages. The parameter of interest is the proportion filling weight of all cereal packages.

  

a-2.	Compute its point estimate as well as the margin of error with 99% confidence. (Round intermediate calculations to 4 decimal places. Round "z-value" to 3 decimal places and final answers to 2 decimal places.)

  

Point estimate
Margin of error

  

b-1.	Calculate the 99% confidence interval. (Use rounded margin of error. Round your final answers to 2 decimal places.)

Confidence interval

to

b-2.	Can we conclude that the packaging machine is operating improperly?
	Yes, since the confidence interval contains the target filling weight of 4.35. Yes, since the confidence interval does not contain the target filling weight of 4.35. No, since the confidence interval contains the target filling weight of 4.35. No, since the confidence interval does not contain the target filling weight of 4.35.

c.	How large a sample must we take if we want the margin of error to be at most 0.02 pound with 99% confidence? (Round intermediate calculations to 4 decimal places. Round "z-value" to 3 decimal places and round up your final answer to the next whole number.)

The SAT is the most widely used test in the undergraduate admissions process. Scores on the math portion of the SAT are believed to be normally distributed and range from 200 to 800. A researcher from the admissions department at the University of New Hampshire is interested in estimating the mean math SAT scores of the incoming class with 99% confidence. How large a sample should she take to ensure that the margin of error is below 24? Use Table 1. (Round intermediate calculations to 4 decimal places and "z-value" to 3 decimal places. Round up your final answer to the nearest whole number.)

  

Sample size

Answer 1

a-1) The parameter of interest is the average filling weight of all cereal packages.

a-2)

from above   Point estimate =4.35

Margin of error =0.03

confidence interval =4.32 to 4.38

b-2)

No, since the confidence interval contains the target filling weight of 4.35

c)

for 99 % CI value of z=	2.576
standard deviation σ=	0.09
margin of error E =	0.02
required sample size n=(zσ/E)2                                         =	135.0

2)for SAT score problem

for 99 % CI value of z=	2.576
standard deviation σ=	100.00
margin of error E =	24
required sample size n=(zσ/E)2                                         =	116.0

(try 260 if above comes wrong and revert)