Question

A producer of a variety of salty snacks would like to estimate the average weight of a bag of BBQ potato chips produced during the filling process at one of its plants. Determine the sample size needed to construct a 99​% confidence interval with a margin of error equal to 0.007 ounces. Assume the standard deviation for the potato chip filling process is 0.05 ounces.

The sample size needed is______________​(Round up to the nearest​ integer.)

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Determine the sample size needed to construct a 95%confidence interval to estimate the average GPA for the student population at a college with a margin of error equal to 0.2. Assume the standard deviation of the GPA for the student population is 2.5.

The sample size needed is________________​(Round up to the nearest​ integer.)

Answer 1

1)

Given ,

= 0.05 ..Population SD

E= 0.007 Margin of error

c= 99% =0.99 ...confidence level

Find sample size required.

c = 0.99

= 1- c = 1- 0.99 = 0.01

  /2 = 0.005

= 2.576 ..using z table

Now, sample size (n) is given by,

= {( 2.576* 0.05)/0.007}²

=  338.56

= 339 ..(round to the next whole number)

The sample size needed is 339

2)

Given ,

= 2.5 ..Population SD

E= 0.2 Margin of error

c= 95% =0.95 ...confidence level

Find sample size required.

c = 0.95

= 1- c = 1- 0.95 = 0.05

  /2 = 0.025

= 1.96 ..using z table

Now, sample size (n) is given by,

= {( 1.96* 2.5)/0.2}²

=  600.25

= 601 ..(round to the next whole number)

The sample size needed is 601