Question

A soft drink manufacturer wishes to know how many soft drinks adults drink each week. They want to construct a 85% confidence interval with an error of no more than 0.08 A consultant has informed them that a previous study found the mean to be 3.13.1 soft drinks per week and found the variance to be 1.691.69. What is the minimum sample size required to create the specified confidence interval

Answer 1

Answer: 547

Step-by-step explanation: The margin of error formulae is given below as

Margin of error = critical value ×(σ/√n)

Where σ = standard deviation and n is the sample size.

From our question, margin of error = 0.08

Variance is 1.691,

hence σ = √variance = √1.691

= 1.3.

We will be using a z test for our critical value this is because a soft drink manufacturer will always produce drinks more than 30 in numbers.

The critical value for a 85% confidence interval is 1.44.

Hence critical value is 1.44.

By substituting the parameters, we have that

0.08 = 1.44 × 1.3/ √n

0.08 = 1.873/ √n

By cross multiplying

0.08 × √n = 1.873

√n = 1.873/ 0.08

√n = 23.41

n = (23.41)²

n = 547.