Question

a market surveyor wishes to know how many energy drinks adults drink each week. they want to construct a 99% confidence interval with an error of no more than 0.06. a consultant has informed them that a previous study found the mean to be 5.5 energy drinks per week and found the standard deviation to be 0.7. what is the minimum sample size required to create the specified confidence interval? round your answer up to the next integer.

Answer 1

The minimum sample size required to create a 99% confidence interval with an error of no more than 0.06, given a standard deviation of 0.7, is 904. This calculation uses the z-score for a 99% confidence level and rounds up to the nearest whole number.

Step-by-step explanation:

Calculating the Minimum Sample Size for a Confidence Interval

To calculate the minimum sample size required for a 99% confidence interval with an error of no more than 0.06 when the standard deviation is 0.7, the following formula from statistics is used:

n = (Z * σ / E)^2

Where:

• Z is the z-score corresponding to the 99% confidence level
• σ (sigma) is the standard deviation, which is 0.7
• E is the desired margin of error, which is 0.06

Using the z-score table, the z-score that corresponds to a 99% confidence level is approximately 2.576. Plugging in the values into the formula:

n = (2.576 * 0.7 / 0.06)^2

n = (1.8032 / 0.06)^2

n = 30.0536^2

n = approximately 903.22

Since we always round up to ensure a large enough sample size for the specified confidence interval, the minimum sample size required is 904.