Question

A soft drink manufacturer wishes to know how many soft drinks teenagers drink each week. They want to construct a 99%99% confidence interval for the mean and are assuming that the population standard deviation for the number of soft drinks consumed each week is 0.90.9. The study found that for a sample of 10971097 teenagers the mean number of soft drinks consumed per week is 6.36.3. Construct the desired confidence interval. Round your answers to one decimal place.

Answer 1

For the given sample details with known population standard deviation, the confidence interval is calculated as:

μ = M ± Z(s_M)

where:

M = sample mean
Z = Z statistic determined by the confidence level
s_M = standard error = √(s²/n)

M = 6.3
Z = 2.58 calculated using the excel formula for normal distribution =NORM.S.INV(0.995)
s_M = √(0.9²/1097) = 0.03

μ = M ± Z(s_M)
μ = 6.3 ± 2.58*0.03
μ = 6.3 ± 0.07

The confidence inetrval is computed as:

[6.2, 6.4].