Question

pepsi wants to identify the mean age of its consumers. a sample of 70 consumer's was taken. the average age the sample was 15 years with a standard deviation of 3 years. construct a 95% confidence interval for the trye average age of the consumers.

Answer 1

To construct a 95% confidence interval using the given data (average age 15 years, standard deviation 3 years, sample size 70), we calculate the margin of error using the z-score for 95% confidence (1.96) and find the interval to be approximately between 14.3 and 15.7 years old.

Step-by-step explanation:

To construct a 95% confidence interval for the true average age of Pepsi consumers, we can use the sample mean (15 years) and the standard deviation (3 years) along with the sample size (70 consumers). Since the sample size is greater than 30, we may use the z-distribution to approximate the Student's t-distribution.

The formula for a confidence interval is:

sample mean ± z* (⁰ / √), where z is the z-score that corresponds to the desired level of confidence, ⁰ is the standard deviation, and is the sample size.

For a 95% confidence interval, the z-score is typically 1.96. The calculation of the margin of error is:

1.96 * (3 / √70) = 0.7034

The confidence interval is then:

15 ± 0.7034 = (14.2966, 15.7034)

Therefore, we can be 95% confident that the true mean age of Pepsi consumers is between approximately 14.3 and 15.7 years old.