The makers of a soft drink want to identify the average age of its consumers. a sample of 16 consumers is taken. the average age in the sample was 22.5 years with a standard deviation of 5 years. a) construct a 95% confidence interval for the true average age of the consumers. b) construct an 80% confidence interval for the true average age of the consumers. c) discuss why the 95% and 80% confidence intervals are different.

Step-by-step explanation:

Assuming a normal distribution for the age of the consumers. We want to determine a 95% confidence interval for the true average age of the consumers.

Number of sample, n = 16

Mean, u = 22.5 years

Standard deviation, s = 5 years

For a confidence level of 95%, the corresponding z value is 1.96. This is determined from the normal distribution table.

We will apply the formula

Confidence interval

= mean ± z ×standard deviation/√n

It becomes

22.5 ± 1.96 × 5/√16

= 22.5 +/- 1.96 × 1.25

= 22.5 +/- 2.45

The lower end of the confidence interval is 22.5 - 2.45 =20.05

The upper end of the confidence interval is 22.5 + 2.45 =24.95

For 80% confidence interval,

the corresponding z value is 1.28. This is determined from the normal distribution table.

We will apply the formula

Confidence interval

= mean ± z ×standard deviation/√n

It becomes

22.5 ± 1.28 × 5/√16

= 22.5 +/- 1.28× 1.25

= 22.5 +/- 1.6

The lower end of the confidence interval is 22.5 - 1.6 =20.9

The upper end of the confidence interval is 22.5 + 1.6 =24.1

95% provides a wider interval than 80%. The wider the possible values of the true mean, the more confident we are. The lesser the possible values of the true mean, the less confident we are

this is a very good question

step-by-step explanation:

i got a hair cut today from my mom not to flex just to flex kim jon un is one rad fellow i'd say you'd need to take the hairline in kinda like a box shape like someone rammed a lego brick into your head. from there you really need to take the top up keeping with that boxy aesthetic, finally coat the whole thing with gel if your country economics are failing or whatever you can just coat it with the starving children's food rations. about 5 orphans per strand is a good ratio. good luck with the fresh cut my dude