Question

A nation-wide delivery company would like to estimate the proportion of packages that were delivered on time last month. To do so, they select a random sample of 120 packages that were delivered last month and examine tracking information to determine if they were delivered on time. They find that 87.5% of these packages were delivered on time. Construct and interpret a 95% confidence interval for the proportion of all packages that this company delivered on time last month.

Answer 1

To construct a 95% confidence interval for the on-time delivery rate, calculate the sample proportion, compute the standard error, and apply the z-score to obtain the interval range which estimates the true on-time delivery proportion.

Step-by-step explanation:

The question involves constructing a 95% confidence interval for the proportion of packages delivered on time by a company using a sample finding of 87.5% on-time delivery rate from 120 packages. First, calculate the sample proportion, which is given as 0.875. Then, use the standard formula for a confidence interval for a population proportion, which is p' ± z*(√(p'(1-p')/n)), where p' is the sample proportion and n is the sample size. The z-score for a 95% confidence interval is approximately 1.96.

The calculation steps include:

1. Compute the standard error using the formula: SE = √(p'(1-p')/n).
2. Multiply the standard error by z-score (1.96 for 95% level).
3. Add and subtract this product from the sample proportion to get the interval.

After calculating, you will get a range of values that, with 95% confidence, includes the true proportion of on-time deliveries made by the company.

Answer 2

PLAN: Select 3 true statements.


We have a random sample of 120 packages that were delivered last month


The sample size, 120, is less than 10% of all packages delivered last month.


The Random condition is not met.


One-sample interval for

The 10% condition is not met.


One-sample interval for