Question

A toy manufacturer wants to know how many new toys children buy each year. A sample of 601 children was taken to study their purchasing habits. Construct the 95% confidence interval for the mean number of toys purchased each year if the sample mean was found to be 6.7. Assume that the population standard deviation is 1.5. Round your answers to one decimal place.

Answer 1

Answer:

The confidence interval is 6.6<μ<6.8.

Step-by-step explanation:

We have:

Number of observations = 601

Mean = 6.7

Standard deviation σ = 1.5

The z-score for a 95% confidence interval is 1.96.

The limits of the confidence interval can be calculated as

$X \pm z*\frac{\sigma}{\sqrt{n}}\\\\LL=X-z*\frac{\sigma}{\sqrt{n}}=6.7-1.96*\frac{1.5}{\sqrt{601} } =6.7-0.1199=6.6\\\\UL=X+z*\frac{\sigma}{\sqrt{n}}=6.7+1.96*\frac{1.5}{\sqrt{601} } =6.7+0.1199=6.8$

The confidence interval is 6.6<μ<6.8.