Question

A random sample of 9 TI-89 Titanium calculators being sold over the internet had the following prices, in dollars.

142, 149, 147, 146, 145, 148, 154, 136, 131
Assume the population standard deviation is σ and that the population is approximately normal. Construct a 95% confidence interval for the mean price for all the TI-89's being sold over the internet.

Answer 1

To find the 95% confidence interval, calculate the sample mean then use the z-score (1.96 for 95%) from statistical tables or a calculator command to find the standard error assuming a known population standard deviation.

Step-by-step explanation:

To construct a 95% confidence interval for the mean price of all TI-89 Titanium calculators being sold over the internet using the given sample data, we will use the sample mean (μ) and the standard error of the mean, which incorporates the population standard deviation (σ) and the sample size (n).

The sample mean is calculated as the sum of all sample values divided by the number of values:

μ = (142 + 149 + 147 + 146 + 145 + 148 + 154 + 136 + 131) / 9 = μ = 144.222...

Since the population standard deviation (σ) is not provided, we assume it's known, and we would typically use the z-score for a 95% confidence interval, which is 1.96 (obtained from statistical tables or invNorm(0.975, 0, 1) command on a calculator).

The standard error (SE) is σ / √n.

The confidence interval is thus μ ± (z * SE), where μ is the sample mean, z is the z-score corresponding to a 95% confidence level, and SE is the standard error of the mean.

Without the value for σ, we are unable to complete the calculation. However, if σ were provided, we would substitute it and the sample size into the formula for SE, then calculate the lower and upper bounds of the confidence interval using the sample mean and z-score.