Question

Based on information from Consumer Reports, a random sample of 35 thirty-gram cookies had a sample mean of 146 calories. The standard deviation is know to be σ = 12. Find a 90% confidence interval for mean calories in a 30-gram serving of all chocolate chip cookies. Round the numbers in your interval to the nearest whole number.

Answer 1

Using the z-distribution, it is found that the 90% confidence interval for mean calories in a 30-gram serving of all chocolate chip cookies is (143, 149).

We are given the standard deviation for the population, which is why the z-distribution is used to solve this question.

The information given is:

• Sample mean of $\overline{x} = 146$.

• Population standard deviation of $\sigma = 12$.

• Sample size of $n = 65$.

The confidence interval is:

$\overline{x} \pm z\frac{\sigma}{\sqrt{n}}$

The critical value, using a z-distribution calculator, for a 95% confidence interval is z = 1.645, hence:

$\overline{x} - z\frac{\sigma}{\sqrt{n}} = 146 - 1.645\frac{12}{\sqrt{35}} = 143$

$\overline{x} + z\frac{\sigma}{\sqrt{n}} = 146 + 1.645\frac{12}{\sqrt{35}} = 149$

The 90% confidence interval for mean calories in a 30-gram serving of all chocolate chip cookies is (143, 149).

A similar problem is given at brainly.com/question/16807970