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DiKsa [7]
3 years ago
5

Based on information from Consumer Reports, a random sample of 35 thirty-gram cookies had a sample mean of 146 calories. The sta

ndard 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.
Mathematics
1 answer:
Nonamiya [84]3 years ago
8 0

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 <em>standard deviation</em> for the population, which is why the <em>z-distribution </em>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 <u>95% confidence interval</u> 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

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