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Out of 2100 students in a random sample, 656 enjoyed hard rock music the most. Construct a 90% confidence interval

Out of 2100 students in a random sample, 656 enjoyed hard rock music the most. Construct a 90% confidence interval for the population percentage of students that like hard rock.

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Bryce S. | Experienced, Patient, Empathic Tutor for Math, WritingExperienced, Patient, Empathic Tutor for...
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Alexis,
 
You need the formula for a confidence interval for a proportion. Why is yours a proportion problem?

That formula relies on the sample proportion, the standard deviation of the sample proportion, and the appropriate z-score for a 90 percent confidence interval.

Here are some hints for finding those.

The sample proportion is the share of people who enjoy hard rock music. It's usually denoted as p with a "hat" or carrot or half-arrow above it.

The standard deviation is given by a formula that you will need to find. That formula is usually written with an n, which denotes the sample size. What is the sample size in your case?

The z-score can be found on a table of z-score values. There should be one in the appendix of your statistics textbook. You can also find one online.

Quickly, here is how a z-score table works: Go down to -2.9 in the left-most column, then move your finger to the right until it is under 0.07; the entry is 0.0015. This means that 0.15% of the area of the distribution is to the left of z = -2.97.

A 90 percent confidence interval corresponds having 90 percent of the distribution between your z's. That means 10% of the distribution will not be between the z's. 5% on the left and 5% on the right.

What z will get you 5% on the left? What z will leave you 5% on the right?

I hope this helps! Good luck.