A random sample of 40 men drank an average of 20 cups of coffee per week during examination final,

Question

A random sample of 40 men drank an average of 20 cups of coffee per week during examination final,

with the population standard deviation equal to 6 cups. A lower limit of an approximate 95% confidence
interval the population average cup of coffee is
(1) 20.000
(2) 21.859
(3) 19.708
(4) 18.141
(5) 19.051
I calculated the answer as no4?

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3 answers
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Answer 1

Diamond answered
9 years ago

Use the confidence level and sample data to find a confidence interval for estimating the population μ. Round your answer to the same number of decimal places as the sample mean.

A group of 64 randomly selected students have a mean score of 38.6 with a standard 9) deviation of 4.9 on a placement test. What is the 90% confidence interval for the mean score, μ, of all students taking the test?

Answer 2

Anonymous answered
4 years ago

1. The average number of cups of coffee people in the population drink per week is 62, with a standard deviation of 15.75. We are interested in whether college students drink more coffee per week. In a sample of 100 college students, the average number of cups of coffee consumed per week was 64. Do college students drink significantly more cups of coffee a week than the population? The level of significance is .05.

What are the null and alternative hypotheses?

Answer 3

Explain Bot answered
1 year ago

To calculate the lower limit of an approximate 95% confidence interval for the population average number of cups of coffee, you can use the formula:

Lower limit = sample mean - (critical value * standard error)

First, calculate the standard error using the formula:

Standard error = population standard deviation / √(sample size)

In this case, the population standard deviation is given as 6 cups and the sample size is 40. Plugging these values in:

Standard error = 6 / √40 ≈ 0.9486833

Next, find the critical value corresponding to a 95% confidence level. This critical value depends on the sample size and is obtained from a t-distribution table. Since your sample size is 40, you will use a t-distribution with 39 degrees of freedom. The critical value for a 95% confidence level with 39 degrees of freedom is approximately 2.022.

Now you can calculate the lower limit:

Lower limit = 20 - (2.022 * 0.9486833) ≈ 20 - 1.920651 ≈ 18.079

Rounding to three decimal places, the lower limit of an approximate 95% confidence interval for the population average cup of coffee is approximately 18.079.

The closest option is (4) 18.141, so your calculation is correct!