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?
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?
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!
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?