SOLUTION: You intend to estimate a population mean μ from the following sample. 51.7 41.4 56.8 74.3 82 101.6 78 104.9 55.5 77.3 72.6 72.2 63.5 82.6 66.2 68.2 79.5 64.5 56.4 55.8 64.7

Question 1175141: You intend to estimate a population mean μ from the following sample.
51.7 41.4 56.8 74.3
82 101.6 78 104.9
55.5 77.3 72.6 72.2
63.5 82.6 66.2 68.2
79.5 64.5 56.4 55.8
64.7 63 43.6 35.4
82.7 59.8 89.7 83.5
71.2 48.8 64 62.4
83.7 77 64.7 60.6
52.7 78.8 59.5 74.2
65.5 83.8 43.7 63.4
74 32 93.1 57.8
86.6

Find the 90% confidence interval. Enter your answer as a tri-linear inequality accurate to two decimal place (because the sample data are reported accurate to one decimal place) ... <μ< ...
2. You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ = 36.7. You would like to be 90% confident that your esimate is within 0.1 of the true population mean. How large of a sample size is required? n = Do not round mid-calculation. However, use a critical value accurate to three decimal places — this is important for the system to be able to give hints for incorrect answers.
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Problem 1
Use a spreadsheet or calculator to compute the following
xbar = 67.8551020408163
s = 15.8895151649404

xbar is the sample mean, while s is the sample standard deviation
Because we have n = 49 items here, this means we have enough to use the Z distribution. We can use this if we know sigma, or if n > 30. When n > 30, the student T distribution is approximately the same as the standard normal distribution.

At 90% confidence, the z critical value is roughly z = 1.645; use a table or calculator to compute this

L = lower bound of confidence interval
L = xbar - z*s/sqrt(n)
L = 67.8551020408163 - 1.645*15.8895151649404/sqrt(49)
L = 67.8551020408163 - 3.734036063761
L = 64.1210659770552
L = 64.12

U = upper bound of confidence interval
U = xbar + z*s/sqrt(n)
U = 67.8551020408163 + 1.645*15.8895151649404/sqrt(49)
U = 67.8551020408163 + 3.734036063761
U = 71.5891381045772
U = 71.59

The 90% confidence interval of the form L < mu < U is therefore 64.12 < mu < 71.59

=========================================================
Problem 2

z = 1.645 from earlier (critical value for 90% confidence interval)
sigma = 36.7 = given population standard deviation
E = 0.1 = desired error

n = minimum sample size needed
n = (z*sigma/E)^2
n = (1.645*36.7/0.1)^2
n = 364,471.801225
n = 364,472
Always round up to the nearest whole number for this type of problem.

The min sample size needed is 364,472

Side note: you may need to ignore the comma if you are typing this answer into a computer system

RELATED QUESTIONS
Weeks Unit dispensed 11 1 20 1 48 1 55 1 85 1 12 2 32 2 42 2 56 2 67 2 (answered by ikleyn)

A pharmacist working in Black lion Specialized Hospital wants to secure the availability... (answered by ikleyn)

1. You measure 33 backpacks' weights, and find they have a mean weight of 44 ounces.... (answered by ewatrrr)

A cute otisis media, an infection of the middele ear, is a common childhood illness.... (answered by haileytucki,Alan3354)

10.60 interpret it. Heart Rate Before and After Class Break Person Before After (answered by stanbon)

The following data represents the number of repairs conducted in a month by 28... (answered by mananth)

The R.R Bowker Company collects information on the retail prices of books and publishes... (answered by Theo)

Refer to the North Valley Real Estate data, which report information on homes sold during (answered by Alan3354,ikleyn)