Construct the confidence intervals specified to estimate µ

50. Use the following information to construct the confidence intervals specified to estimate µ
a) 95% confidence; = 25, σ2 = 12.25, and n = 60.
b) 98% confidence; = 119.6, S2 = 570.7321, and n = 75.
c) 90% confidence; ∑X = 1814.4, σ2 = 0.948676, and n = 32.

51. A sample of size n = 10 is randomly selected from a normal population with mean µ = 52 and variance σ2 = 22.5. The sample value X-bar is calculated.
d) find P( > 55)
e) find P(50 ≤ ≤ 60)
f) find P( ≤ 55)

See the attached file for complete solution. The text here may not be copied exactly as some of the symbols / tables may not print. Thanks

50. Use the following information to construct the confidence intervals specified to estimate µ
a) 95% confidence; = 25, σ2 = 12.25, and n = 60.

n>30 and σ2 known we will use z-value to construct the confidence interval. The value of z for 95% confidence is +/-1.96
Now calculate the standard error
Standard Error = σ/n0.5 = (12.25/60)^0.5=0.4518
Confidence interval = ...

Solution Summary

Illustrates in simple steps in document file (no excel used) how to construct the confidence intervals and calculate the probabilities for mean of a normal distribution.

We will be constructing confidenceintervals for the proportion of each color as well as the mean number of candies per bag.
Construct a 95% Confidence Interval for the proportion of blue M&Ms® candies.
Construct a 95% Confidence Interval for the proportion of orange M&Ms® candies.
Construct a 95% Confidence Interva

A sample of 100 cans of coffee showed an average weight of 13 ounces. The population standard deviation is 0.8 ounces.
a. Construct a 95% confidence interval for the mean of the population.
b. Construct a 95.44% confidence interval for the mean of the population.
c. Discuss why the answers in parts a and b are differe

Listed below are weights (in grams) from a sample of bats. Construct a 95% confidence interval estimate of their mean weight. Are theconfidence interval limits very different from the limits of 1.56 and 1.87 that are found when assuming that σ is known to be 0.30g ?
1.7
1.6
1.5
2.0
2.3
1.6
1.6
1.8
1.5

A random sample of n = 9 wheels of cheese yielded the following weights in pounds, assumed to be
N(μ, σ^2):
21.50 18.95 19.40 19.15 22.35 22.90 22.20 23.10
(a) Give a point estimate for σ.
(b) Find a 95% confidence interval for σ and then find a 90% confidence interval for σ.

See the data in the attached file and answer the following questions.
Question 1
Construct a 95% confidence interval for an average value of y given that x = 4. Remember the format is (x.xx, x.xx)
Question 2
Construct a 95% prediction interval for y given that x = 4.

Compare and contrast the use of confidenceintervals and point estimates in research applications. Which one or both would be more useful in a business setting? Why? What is the most controllable method of increasing the precision (narrowing) of theconfidence interval?

Motorola wishes to estimatethe mean talk time for one of their new phones before the battery must be recharged. In a random sample of 35 phones, the sample mean talk time is 325 minutes.
A) Why can we say that the sampling distribution of x-bar is appropriately normal?
B) Construct a 98% Confidence Interval for the mean

The average monthly electric bill of a random sample of 256 residents of a city is $90 with a standard deviation of $24.
a. Construct a 90% confidence interval for the mean monthly electric bills of all residents.
b. Construct a 95% confidence interval for the mean monthly electric bills of all residents.