|
Please show your work before checking the answer and explanations.
An Important Tip. Please draw a density curve and label all given in information on the curve before use the standard normal distribution table to find answers for any normal distribution related problems.
Find the confidence interval specified.
Problem 1. A random sample of 105 light bulbs had a mean life of x̄=401 hours. Assume that σ=39 hours. Construct a 90% confidence interval for the mean life, μ, of all light bulbs of this type.
.
A) 394.7 to 407.3 hours
B) 391.2 to 410.8 hours
C) 392.1 to 409.9 hours
D) 393.5 to 408.5 hours
View Answer
Ans : A
Explanation: CI=(x̄-z(σ/√n), x̄+z(σ/√n))
x̄=401, σ=39, and n=105. It is a 90% CI, therefore z=z0.05=1.6449. Therefore, the CI is (394.7, 407.3) and the answer is A.
Problem 2. A sample of 32 people were randomly selected from among the workers in a shoe factory. The time taken for each person to polish a finsihed shoe was measured. The sample mean was 3.1 minutes. Assume that σ=0.94 minutes. Construct a 90% confidence interval for the true mean time , μ, to polish a shoe.
A) 2.71 to 3.49 minutes
B) 2.83 t0 3.37 minutes
C) 2.67 to 3.53 minutes
D) 2.77 to 3.43 minutes
View Answer
Ans : B
Explanation:CI=(x̄-z(σ/√n) ,x̄+z(σ/√n))
x̄=3.1, σ=0.94, and n=32. It is a 90% CI, therefore z=z0.05=1.6449. Therefore, the CI is (2.83, 3.37) and the answer is B.
Solve the problem..
Problem 3. Based on a sample of 40 randomly selected years, a 90% confidence interval for the mean annual precipitation in one city is from 42.7 inches to 45.3 inches. Find the margin of errror.
A) 2.6 inches
B) 0.34
C) There is not enough information to find the margin of error
D) 1.3 inches
View Answer
Ans : D
Explanation:CI=(x̄-E, x̄+E)
45.3-42.7=2.6. E=2.6/2=1.3.
Problem 4. Based on a sample size of 44, a 95% confidence interval for the mean score of all students, μ, on an aptitude test is from 62.3 to 69.7. Find the margin of error.
A) There is not enough information to find the the margin of error.
B) 3.7
C) 1.09
D) 7.4
View Answer
Ans : B
Explanation: CI=(x̄-E, x̄+E).
69.7-62.3=7.4. E=7.4/2=3.7.
Problem 5. A sample of 51 eggs yields a mean weight of 1.58 ounces. σ=0.58 ounces, find the margin of error in estimating , μ, at the 95% level of confidence.
A) 0.43 oz
B) 0.02 oz
C) 0.13 oz
D) 0.16 oz
View Answer
Ans : D
Explanation: E=z(σ/√n). z0.025 as it is a CI of 95%. σ=0.58 and n=51. Therefore E=1.96(0.58/√51)=0.16.
Problem 6. A sample of 80 college students yields a mean annual income of $3673. Assuming that σ= $812, find the margin of error in estimating μ at the 99% level of confidence.
A) $234
B) $212
C) $1057
D) $178
View Answer
Ans : A
Explanation: E=z(σ/√n). z0.005 as it is a CI of 99%. σ=812 and n=80. Therefore E=2.5758(812/√80)=234.
Provide an appropiate response.
Problem 7. A confidence interval for a population mean has a margin of error of 2.3. If the sample mean is 69.7, obtain the confidence interval.
A) From 67.4 to 69.7
B) From 69.7 to 72
C) From 67.4 to 72
D) From 68.55 to 70.85
View Answer
Ans : C
Explanation: CI=(x̄-E, x̄+E) x̄=69.7, E=2.3 therefore CI: (69.7-2.3, 69.7+2.3), which is (67.4,72).
|