Question

Find the confidence interval specified. 7) A random sample of 81 light bulbs had a mean life of ?x = 402 hours. Assume that ?? = 32 hours. Construct a 90% confidence interval for the mean life, ?, of all light bulbs of this type. (6.1) A) 393.7 to 410.3 hours B) 396.1 to 407.9 hours C) 395.0 to 409.0 hours D) 392.8 to 411.2 hours 8) An economist is interested in studying the incomes of college graduates in China. The population standard deviation is known to be $1,200. What sample size would the economist need to use for a 95% confidence interval if the margin of error is $62.50? (6.1) A) 114 B) 1417 C) 93 D) 354 Provide an appropriate response. 9) Find the critical value, tc, for c = 0.95 and n = 16. (6.2) A) 2.120 B) 2.602 C) 2.131 D) 2.947 10) Construct a 90% confidence interval for the population mean, ?. Assume the population has a normal distribution. A sample of 15 randomly selected students has a grade point average of 2.86 with a standard deviation of 0.78. (6.2) A) (2.41, 3.42) B) (2.28, 3.66) C) (2.51, 3.21) D) (2.37, 3.56)

          Find the confidence interval specified.
7) A random sample of 81 light bulbs had a mean life of ?x = 402 hours. Assume that ?? = 32 hours. Construct a 90% confidence interval for the mean life, ?, of all light bulbs of this type. (6.1)
A) 393.7 to 410.3 hours
B) 396.1 to 407.9 hours
C) 395.0 to 409.0 hours
D) 392.8 to 411.2 hours
8) An economist is interested in studying the incomes of college graduates in China. The population standard deviation is known to be $1,200. What sample size would the economist need to use for a 95% confidence interval if the margin of error is $62.50? (6.1)
A) 114
B) 1417
C) 93
D) 354
Provide an appropriate response.
9) Find the critical value, tc, for c = 0.95 and n = 16. (6.2)
A) 2.120
B) 2.602
C) 2.131
D) 2.947
10) Construct a 90% confidence interval for the population mean, ?. Assume the population has a normal distribution. A sample of 15 randomly selected students has a grade point average of 2.86 with a standard deviation of 0.78. (6.2)
A) (2.41, 3.42)
B) (2.28, 3.66)
C) (2.51, 3.21)
D) (2.37, 3.56)

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Find the confidence interval specified.
7) A random sample of 81 light bulbs had a mean life of ?x = 402 hours. Assume that ?? = 32 hours. Construct a 90% confidence interval for the mean life, ?, of all light bulbs of this type. (6.1)
A) 393.7 to 410.3 hours
B) 396.1 to 407.9 hours
C) 395.0 to 409.0 hours
D) 392.8 to 411.2 hours
8) An economist is interested in studying the incomes of college graduates in China. The population standard deviation is known to be 1,200. What sample size would the economist need to use for a 95% confidence interval if the margin of error is $62.50? (6.1)
A) 114
B) 1417
C) 93
D) 354
Provide an appropriate response.
9) Find the critical value, tc, for c = 0.95 and n = 16. (6.2)
A) 2.120
B) 2.602
C) 2.131
D) 2.947
10) Construct a 90% confidence interval for the population mean, ?. Assume the population has a normal distribution. A sample of 15 randomly selected students has a grade point average of 2.86 with a standard deviation of 0.78. (6.2)
A) (2.41, 3.42)
B) (2.28, 3.66)
C) (2.51, 3.21)
D) (2.37, 3.56)

Added by Jose Miguel W.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Sheryl Ezze

09/02/2023

Step 1

We are given: - Sample mean (x̄) = 402 hours - Sample size (n) = 81 - Population standard deviation (σ) = 32 hours - Confidence level = 90% Show more…

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Find the confidence interval specified. 7) A random sample of 81 light bulbs had a mean life of x = 402 hours. Assume that the standard deviation is 32 hours. Construct a 90% confidence interval for the mean life, μ, of all light bulbs of this type. (6.1) A) 393.7 to 410.3 hours B) 396.1 to 407.9 hours C) 395.0 to 409.0 hours D) 392.8 to 411.2 hours 8) An economist is interested in studying the incomes of college graduates in China. The population standard deviation is known to be $1,200. What sample size would the economist need to use for a 95% confidence interval if the margin of error is $62.50? (6.1) A) 114 B) 1417 C) 93 D) 354 Provide an appropriate response. 9) Find the critical value, tc, for c = 0.95 and n = 16. (6.2) A) 2.120 B) 2.602 C) 2.131 D) 2.947 10) Construct a 90% confidence interval for the population mean, μ. Assume the population has a normal distribution. A sample of 15 randomly selected students has a grade point average of 2.86 with a standard deviation of 0.78. (6.2) A) (2.41, 3.42) B) (2.28, 3.66) C) (2.51, 3.21) D) (2.37, 3.56)

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00:01 So on question 7 we have a random sample of 81 light bulbs and have a mean life of 400, 400 and i'm going to look at another screen, 402 small hours and it says assume that the standard deviation is 32 and we want to construct a 90 % confidence interval for the mean and this is a z interval for the mean.

00:28 And so this is a z interval.

00:30 You can put this in your software to find that and so if i go to stat and task and go to z interval, we have statistics, we have our standard deviation is 32, our 402 for our x bar, our sample size is 81 and we're using .9 and this comes to be a 396 .15 to 407 .85 and when we look at your alternatives, .85 that looks like that is letter b, letter b.

01:09 Now moving on to number eight.

01:14 Number eight, we have an economist that's interested in studying the incomes of college graduates and the population standard deviation is known to be $1 ,200.

01:25 What sample size would be necessary for a 95 % confidence interval with a margin of error equal to 62 .50? so our margin of error is going to be that 1 .96 times the 1 ,200 divided by the square root of n and that needs to equal that 62 .50 and so solving for n, we find out that n will equal 1 .96 times that 1 ,200 divided by the 62 .50 and then that quantity will be squared and we round up.

02:02 So left parenthesis 1 .96 times 1 ,200 divided by that 62 .50, close that parenthesis and square it and it rounds to 1 ,400 and it would round up to 17 and that corresponds with your letter b.

02:24 Now question nine.

02:26 Question nine, we want to find the critical value if we want the c value to be .95 and we want a sample size of 16 and the critical value for, and assumingly you're finding a confidence interval...

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