PART B (b)How many of the 90% confidence intervals constructed from the 20 samples contain the population mean, μ =100 ? ANSWER _____ PART C (c)Choose ALL that are true. ___ For each sample, the 75% confidence interval for the sample is included in the 90% confidence interval for the sample. ____ We would expect to find more 75% confidence intervals that contain the population mean than 90% confidence intervals that contain the population mean. Given a sample, a higher confidence level results in a narrower interval. ___ It is not surprising that some 75% confidence intervals are different from other 75% confidence intervals. Each confidence interval depends on its sample, and different samples may give different confidence intervals. ___ The sample means for Sample 19 and Sample 20 are different, so the center of the 90% confidence interval for Sample 19 is different from the center of the 90% confidence interval for Sample 20. ____ None of the choices above are true S8 97.8 96.0 99.6 95.2 100.4S9 100.3 98.5 102.1 97.7102.9S10| 97.8 96.0 99.6 95.2100.4S11 101.1 99.3102.998.5103.7S12 101.2 99.4 103.0 98.6 103.8S13 101.1 99.3102.9 98.5 103.7S14 98.9 97.1 100.7 96.3101.5S15 102.2 | 100.4 | 104.0 99.6104.8S16 99.1 97.3 100.9 96.5 101.7S17 99.998.1 101.7 97.3102.5S18 99.3 97.5 101.196.7101.9S19 100.8 99.0 102.6 98.2 103.4S20 99.3 97.5 101.1 96.7 101.994.0I-I106.0 94.0106.0(a) How many of the 75% confidence intervals constructed from the 20 samples contain the population mean, µ =100? | Suppose we are interested in studying a population to estimate its mean. The population is normal and has a standard deviation of a=5. We have taken arandom sample of size n = 10 from the population. This is Sample 1 in the table below. (In the table, Sample 1 is written "S1", Sample 2 is written "S2", etc.) Asshown in the table, the sample mean of Sample 1 is x =98.9. Also shown are the lower and upper limits of the 75% confidence interval for the population meanusing this sample, as well as the lower and upper limits of the 90% confidence interval. Suppose that the true mean of the population is µ = 100, which is shownon the displays for the confidence intervals.Press the "Generate Samples" button to simulate taking 19 more random samples of size n = 10 from this same population. (The 75% and 90% confidenceintervals for all of the samples are shown in the table and graphed.) Then complete parts (a) through (c) below the table.75% 75% 90% 90%lower upper lower upperlimit limit limit limitS1 98.997.1 100.7 96.3101.5S2 101.1 99.3 102.9 98.5 103.7S3 101.1 99.3 102.9 98.5 103.7S4 97.0 95.2 98.8 94.4 99.6S5 100.6 98.8102.4 98.0 103.2S698.9 97.1 100.7 96.3 101.5S7 99.5 97.7101.3 96.9102.1S8 97.8 96.0 99.6 95.2 100.4X75% confidence intervals90% confidence intervals

Part B(b). Given sample size n=20 confidence coefficient 1- = 0.9 Therefore 20*0.9 =18…

Answered: PART B (b)How many of the 90%…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Related questions

Question

PART B

(b)How many of the 90% confidence intervals constructed from the 20 samples contain the population mean,

μ =100 ? ANSWER _____

PART C

(c)Choose ALL that are true.

___ For each sample, the 75% confidence interval for the sample is included in the 90% confidence interval for the sample.

____ We would expect to find more 75% confidence intervals that contain the population mean than 90%
confidence intervals that contain the population mean. Given a sample, a higher confidence level results in a narrower interval.

___ It is not surprising that some 75% confidence intervals are different from other 75% confidence intervals. Each confidence interval depends on its sample, and different samples may give different confidence intervals.

___ The sample means for Sample 19 and Sample 20 are different, so the center of the 90% confidence interval for Sample 19 is different from the center of the 90% confidence interval for Sample 20.

____ None of the choices above are true

S8 97.8 96.0 99.6 95.2 100.4
S9 100.3 98.5 102.1 97.7
102.9
S10| 97.8 96.0 99.6 95.2
100.4
S11 101.1 99.3
102.9
98.5
103.7
S12 101.2 99.4 103.0 98.6 103.8
S13 101.1 99.3
102.9 98.5 103.7
S14 98.9 97.1 100.7 96.3
101.5
S15 102.2 | 100.4 | 104.0 99.6
104.8
S16 99.1 97.3 100.9 96.5 101.7
S17 99.9
98.1 101.7 97.3
102.5
S18 99.3 97.5 101.1
96.7
101.9
S19 100.8 99.0 102.6 98.2 103.4
S20 99.3 97.5 101.1 96.7 101.9
94.0
I-I
106.0 94.0
106.0
(a) How many of the 75% confidence intervals constructed from the 20 samples contain the population mean, µ =100? |

Suppose we are interested in studying a population to estimate its mean. The population is normal and has a standard deviation of a=5. We have taken a
random sample of size n = 10 from the population. This is Sample 1 in the table below. (In the table, Sample 1 is written "S1", Sample 2 is written "S2", etc.) As
shown in the table, the sample mean of Sample 1 is x =98.9. Also shown are the lower and upper limits of the 75% confidence interval for the population mean
using this sample, as well as the lower and upper limits of the 90% confidence interval. Suppose that the true mean of the population is µ = 100, which is shown
on the displays for the confidence intervals.
Press the "Generate Samples" button to simulate taking 19 more random samples of size n = 10 from this same population. (The 75% and 90% confidence
intervals for all of the samples are shown in the table and graphed.) Then complete parts (a) through (c) below the table.
75% 75% 90% 90%
lower upper lower upper
limit limit limit limit
S1 98.9
97.1 100.7 96.3
101.5
S2 101.1 99.3 102.9 98.5 103.7
S3 101.1 99.3 102.9 98.5 103.7
S4 97.0 95.2 98.8 94.4 99.6
S5 100.6 98.8
102.4 98.0 103.2
S6
98.9 97.1 100.7 96.3 101.5
S7 99.5 97.7
101.3 96.9
102.1
S8 97.8 96.0 99.6 95.2 100.4
X
75% confidence intervals
90% confidence intervals

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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