You have taken a random sample of size n=85 from a normal population that has a population mean of u = 120 and a population standard deviation of a = 19. Your sample, which is Sample 1 in the table below, has a mean of x=121.8. (In the table, Sample 1 is written "S1", Sample 2 is written "S2", etc.) (a) Based on Sample 1, graph the 75% and 95% confidence intervals for the population mean. Use 1.150 for the critical value for the 75% confidence interval, and use 1.960 for the critical value for the 95% confidence interval. (If necessary, consult a list of formulas.) • Enter the lower and upper limits on the graphs to show each confidence interval. Write your answers with one decimal place. . For the points (and), enter the population mean, μ = 120.

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You have taken a random sample of size n=85 from a normal population that has a population mean of μ = 120 and a population standard deviation of a = 19.
Your sample, which is Sample 1 in the table below, has a mean of x = 121.8. (In the table, Sample 1 is written "S1", Sample 2 is written "S2", etc.)
(a) Based on Sample 1, graph the 75% and 95% confidence intervals for the population mean. Use 1.150 for the critical value for the 75% confidence
interval, and use 1.960 for the critical value for the 95% confidence interval. (If necessary, consult a list of formulas.)
S4
S5
S6
S7
S1 121.8
S2
S3
S8
S9
$10
S11
S12
S13
S14
$15
S16
S17
S18
• Enter the lower and upper limits on the graphs to show each confidence interval. Write your answers with one decimal place.
• For the points (and), enter the population mean, μ = 120.
S19
111.0
S20
111.0
x
75% confidence interval
120.5
X
Generate Samples
130.0
130.0
Ś
(b) Press the "Generate Samples" button below to simulate taking 19 more samples of size n=85 from the population. Notice that the confidence
intervals for these samples are drawn automatically. Then complete parts (c) and (d) below the table.
75% 75% 95% 95%
lower upper lower upper
limit limit limit limit
?
?
?
?
111.0
H+H
|+++
111.0
111.0
75% confidence intervals
95% confidence interval
+||||||||
120.5
H+++
130.0 111.0
X
H+H.
130.0
95% confidence intervals
5
130.0
|||||||||||
130.0
Transcribed Image Text:You have taken a random sample of size n=85 from a normal population that has a population mean of μ = 120 and a population standard deviation of a = 19. Your sample, which is Sample 1 in the table below, has a mean of x = 121.8. (In the table, Sample 1 is written "S1", Sample 2 is written "S2", etc.) (a) Based on Sample 1, graph the 75% and 95% confidence intervals for the population mean. Use 1.150 for the critical value for the 75% confidence interval, and use 1.960 for the critical value for the 95% confidence interval. (If necessary, consult a list of formulas.) S4 S5 S6 S7 S1 121.8 S2 S3 S8 S9 $10 S11 S12 S13 S14 $15 S16 S17 S18 • Enter the lower and upper limits on the graphs to show each confidence interval. Write your answers with one decimal place. • For the points (and), enter the population mean, μ = 120. S19 111.0 S20 111.0 x 75% confidence interval 120.5 X Generate Samples 130.0 130.0 Ś (b) Press the "Generate Samples" button below to simulate taking 19 more samples of size n=85 from the population. Notice that the confidence intervals for these samples are drawn automatically. Then complete parts (c) and (d) below the table. 75% 75% 95% 95% lower upper lower upper limit limit limit limit ? ? ? ? 111.0 H+H |+++ 111.0 111.0 75% confidence intervals 95% confidence interval +|||||||| 120.5 H+++ 130.0 111.0 X H+H. 130.0 95% confidence intervals 5 130.0 ||||||||||| 130.0
19
(c) Notice that for =95% of the samples, the 95% confidence interval contains the population mean. Choose the
20
correct statement.
When constructing 95% confidence intervals for 20 samples of the same size from the population, at most 95% of
the samples will contain the population mean.
When constructing 95% confidence intervals for 20 samples of the same size from the population, it is possible that
more or fewer than 95% of the samples will contain the population mean.
When constructing 95% confidence intervals for 20 samples of the same size from the population, exactly 95% of
the samples will contain the population mean.
(d) Choose ALL that are true.
If there were a Sample 21 of size n=170 taken from the same population as Sample 10, then the 95% confidence
interval for Sample 21 would be narrower than the 95% confidence interval for Sample 10.
The 75% confidence interval for Sample 10 is narrower than the 95% confidence interval for Sample 10. This is
coincidence; when constructing a confidence interval for a sample, there is no relationship between the level of
confidence and the width of the interval.
The 95% confidence interval for Sample 10 does not indicate that 95% of the Sample 10 data values are between
115.3 and 123.3.
From the 75% confidence interval for Sample 10, we know that there is a 75% probability that the population
mean is between 116.9 and 121.7.
None of the choices above are true.
Transcribed Image Text:19 (c) Notice that for =95% of the samples, the 95% confidence interval contains the population mean. Choose the 20 correct statement. When constructing 95% confidence intervals for 20 samples of the same size from the population, at most 95% of the samples will contain the population mean. When constructing 95% confidence intervals for 20 samples of the same size from the population, it is possible that more or fewer than 95% of the samples will contain the population mean. When constructing 95% confidence intervals for 20 samples of the same size from the population, exactly 95% of the samples will contain the population mean. (d) Choose ALL that are true. If there were a Sample 21 of size n=170 taken from the same population as Sample 10, then the 95% confidence interval for Sample 21 would be narrower than the 95% confidence interval for Sample 10. The 75% confidence interval for Sample 10 is narrower than the 95% confidence interval for Sample 10. This is coincidence; when constructing a confidence interval for a sample, there is no relationship between the level of confidence and the width of the interval. The 95% confidence interval for Sample 10 does not indicate that 95% of the Sample 10 data values are between 115.3 and 123.3. From the 75% confidence interval for Sample 10, we know that there is a 75% probability that the population mean is between 116.9 and 121.7. None of the choices above are true.
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