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Hello!
You have the 95% CI for the mean [50; 70]
The amplitude for this interval is a= 20 and its margin of error is d= 10.
If the interval was constructed as X[bar] ± margin of error
Where the margin of error is the product of the statistic value due to the standard deviation of the distribution.
If you reduce the confidence level, the value of the statistic will be also reduced, so you would expect a shorter margin of error and amplitude for the 90% CI
Symbolically: d= [tex]Z_{1-\alpha/2}[/tex] * (δ/√n) ⇒ d↓= [tex]Z_{1-\alpha/2}[/tex]↓ * (δ/√n) if d↓ ⇒ a↓
50 to 100 has an a= 50 and d= 25
70 to 90 has an a= 20 and d= 10
60 to 80 has an a= 20 and d= 10
55 to 95 has an a= 40 and d= 20
65 to 85 has an a=20 and d= 10
None of the given intervals corresponds to a 90% interval for the same sample as the first interval 50 to 70.
Another detail to keep in mind is that the intervals for the population mean are centered in the sample mean. From the first interval you can deduce that it is centered in X[bar]= 60 (Upper bond - margin of error = sample mean), if the other intervals were constructed with the same sample values, they should all be centered in 60.
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The 90% confidence interval using the same sample values is E. 65 to 85.
How to depict the confidence interval?
The 90% confidence interval would be narrower than the 95% confidence interval but the middle point always remains the same.
The middle point there should be (60 + 90)/2 = 75 for the confidence interval. The confidence interval width for a 95% confidence interval width is 30.
For the 65 to 85 confidence interval, the width is 20, therefore this can be true because 20 < 30, therefore 65 to 85 could be the possible confidence interval required here.
Learn more about confidence interval on:
https://brainly.com/question/15712887
