Question

Suppose that you construct a 95% confidence interval for the population mean, using some sample values, and you obtain the range of 50 to 70. Then, which of the following might be the 90% confidence interval using the same sample values. 50 to 100
70 to 90

60 to 80

55 to 95

65 to 85

Answer 1

Answer:

Step-by-step explanation:

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= $Z_{1-\alpha/2}$ * (δ/√n) ⇒ d↓= $Z_{1-\alpha/2}$↓ * (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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