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 10070 to 9060 to 8055 to 9565 to 85

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 errorWhere 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= 2570 to 90 has an a= 20 and d= 1060 to 80 has an a= 20 and d= 1055 to 95 has an a= 40 and d= 2065 to 85 has an a=20 and d= 10None 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.I hope you have a SUPER day!