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EQuestion Help sample of 100 observations from a normally distributed population

ID: 3042722 • Letter: E

Question

EQuestion Help sample of 100 observations from a normally distributed population possesses a mean equal to 90 2 and a standard deviation equal to 6.2 Use this information to complete parts a through e below OD to two decimal places as needed) b. What do you mean when you say that a confidence coofficient is 0 95 A A confidence coeficient of 0 95 means that there is a probability o 0 95 that an interval estimator constructed using this coefficient will enclose the B A con de ce coefficient of 95 means that 95% of the values in the population wil be contained in an interval osti nator constructed using this coefficient O C. A D c.Find a D coefficient of 0 95 means that 95% of the values in any sample taken from the population will be contained in an interval estimator constructed using this coefficient A conld e coeficient of 0 95 means that there is a probability of 0 95 that an interval esi ator constructed using this coefficient will contain all of the values in the relevant sample confidence interval for Round to to decimal places as needed

Explanation / Answer

a)

The formula for a 100(1)% confidence interval for is

¯x bar ±( t/2, n-1×s/n)

For a 95% confidence interval, =0.05, because

100(10.05)% =100(0.95)%= 95%.

To compute the confidence interval desired, we simply plug in our values (and, in the case of the t/2 value, look it up) and

¯x ±(t/2, n-1×sn)

90.2 ± (t/2, (100-1)× 6.2/100 =90.2  ± (1.982,99))* 0.62 = 90.2  ± 1.228= (61.42,58.972)

b) b solution .

c) 99% confindence interval

¯x ±(t/2, n-1×sn)

90.2 ± (t/2, (100-1)× 6.2/100 =90.2  ± (2.626,99))* 0.62 = 90.2  ± 1.6281 = (91.82,88.57)