Construct a 98% confidence interval when n = 20, x = 67.5 and σ = 3.7.

Solutions

Expert Solution

Solution :

Given that,

Point estimate = sample mean = =67.5

Population standard deviation = = 3.7

Sample size = n =20

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

Z/2 = Z0.01 = 2.326 ( Using z table )

Margin of error = E = Z/2 * ( / $\sqrt$ n)

= 2.326 * ( 3.7/ $\sqrt$ 20 )

= 1.92
At 98% confidence interval estimate of the population mean
is,

- E < < + E

67.5 - 1.92 < < 67.5+ 1.92

65.58 < < 69.42

( 65.58, 69.42 )

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Construct a 98% confidence interval to estimate the population mean with x =59 and σ=13 for...

Construct a 98% confidence interval to estimate the population mean with x =59 and σ=13 for the following sample sizes. a) n e= 33 b) n = 42 c) n = 60 a) With 98% confidence, when n=33 the population mean is between the lower limit of ? and the upper limit of ? (Round to two decimal places as needed.) b) With 98%confidence, when n=42 the population mean is between the lower limit of ? and the upper limit...

If n=16, ¯x(x-bar)=32, and s=7, construct a confidence interval at a 98% confidence level. Assume the...

If n=16, ¯x(x-bar)=32, and s=7, construct a confidence interval at a 98% confidence level. Assume the data came from a normally distributed population. Give your answers to one decimal place. < μ <

Construct a 98% confidence interval to estimate the population mean when x overbar125 and s =...

Construct a 98% confidence interval to estimate the population mean when x overbar125 and s = 27 for the sample sizes below. a) n=20 b) n=50 c) n=80 a) The 98% confidence interval for the population mean when nequals20 is from a lower limit of _ to an upper limit of _.

Construct the confidence interval for the population mean μ. c= 0.98, x̄=6.6, σ=0.7, n=41 A 98...

Construct the confidence interval for the population mean μ. c= 0.98, x̄=6.6, σ=0.7, n=41 A 98 % confidence interval for μ is ( _ , _ ) Round two decimal places as needed.

If n=23, ¯xx¯(x-bar)=48, and s=3, construct a confidence interval at a 98% confidence level. Assume the...

If n=23, ¯xx¯(x-bar)=48, and s=3, construct a confidence interval at a 98% confidence level. Assume the data came from a normally distributed population. Give your answers to one decimal place. < μμ <

Construct a 98% confidence interval to estimate the population mean when x=65 and s=14.7 for the...

Construct a 98% confidence interval to estimate the population mean when x=65 and s=14.7 for the sample sizes below. a) n=19 b) n=43 c) n=58 a) The 98% confidence interval for the population mean when n=19 is from a lower limit of to an upper limit of . (Round to two decimal places as needed.) b) The 98% confidence interval for the population mean when n=43 is from a lower limit of to an upper limit of....

Question