To construct a confidence interval for the difference between two population means mu 1 minus mu 2, use the formula shown below when both population standard deviations are known, and either both populations are normally distributed or both n 1 greater than or equals 30 and n 2 greater than or equals 30. Also, the samples must be randomly selected and independent. left parenthesis x overbar 1 minus x overbar 2 right parenthesis minus z Subscript c Baseline StartRoot StartFraction sigma Subscript 1 Superscript 2 Over n 1 EndFraction plus StartFraction sigma Subscript 2 Superscript 2 Over n 2 EndFraction EndRoot less thanmu 1 minus mu 2less thanleft parenthesis x overbar 1 minus x overbar 2 right parenthesis plus z Subscript c Baseline StartRoot StartFraction sigma Subscript 1 Superscript 2 Over n 1 EndFraction plus StartFraction sigma Subscript 2 Superscript 2 Over n 2 EndFraction EndRoot The descriptive statistics for the annual salaries from a random sample of microbiologists from two regions are shown below. Construct a 95% confidence interval for the difference between the mean annual salaries. x overbar 1equals$108 comma 510, n 1equals38, and sigma 1equals$9170; x overbar 2equals$85 comma 460, n 2equals42, and sigma 2equals$9165 Complete the 95% confidence interval for mu 1 minus mu 2 below. $ nothingless thanmu 1 minus mu 2less than$ nothing
for 95 % CI value of z= | 1.96 | ||
margin of error E=z*std error = | 4022.847 | ||
lower bound=(x1-x2)-E = | 19027.15 | ||
Upper bound=(x1-x2)+E = | 27072.85 |
from above 95% confidence interval for population mean =(19027.15 , 27072.85) |
To construct a confidence interval for the difference between two population means mu 1 minus mu...
Evaluate the following formula for ModifyingAbove p with caret 1 equals0.5 , ModifyingAbove p with caret 2 equals0.8 , p 1 minusp 2equals 0, p overbar equals0.835496 , q overbar equals0.273634 , n 1 equals60 , and n 2 equals64 . z equals StartFraction left parenthesis ModifyingAbove p with caret 1 minus ModifyingAbove p with caret 2 right parenthesis minus left parenthesis p 1 minus p 2 right parenthesis Over StartRoot StartFraction p overbar times q overbar Over n 1...
Construct a 90% confidence interval, using the inequality d overbarminust Subscript c Baseline StartFraction s Subscript d Over StartRoot n EndRoot EndFraction less thanmu Subscript dless thand overbarplust Subscript c Baseline StartFraction s Subscript d Over StartRoot n EndRoot EndFraction . To test the effectiveness of a new drug that is reported to increase the number of hours of sleep patients get during the night, researchers randomly select 13 patients and record the number of hours of sleep each gets...
Suppose a random sample of nequals=100100 measurements is selected from a population with mean muμ and standard deviation sigmaσ. For each of the following values of muμ and sigmaσ, give the values of mu Subscript x overbarμx and sigma Subscript x overbar Baseline .and σx. a. muμequals=5, sigmaσequals=2 b. muμequals=25, sigmaσequals=100 c. muμequals=10 sigmaσequals=80 d. muμequals=5, sigmaσequals=190 a. mu Subscript x overbarμxequals=55 sigma Subscript x overbarσxequals=2.2 (Type an integer or a decimal.) Both of your answers are incorrect. For a...
In calculating 95% confidence interval for mu subscript 1 minus mu subscript 2; the difference between the means of two normally distributed populations, summary statistics from two independent samples are: m equals 10,x with bar on top equals 50,s squared subscript 1 equals.64, n equals 10, y with bar on top equals 40, and s squared subscript 2 equals 1.86 Then, the upper limit of the confidence interval is
Let z equals f left parenthesis x comma y right parenthesis commaz=f(x,y) , where x equals u squared plus v squared and y equals StartFraction u Over v EndFractionx=u2+v2 and y=uv. Find StartFraction partial derivative z Over partial derivative u EndFraction and StartFraction partial derivative z Over partial derivative v EndFraction∂z∂u and ∂z∂v at left parenthesis u comma v right parenthesis equals left parenthesis negative 6 comma negative 6 right parenthesis(u,v)=(−6,−6) , given that : f Subscript x Baseline left parenthesis negative 6 comma...
Construct the indicated confidence interval for the population mean mu μ using the t-distribution. Assume the population is normally distributed. c equals = 0.90 0.90, x overbar x equals = 14.1 14.1, s equals = 4.0 4.0, n equals = 6 6 The 90 90% confidence interval using a t-distribution is left parenthesis nothing comma nothing right parenthesis . , .
Use the equation m Subscript PQ Baseline equals StartFraction f left parenthesis x 1 plus h right parenthesis minus f left parenthesis x 1 right parenthesis Over h EndFraction mPQ= fx1+h−fx1 h to calculate the slope of a line tangent to the curve of the function y equals f left parenthesis x right parenthesis equals 2 x squared y=f(x)=2x2 at the point Upper P left parenthesis x 1 comma y 1 right parenthesis equals Upper P left parenthesis 3 comma...
Consider the data to the right from two independent samples. Construct a 90 % confidence interval to estimate the difference in population means.Click here to view page 1 of the standard normal table. LOADING... Click here to view page 2 of the standard normal table. LOADING... x overbar 1 equals 43 x overbar 2 equals 51 sigma 1 equals 10 sigma 2 equals 14 n 1 equals 35 n 2 equals 40 The confidence interval is left parenthesis nothing comma...
Find the critical value, t 0 t0, to test the claim that mu 1 μ1 not equals ≠ mu 2 μ2. Two samples are randomly selected and come from populations that are normal. The sample statistics are given below. Assume that sigma Subscript 1 Superscript 2 σ21 not equals ≠ sigma Subscript 2 Superscript 2 σ22. Use alpha equals 0.02 . Use α=0.02. n 1 n1 equals =11, n 2 n2 equals =18, x overbar 1 x1 equals = 8.6...
Construct the confidence interval for the population mean mu. cequals0.95, x overbar equals 15.2, sigmaequals4.0, and nequals55 A 95% confidence interval for mu is