--%>
Assignment Help - homework help

Sample z test and Sample t test

A random sample X1, X2, …, Xn is from a normal population with mean µ and variance σ2. If σ is unknown, give a 95% confidence interval of the population mean, and interpret it. Discuss the major difference between one sample z test and one sample t test.

E

Expert

Verified

Suppose X1, X2, …, Xn be a random sample from a normal population with mean µ and variance σ2.

Assume that σ is unknown.

Define:

X‾: Sample mean
S: sample standard deviation
n: Sample Size

In this case the population variance is unknown, consequently we use t test for estimation of confidence interval.

A 95 % confidence interval for the population mean is given by:

461_stats1.jpg

here α = 0.05.

Note that if there population variance is known, we have to use normal distribution i.e. Z test instead of t distribution.

   Related Questions in Basic Statistics

  • Q : Simplified demonstration of Littles Law

    Simplified demonstration of Little’s Law:

    Q : Regression Analysis 1. A planning

    1. A planning official in the Texas Department of Community Affairs, which works in the office next to you, has a problem. He has been handed a data set from his boss that includes the costs involved in developing local land use plans for communities wi

    		•
  • Q : Variance and standard error A hospital

    A hospital treated 412 skin cancer patients over a year. Of these, 197 were female. Give the point estimate of the proportion of females seeking treatment for skin cancer. Give estimates of the

    		•
  • Q : Time series what are the four

    what are the four components of time series?

    		•
  • Q : FIN512 Entrepreneurial Finance Chapter

      Chapter 6: Discussion Question: #4 p. 223  It is usually easier to forecast sales for a seasoned firm contrast to an early-stage venture because an early-stage venture has limited access to bank credit lines, sho

    		•
  • Q : Explain Queuing theory Queuing theory :

    Queuing theory: • Queuing theory deals with the analysis of lines where customers wait to receive a service:

    Q : Compute two sample standard deviations

    Consider the following data for two independent random samples taken from two normal populations. Sample 1 14 26 20 16 14 18 Sample 2 18 16 8 12 16 14 a) Com

    		•
  • Q : Get Solved LP Problems Solve Linear

    Solve Linear Programming Questions A producer manufactures 3 models (I, II and III) of a particular product. He uses 2 raw materials A and B of which 4000 and 6000 units respectively are obtainable. The raw materials per unit of 3

    		•
  • Q : Creating Grouped Frequency Distribution

    Creating Grouped Frequency Distribution: A) At first we have to determine the biggest and smallest values. B) Then we have to Calculate the Range = Maximum - Minimum C) Choose the number of classes wished for. This is generally between 5 to 20. D) Find out the class width by dividing the range b

    		•
  • Q : Explain Service times Service times: A)

    Service times:A) In most cases, servicing a request takes a “short” time, but in a few occasions requests take much longer.B) The probability of completing a service request by time t, is independent of how much tim

    		•