--%>
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 : 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 : Data Description 1. If the mean number

    1. If the mean number of hours of television watched by teenagers per week is 12 with a standard deviation of 2 hours, what proportion of teenagers watch 16 to 18 hours of TV a week? (Assume a normal distribution.) A. 2.1% B. 4.5% C. 0.3% D. 4.2% 2. The probability of an offender having a s

    		•
  • Q : What is Inter-arrival times

    Inter-arrival times:A) Requests arrive randomly, often separated by small time intervals with few long separations among themB) The time until the next arrival is independent of when the last arrival occurredC) Coro

    		•
  • 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 : Point of estimate standing data se to

    standing data se to develop a point of estimate

    		•
  • 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

    		•
  • Q : Define Operational Analysis

    Operational Analysis: • Analysis method based on the measurement of the operational characteristics of the system.

    Q : Define SPIN simulation modes SPIN: •

    SPIN: • SPIN generates C program that is the model checker – The pan verifier • Process Analyzer – Run the pan executable to do the model check

    		•
  • Q : OIL I need to product when oil will

    I need to product when oil will finish time (by years) for 6 countries if the keep their production (per day) in the same level. So, the 6 countries have fixed reserves and production 1. statistics for Bahrain Crude oil reserves (million barrels) = 124.6 be careful in million Crude oil producti

    		•
  • Q : Probability how can i calculate

    how can i calculate cumulative probabilities of survival

    		•