--%>
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 : Point of estimate standing data se to

    standing data se to develop a point of estimate

    		•
  • Q : Define Utilization Law Utilization Law

    Utilization Law: • ρk = XK . SK = X . DK • Utilization of a resource is the fraction

    		•
  • 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 : Define Service Demand Law

    Service Demand Law:• Dk = SKVK, Average time spent by a typical request obtaining service from resource k• DK = (ρk/X

    		•
  • 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 : Safety and Liveness in Model Checking

    Safety and Liveness in Model Checking Approach; •? Safety: Nothing bad happens •? Liveness: Something good happens •? Model checking is especially good at verifying safety and liveness properties    –?Concurrency i

    		•
  • Q : Problem on queuing diagram Draw a 

    Draw a queuing diagram for the systems below and describe them using Kendall’s notation: A) Single CPU system <

    		•
  • Q : MANOVA and Reflection Activity

    Activity 10:   MANOVA and Reflection   4Comparison of Multiple Outcome Variables This activity introduces you to a very common technique - MANOVA. MANOVA is simply an extension of an ANOV

    		•
  • Q : Problem on Model Checking Part (a).

    Part (a). Draw a state diagram for a car with the following state variables: D indicating whether the car is in drive; B indicating the brake pedal is depressed; G indicating the gas pedal is depressed; and M indicating whether the car is moving. (For example, the sta

    		•
  • Q : Networks of queues Networks of queues •

    Networks of queues • Typically, the flow of customers/request through a system may involve a number of different processing nodes.– IP packets through a computer network– Orders through a manufactur

    		•