--%>
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 : Hypothesis homework A sample of 9 days

    A sample of 9 days over the past six months showed that a clinic treated the following numbers of patients: 24, 26, 21, 17, 16, 23, 27, 18, and 25. If the number of patients seen per day is normally distributed, would an analysis of these sample data provide evidence that the variance in the numbe

    		•
  • Q : Use the NW corner rule to find an

      (a) Use the NW corner rule to find an initial BFS, then solve using the transportation simplex method. Indicate your optimal objective function value. (b) Suppose we increase s1 from 15 to 16, and d3 from 10 to 11. S

    		•
  • Q : Compute the stoke statistics Please do

    Please do the following and submit your results in the table format in a word file on canvas: a)      Go to Yahoo finance/Investing/Stocks/Research tools/Historical quotes/Historical prices and download adjusted monthly closing prices for the period 1/1/2006 to 31

    		•
  • Q : Sample Questions in Graphical Solution

    Solved problems in Graphical Solution Procedure, sample assignments and homework Questions: Minimize Z = 10x1 + 4x2 Subject to

  • Q : Computers playing games How Computers

    How Computers playing games can be categorized according to different dimensions?

    		•
  • Q : Help An experiment is conducted in

    An experiment is conducted in which 60 participants each fill out a personality test, but not according to the way they see themselves. Instead, 20 are randomly assigned to fill it out according to the way they think a parent sees them (i.e. how a parent would fill it out to describe the participant

    		•
  • Q : Principles of data analysis For the

    For the data analysis project, you will address some questions that interest you with the statistical methodology we are learning in class. You choose the questions; you decide how to collect data; you do the analyses. The questions can address almost any topic,

    		•
  • Q : Sample z test and Sample t test A

    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 diff

    		•
  • Q : State Littles Law Little’s Law : • L =

    Little’s Law: • L = λR = XR • Lq = λW = XW • Steady state system • Little’s Law holds as long as customers are not destroyed or&nbs

    		•
  • 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

    		•