--%>
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 : 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 : 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 : 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 : 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 : STATISTICS Question This week you will

    This week you will analyze if women drink more sodas than men.  For the purposes of this Question, assume that in the past there has been no difference.  However, you have seen lots of women drinking sodas the past few months.  You will perform a hypothesis test to determine if women now drink more

    		•
  • 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 : What is your conclusion The following

    The following data were collected on the number of emergency ambulance calls for an urban county and a rural county in Florida. Is County type independent of the day of the week in receiving the emergency ambulance calls? Use α = 0.005. What is your conclusion? Day of the Week<

    		•
  • Q : Calculate the p- value Medical tests

    Medical tests were conducted to learn about drug-resistant tuberculosis. Of 284 cases tested in New Jersey, 18 were found to be drug- resistant. Of 536 cases tested in Texas, 10 were found to be drugresistant. Do these data indicate that New Jersey has a statisti

    		•
  • Q : Report on Simple Random Sampling with

    One of my friend has a problem on simple random sampling. Can someone provide a complete Report on Simple Random Sampling with or without replacement?

    		•
  • 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

    		•