--%>

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 : 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 : 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 : How to solve statistics assignment in

    How to solve staistics assignment, i need some help in solving stats assignment on AVOVA based problems. Could you help in solving this?

  • 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 : Computers playing games How Computers

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

  • Q : Probability how can i calculate

    how can i calculate cumulative probabilities of survival

  • Q : Spss in Business and Management Please

    Please tell me the cost of this current assignment. Note : I do not want the Solutions but please tell me the price as the assignment is .. Is the cost 3 euro? Do you sell those questions?

  • Q : Statics for each of the following

    for each of the following studies a and b decide whether to reject the null hypothesis that groiups come from identical populations. Use the .01 level. (c) Figure the effects size for each study. (d) ADVANCED TOPIC: Carry out an analysis of variance for study (a) using the strucurtal method.

  • 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 : Homework help on Human memory & SPSS

    Effect of Scopolamine on Human Memory: A Completely Randomized Three Treamtent Design (N = 28) Scopolamine is a sedative used to induce sle