--%>
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 : 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 : State the hypotheses At Western

    At Western University the historical mean of scholarship examination score for freshman applications is 900. Population standard deviation is assumed to be known as 180. Each year, the assistant dean uses a sample of applications to determine whether the mean ex

    		•
  • 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 : Sample Questions in Graphical Solution

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

  • Q : Probability how can i calculate

    how can i calculate cumulative probabilities of survival

    		•
  • Q : Time series what are the four

    what are the four components of time series?

    		•
  • Q : Compute two sample standard deviations

    Consider the following data for two independent random samples taken from two normal populations. Sample 1 14 26 20 16 14 18 Sample 2 18 16 8 12 16 14 a) Com

    		•
  • Q : Cumulative Frequency and Relative

    Explain differences between Cumulative Frequency and Relative Frequency?

    		•
  • Q : Average think time Software monitor

    Software monitor data for an interactive system shows a CPU utilization of 75%, a 3 second CPU service demand, a response time of 15 seconds, and 10 active users. Determine the average think time of these users?

    		•
  • Q : Statistics basic question This week you

    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

    		•