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Discuss the basic strategy for performing a hypothesis test to compare the means of two populations, based on independent samples.

Short Answer

Expert verified

To compare the means of two populations using an independent sample, a hypothesis test can be used as follows:

  • Take a sample of data from population 1 and a sample of data from population 2 at random.
  • Calculate the mean value of the samples from population 1 x1¯and the mean value of the samples from population 2 x2¯
  • If the sample meansx1¯andx2¯differ by too much, reject the null hypothesis; otherwise, do not reject the null hypothesis.

Step by step solution

01

Given information

Given in the question that, we need to discuss the basic strategy for performing a hypothesis test to compare the means of two populations, based on independent samples.

02

Explanation

The concept of independent and dependent samples is employed when comparing two populations. Independent samples means that a sample taken from one population should have no bearing on samples taken from another. In the case of independent samples, the chance of each conceivable outcome is the same.

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Most popular questions from this chapter

Discuss the relative advantages and disadvantages of using pooled and non pooled -procedures.

In each of Exercises 10.75-10.80, we have provided summary statistics for independent simple random samples from two populations. In each case, use the non pooled t-fest and the non pooled t-interval procedure to conduct the required hypothesis test and obtain the specified confidence interval.

x~1=20,s1=2,n1=30,x2=18,s2=5,n2=40.

a. Right-tailed test, α=0.05

b. 90%confidence interval.


In each of Exercises 10.75-10.80, we have provided summary statistics for independent simple random samples from non populations. In each case, use the non pooled t-test and the non pooled t-interval procedure to conduct the required hypothesis test and obtain the specified confidence interval.

x¯1=15,s1=2,n1=15,x¯2=12,s2=5andn2=15.

a. Two-tailed test, α=0.05

b. 95%confidence interval.

Suppose that you want to perform a hypothesis test to compare the means of two populations, using a paired sample. For each part, decide whether you would use the paired t-test, the paired Wilcoxon signed-rank test, or neither of these tests if preliminary data analyses of the sample of paired differences suggest that the distribution of the paired-difference variable is

a. uniform.

b. neither symmetric nor normal; the sample size is 132.

c. moderately skewed but otherwise roughly bell-shaped.

In each of exercise 10.13-10.18, we have presented a confidence interval for the difference,μ1-μ2, between two population means. interpret each confidence interval

99%CI from-20to15

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