# Statistical Inferences Based on Two Samples

**Topics:**Statistical hypothesis testing, Normal distribution, Standard deviation

**Pages:**28 (6340 words)

**Published:**October 12, 2011

Statistical Inferences Based on Two Samples

True/False

1. An independent sample experiment is an experiment in which there is no relationship between the measurements in the different samples. Answer: True Difficulty: Medium

2. When testing the difference between two proportions selected from populations with large independent samples, the Z test statistic is used. Answer: True Difficulty: Medium

3. In forming a large sample confidence interval for [pic], two assumptions are required: independent samples and sample sizes of at least 30. Answer: True Difficulty: Medium

4. In testing the equality of population variances, two assumptions are required: independent samples and normally distributed populations. Answer: True Difficulty: Medium

5. In an experiment involving matched pairs, a sample of 12 pairs of observations is collected. The degree of freedom for the t statistic is 10. Answer: False Difficulty: Medium

6. When comparing two independent population means, if n1 = 13 and n2 = 10, degrees of freedom for the t statistic is 22. Answer: False Difficulty: Easy

7. When comparing the variances of two normally distributed populations using independent random samples, if [pic], the calculated value of F will always be equal to one. Answer: True Difficulty: Easy

8. In testing the difference between two population variances, it is a common practice to compute the F statistic so that its value is always greater than or equal to one. Answer: True Difficulty: Medium

9. The F statistic can assume either a positive or a negative value. Answer: False Difficulty: Easy

10. There are two types of machines called type A and type B. Both type A and type B can be used to produce a certain product. The production manager wants to compare efficiency of the two machines. He assigns each of the fifteen workers to both types of machines to compare the hourly production rate of the 15 workers. In other words, each worker operates machine A and machine B for one hour each. These two samples are independent. Answer: False Difficulty: Medium (REF)

11. In testing the difference between two means from two independent populations, the sample sizes do not have to be equal to be able to use the Z statistic. Answer: True Difficulty: Medium

12. In testing the difference between the means of two normally distributed populations using large independent random samples, the sample sizes from the two populations must be equal in order to use a Z statistic. Answer: False Difficulty: Easy

13. In testing the difference between the means of two normally distributed populations using large independent random samples, the alternative hypothesis indicates no differences between the two specified means. Answer: False Difficulty: Easy (REF)

14. In testing the difference between the means of two normally distributed populations using large independent random samples, we can only use a two-sided test. Answer: False Difficulty: Easy

15. In testing the difference between the means of two independent populations, if neither population is normally distributed, then the sampling distribution of the difference in means will be approximately normal provided that the sum of the sample sizes obtained from the two populations are at least 30. Answer: False Difficulty: Hard

16. When comparing two population means based on independent random samples, the pooled estimate of the variance is used if both population standard deviations are known. Answer: False Difficulty: Hard

17. Assume that we are constructing confidence interval for the difference in the means of two populations based on independent random samples. If both sample sizes [pic] and the distribution of both populations are highly skewed, then a confidence interval for the difference in the means can be constructed using the t test statistic. Answer: False Difficulty: Hard

18. If the limits of the...

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