Independent random samples were selected from two quantitative populations, with sample sizes, means, and variances given below.
Population 1: Sample Size = 36, Sample Mean = 9.5, Sample Variance = 8.74
Population 2: Sample Size = 46, Sample Mean = 7.2, Sample Variance = 14.72
Construct a 90% confidence interval for the difference in the population means. (Use μ1 − μ2. Round your answers to two decimal places.)
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What does the phrase "90% confident" or "99% confident" mean?
90% (or 99% as the case may be) of all values from populations 1 and 2 will fall within the interval. Hence, we are fairly certain that this particular interval contains μ1 − μ2.
There is a 90% (or 99% as the case may be) probability that the interval will enclose μ1 − μ2. Hence, we are fairly certain that this particular interval contains μ1 − μ2.
In repeated sampling, 90% (or 99% as the case may be) of all intervals constructed in this manner will enclose μ1 − μ2. Hence, we are fairly certain that this particular interval contains μ1 − μ2.
In repeated sampling, 10% (or 1% as the case may be) of all intervals constructed in this manner will enclose μ1 − μ2. Hence, we are fairly certain that this particular interval contains μ1 − μ2.
There is a 90% (or 99% as the case may be) chance that for any two samples, one sample from population 1 and one sample from population 2, the difference between sample means will fall within the interval. Hence, we are fairly certain that this particular interval contains μ1 − μ2.