construct a 95% two-sided confidence interval on the difference of mean impact strength between these two dyes. assume the variances of the two populations are the same.

Respuesta :

Collect a sample of impact strength measurements for each dye.

What are the steps need to be followed?

To construct a 95% two-sided confidence interval on the difference of mean impact strength between two dyes, you can use the following steps:

  1. Collect a sample of impact strength measurements for each dye.
  2. Calculate the sample means and sample variances for each dye.
  3. Calculate the sample size for each dye, and the combined sample size for both dyes.
  4. Calculate the combined sample variance for both dyes. This can be done using the formula:

combined variance = ((n1 - 1) * variance1 + (n2 - 1) * variance2) / (n1 + n2)

lower bound = mean1 - mean2 - t * standard error

upper bound = mean1 - mean2 + t * standard error

The resulting interval represents the range of values for the difference in means that are 95% likely to contain the true difference in means for the two dyes.

It is important to note that these steps assume that the variances of the two populations are the same. If the variances are not the same, you may need to use a different method to calculate the confidence interval.

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