Why do i need to use the T- Chart for this problem? THye gave me a standard devi

Question

Why do i need to use the T- Chart for this problem? THye gave me a standard deviation and it was stated that it was normal distribution.

Acrylic bone cement is sometimes used in hip and knee replacements to fix an artificial joint in place. The force required to break an acrylic bone cement bond was measured for six specimens under specified conditions, and the resulting mean and standard deviation were 303.39 Newtons and 42.97 Newtons, respectively. Assuming that it is reasonable to assume that breaking force under these conditions has a distribution that is approximately normal and using 95% confidence level, estimate the true average breaking force f for acrylic bone cement under the specified conditions. (Use Table 3 in Appendix A. Round your answer to the nearest whole number.)

Explanation / Answer

The statistical software output for this problem is:

One sample T summary confidence interval:
: Mean of population

95% confidence interval results:

Hence,

95% confidence interval will be:

(258, 348)

We used t distribution instead of z because the standard deviation which is given in this problem is the standard deviation of 6 specimens and hence, its the sample standard deviation. We apply z only when we know the population standard deviation.

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