When σ is unknown and the sample size is&nbsp;n≥30, there are tow methods for computing confidence intervals for μμ. Method 1: Use the Student's t distribution with d.f. = n - 1. This is the method used in the text. It is widely employed in statistical studies. The majority of statistical software programs also employ this technique. Method 2: When&nbsp;n≥30, use the sample standard deviation s as an estimate for σσ, and then use the standard normal distribution. This method is based on the fact that for large samples, s is a fairly good approximation for σσ. Also, for large n, the critical values for the Student's t distribution approach those of the standard normal distribution. Consider a random sample of size n = 31, with sample mean x¯=45.2 and sample standard deviation s = 5.3. (c) Compare intervals for the two methods. Would you say that confidence intervals based on a Student's t distribution tend to be longer than intervals based on the conventional normal distribution, making them more conservative?

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When σ is unknown and the sample size is&amp;nbsp;n≥30, there are tow methods for computing confidence intervals for μμ. Method 1: Use the Student&#039;s t distribution with d.f. = n - 1. This is the method used in the text. It is widely employed in statistical studies. The majority of statistical software programs also employ this technique. Method 2: When&amp;nbsp;n≥30, use the sample standard deviation s as an estimate for σσ, and then use the standard normal distribution. This method is based on the fact that for large samples, s is a fairly good approximation for σσ. Also, for large n, the critical values for the Student&#039;s t distribution approach those of the standard normal distribution. Consider a random sample of size n = 31, with sample mean x¯=45.2 and sample standard deviation s = 5.3. (c) Compare intervals for the two methods. Would you say that confidence intervals based on a Student&#039;s t distribution tend to be longer than intervals based on the conventional normal distribution, making them more conservative?

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Result part (a):90%: 43.5846 to 46.815495%: 43.2562 to 47.143899%: 42.5823 to 47.8177Result part (b):90%: 43.6341 to 46.765995%: 43.3343 to 47.065799%: 42.7441 to 47.6559The confidence intervals using a Student&#039;s t distribution are more conservative, because the confidence intervals are a little wider than the confidence intervals using the standard normal distribution.

Compare intervals for the two methods. Would you say that confidence intervals using a Student's t distribution are more conservative ?

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