Question

Math

Posted 3 months ago

```
What is the critical value $t^{*}$ for constructing a $90 \%$ confidence interval for a mean with 6 degrees of freedom?
Choose 1 answer:
(A) $t^{*}=1.440$
(B) $t^{*}=1.645$
(C) $t^{*}=1.943$
(D) $t^{*}=2.015$
(E) $t^{*}=2.447$
```

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Answer from Sia

Verified answer

Posted 3 months ago

Solution by Steps

step 1

Identify the appropriate t-distribution table to use for finding the critical value $t^*$ for a 90% confidence interval with 6 degrees of freedom

step 2

Locate the row corresponding to 6 degrees of freedom in the t-distribution table

step 3

Find the column that corresponds to the 90% confidence level. This typically means finding the value of $t^*$ that has 5% in each tail of the t-distribution, since 90% confidence implies 10% is split between the two tails

step 4

Read off the critical value $t^*$ from the intersection of the row and column identified in the previous steps

Answer

The critical value $t^*$ for constructing a 90% confidence interval for a mean with 6 degrees of freedom is 1.943 (Option C).

Key Concept

Critical Value for t-Distribution

Explanation

The critical value $t^*$ is the value that separates the central 90% of the t-distribution from the 5% in each tail when you have 6 degrees of freedom.

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