Q.5 - The Practice of Statistics for AP

Question

You want to compute a $90\%$ confidence interval for the mean of a population with unknown population standard deviation. The sample size is $30$ . The value of $t$ you would use for this interval is

(a)$1.645$ (b).$1.699$ (c)$1.697$

(d) $1.96$ (e) $2.045$

Step-by-Step Solution

Answer

(b) $1.699$

Step-1 Given Information

  Given in the question that,

Sample size$\left(n\right)=30$

confidence level is $90\%$ we have to find the correct option.

Step-2 Explanation

The degree of freedom is:

$Df=n-1=30-1=29$

The level of significance is:

$Level of significance=1- confidence level$

                                        $=1-0.90$   

                                        $=0.10$                                     

From the t-table at $0.10$significance level and  $29$degree of freedom the critical value is $1.699$

Thus, the correct option is (b).