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 role="math" localid="1649226392559" $t$you would use for this interval is

(a)$1.645$(b).$1.699$(c)$1.697$

(d) $1.96$(e) $2.045$

Short answer

(b)$1.699$

Step-by-step solution

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:

$Levelofsignificance=1-confidencelevel$

$=1-0.90$

$=0.10$

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).