Suggested languages for you:

Americas

Europe

Q. 57

Expert-verifiedFound in: Page 518

Book edition
4th

Author(s)
David Moore,Daren Starnes,Dan Yates

Pages
809 pages

ISBN
9781319113339

57. Critical values What critical value t* from Table B would you use for a confidence interval for the population mean in each of the following situations?(a) A $95\%$ confidence interval based on $n=10$ observations.(b) A $99\%$ confidence interval from an SRS of $20$ observations.

(a) The critical value for 95% confidence interval based on n=10 observations is ${t}^{*}=2.262$.

(b)The critical value for 99% confidence interval based an SRS of 20 observations is ${t}^{*}=2.861$.

When the confidence level is $95\%$ and the population mean is $10$, the critical value $t*$ is calculated.

Utilize the formula $df=n-1$ to estimate the degree of freedom. Where, the population mean is $n=10$.

$df=n-1$$=10-1=9$The row in table $B$is represented by the degree of freedom $df$.

Convert the confidence level $95\%$ into decimal.$\frac{95}{100}=0.95$Determine the column:$\frac{1-c}{2}=\frac{1-0.95}{2}\phantom{\rule{0ex}{0ex}}=0.025$Using the table$B$, to determine the critical value $t*,$ for row $9$ and the column $0.025$:${t}^{*}=2.262$

Therefore, the critical value is ${t}^{*}=2.262$.

When the confidence level is $99\%$ and the population mean is $20$, the critical value $t$ is calculated.

Using the formula $df=n-1$, to determine the degree of freedom. Where, the population mean is $n=20$.

$df=n-1=20-1=19$.

Convert the confidence level $99\%$ into decimal as:

$\frac{99}{100}=0.99$

Determine the column by:

$\frac{1-c}{2}=\frac{1-0.99}{2}\phantom{\rule{0ex}{0ex}}=0.005$

Using the table B, determine the critical value ${t}^{*}$, for row $19$ and the column $0.005$:

${t}^{*}=2.861$

Therefore, the critical value is ${t}^{*}=2.861$.

94% of StudySmarter users get better grades.

Sign up for free