Q.2.1 - The Practice of Statistics for AP

Question

Use Table B to find the critical value t* that you would use for a confidence interval for a population mean M in each of the following situations. If possible, check your answer with technology. 

(a) A 98% confidence interval based on $n =22$ observations.

 (b) A $90\%$ confidence interval from an SRS of $10$ observations.

(c) A $95\%$ confidence interval from a sample of size $7$.

Step-by-Step Solution

Answer

(a)The critical value is $2.518$

(b)The critical value is $1.833$

(c)The critical value is $2.447$

part (a) Step 1: Given information

Given in the question that, Use Table B to find the critical value t* that you would use for a confidence interval for a population mean M in each of the following situations. A 98%  confidence interval based on$n = 22$observations.

Part (a) Step 2: Explanation

Given:

Confidence level $=98\%$

Sample size $\left(n\right)=22$

The level of significance is:

Level of significance  

Level of significance$=1-$ Confidence level

$=1-0.98$

$=0.02$

The degree of freedom is $22-1=21$

The critical value using standard normal table is calculated as:

$t_{a/2df}=t_{0.02/2,21}$

$=2.518$

The critical value is$2.518$

part (b) Step 1: Given information

Given in the question that, Use Table B to find the critical value t* that you would use for a confidence interval for a population mean M in each of the following situations. If possible, check your answer with technology. A $90\%$ confidence interval from an SRS of$10$ observations.

Part (b) Step 2: Explanation

Given:

Confidence level $=90\%$

Sample size $\left(n\right)=10$

The level of significance is:

Level of significance$=1-$ Confidence level

$=1-0.90$

$=0.10$

The degree of freedom is $10-1=9$

The critical value using standard normal table is calculated as:

$t_{a/2df}=t_{0.10/2,9}$

$=1.833$

The critical value is$1.833$.

part (c) step 1: Given information

Given in the question that, Use Table B to find the critical value t* that you would use for a confidence interval for a population mean M in each of the following situations. If possible, check your answer with technology. (c) A$95\%$ confidence interval from a sample of size$7$.

Part (c) Step 2: Explanation

Given:

Confidence level $=95\%$

Sample size $\left(n\right)=7$

The level of significance is:

Level of significance$=1-$ Confidence level

$=1-0.95$

$=0.05$

The degree of freedom is$7-1=6$

The critical value using standard normal table is calculated as:

$t_{a/22d}=t_{0.05/2,6}$

$=2.447$

The critical value is $2.447$