Suppose we take two different random samples from the same population of test scores. the population mean and standard deviation are unknown. the first sample has 25 data values. the second sample has 64 data values. then we construct a 95% confidence interval for each sample to estimate the population mean. which confidence interval will have greater precision (smaller width) for estimating the population mean?
a. the confidence interval based on the sample of 64 data values will be more precise.
b. both confidence intervals will have the same precision.
c. the confidence interval based on thesample of a5 data valus will b moreprecisa

A.The confidence interval based on the sample of 64 data values will be more precise.

Step-by-step explanation:

Given that we take two different random samples from the same population of test scores.

The population mean and standard deviation are unknown.

The first sample has 25 data values. The second sample has 64 data values.

When sample sizes grow the confidence interval will be narrower this is due to the reason that margin of error depends on standard error which in turn is inversely proportional to square root of sample size.

So we find that A.The confidence interval based on the sample of 64 data values will be more precise.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: