Question

question 11 a statistician wants to obtain a systematic random sample of size 65 from a population of 7355. what is k? 113 to do so they randomly select a number from 1 to k, getting 52. starting with this person, list the numbers corresponding to all people in the sample. 52, , , ... basic funcs trig... enter a mathematical expression more...

Explanation:

Step1: Recall systematic sampling formula

In systematic sampling, the sampling interval \( k \) is calculated as \( k=\frac{N}{n} \), where \( N \) is the population size and \( n \) is the sample size. Here, \( N = 7355 \) and \( n=65 \), so \( k=\frac{7355}{65}=113 \) (given).

Step2: Generate sample numbers

To get the next number in the sample, we add \( k \) to the previous number. Starting with 52, the next number is \( 52 + 113=165 \).

Step3: Get the third number

Add \( k \) to the second number: \( 165+113 = 278 \).

Step4: Get the fourth number

Add \( k \) to the third number: \( 278+113=391 \).

Answer:

52, 165, 278, 391,... (The pattern continues by adding 113 to the previous number for each subsequent sample member)

For the first few blanks (the next three numbers after 52): 165, 278, 391