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A salesperson obtained a systematic sample of size 30 from a list of 750 clients. To do so, he randomly selected a number from 1 to 25, obtaining the number 17. He included in the sample the 17th client on the list and every 25th client thereafter. List the numbers that correspond to the 30 clients selected. Choose the correct answer below.

A. 17, 42, …, 737

B. 17, 42, …, 742

C. 25, 42, …, 518

D. 30, 55, …, 750

Respuesta :

Answer:

B. 17,42, ..., 742

Step-by-step explanation:

In the systematic sampling after choosing the first entry every kth entry is selected according to given procedure

starting entry, starting entry+k, starting entry+2k,..., starting entry+(n-1)k.

Where n denotes the sample size.

we are given that starting entry is 17, sample size is 30 and k=25.

Then the number corresponds to selected clients are

17, 17+25, ..., 17+(30-1)25

17, 42, ..., 742

B. 17, 42, …, 742 are the numbers that selected.

Given that,

  • Starting entry is 17.
  • Sample size (n) is 30.
  • Every 25th client is included, k = 25.

According to the scenario, calculation of the given data are as follows,

By using systematic sampling, calculation are as follows,

Number selected = Starting entry, starting entry + k,..., starting entry + (n-1) k.

By putting the value, we get,

= 17, 17+25,..., 17 + (30-1) 25

= 17, 42,..., 742.

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