Explain the difference between a stratified sample and a cluster sample. (select all that apply.) in a cluster sample, the only samples possible are those including every kth item from the random starting position. in a cluster sample, every sample of size n has an equal chance of being included. in a stratified sample, random samples from each strata are included. in a stratified sample, the only samples possible are those including every kth item from the random starting position. in a cluster sample, the clusters to be included are selected at random and then all members of each selected cluster are included. in a stratified sample, every sample of size n has an equal chance of being included. in a cluster sample, random samples from each strata are included. in a stratified sample, the clusters to be included are selected at random and then all members of each selected cluster are included.

In a cluster sample, every sample of size n has an equal chance of being included.In a stratified sample, random samples from each strata are included. In a cluster sample, the clusters to be included are selected at random and then all members of each selected cluster are included.In a stratified sample, every sample of size n has an equal chance of being included

Step-by-step explanation:

In a stratified sample the population is divided into different segments and then we take random elements from each segment.

In a cluster sample, the sample is divided into segments (or clusters) and then the sample is taken by selecting different clusters.

Therefore, in the cluster sample we take ALL elements from different clusters while in a stratified sample we take SOME elements from the different sections.

Now let's take a look at the options given:

In a cluster sample, the only samples possible are those including every kth item from the random starting position: FALSE. In the cluster sample we select all items from the cluster.In a cluster sample, every sample of size n has an equal chance of being included: TRUE. if we divide the sample into clusters of size n then every cluster has an equal chance of being selected (since we select them at random).In a stratified sample, random samples from each strata are included: TRUE. We already said that we take a random sample from each segment (strata). In a stratified sample, the only samples possible are those including every kth item from the random starting position: FALSE. We can apply different methods to select our sample from each strata.In a cluster sample, the clusters to be included are selected at random and then all members of each selected cluster are included. TRUE. This is the definition of cluster sample we wrote at first. In a stratified sample, every sample of size n has an equal chance of being included: TRUE, we take samples from elements, not from stratas. In a cluster sample, random samples from each strata are included: FALSE. This is the definition of stratified sample. In a stratified sample, the clusters to be included are selected at random and then all members of each selected cluster are included: FALSE. This is the definition of cluster sample.

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step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

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