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Phoenix [80]
3 years ago
12

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.
Mathematics
1 answer:
ziro4ka [17]3 years ago
8 0

Answer:

  • 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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Answer:

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b) 64.40% of cold sufferers experience symptoms for between 7 and 10 days.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 7.5, \sigma = 1.2

a. What proportion of cold sufferers experience fewer than 4 days of symptoms?

This is the pvalue of Z when X = 4. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{4 - 7.5}{1.2}

Z = -2.92

Z = -2.92 has a pvalue of 0.0018.

So 0.18% of cold sufferers experience fewer than 4 days of symptoms.

b. What proportion of cold sufferers experience symptoms for between 7 and 10 days?

This is the pvalue of Z when X = 10 subtracted by the pvalue of Z when X = 7. So

X = 10

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Z = \frac{10 - 7.5}{1.2}

Z = 2.08

Z = 2.08 has a pvalue of 0.9812.

X = 7

Z = \frac{X - \mu}{\sigma}

Z = \frac{7 - 7.5}{1.2}

Z = -0.42

Z = -0.42 has a pvalue of 0.3372.

So 0.9812 - 0.3372 = 0.644 = 64.40% of cold sufferers experience symptoms for between 7 and 10 days.

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Answer:

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Step-by-step explanation:

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or multiply the 6m and 2m it'll become 12m

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