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sasho [114]
3 years ago
8

dentify which type of sampling is​ used: random,​ systematic, convenience,​ stratified, or cluster. To determine customer opinio

n of their pricingpricing​, Greyhound LinesGreyhound Lines randomly selects 3030 bussesbusses during a certain week and surveys all passengers on the bussespassengers on the busses. Which type of sampling is​ used?
Mathematics
1 answer:
Rudik [331]3 years ago
8 0

Answer:

The type of sampling used is the Cluster sampling technique.

Step-by-step explanation:

- Random Sampling

In random sampling, each passenger would have an equal chance of being surveyed. If this particular scenario wanted to use random sampling, they would have used computer generated random passenger numbers and surveyed them, not just passengers all on the same bus picked randomly.

- Systematic sampling is easier than random sampling. In systematic sampling, a particular number, n, is counted repeatedly and each of the nth passengers is picked to be sampled.

- Convenience Sampling

This is the worst sampling technique. It is also the easiest. In Convenience sampling, the surveyor just surveys the first set of passengers that they find.

- Stratified Sampling

Stratified sampling divides the population into groups called strata. A sample is taken from each of these strata using either random, systematic, or convenience sampling.

- Cluster sampling

Cluster Sampling divides the population into groups which are called clusters or blocks (the different buses). The clusters are selected randomly, and every element in the selected clusters is surveyed (each passenger on the selected buses, is surveyed!). Evidently the answer to the question!

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Consider the question of whether the home team wins more than half of its games in the National Basketball Association. Suppose
spayn [35]

Answer:

0.0037 = 0.37% probability that the home team would win 65% or more of its games in a simple random sample of 80 games

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

The home team therefore wins 50% of its games

This means that p = 0.5

Determine the probability that the home team would win 65% or more of its games in a simple random sample of 80 games

Sample of 80 means that n = 80 and, by the Central Limit Theorem:

\mu = p = 0.65

s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.5*0.5}{80}} = 0.0559

This probability is 1 subtracted by the pvalue of Z when X = 0.65. So

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

By the Central Limit Theorem

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

Z = \frac{0.65 - 0.5}{0.0559}

Z = 2.68

Z = 2.68 has a pvalue of 0.9963

1 - 0.9963 = 0.0037

0.0037 = 0.37% probability that the home team would win 65% or more of its games in a simple random sample of 80 games

7 0
2 years ago
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