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Explain what is meant by stratified sampling and cluster sampling - Leaving Cert Mathematics - Question 2 - 2014
Question 2
Explain what is meant by stratified sampling and cluster sampling. Your explanation should include: - a clear indication of the difference between the two methods - ... show full transcript
Worked Solution & Example Answer:Explain what is meant by stratified sampling and cluster sampling - Leaving Cert Mathematics - Question 2 - 2014
Step 1
Explain what is meant by stratified sampling and cluster sampling.
Answer
In stratified sampling, the population is divided into strata and a sample is collected from each stratum, ensuring that the sample size from each stratum is proportional to its size in the overall population. This is beneficial for ensuring representation of all subgroups. Conversely, in cluster sampling, the population is divided into clusters, and a few clusters are randomly selected. All members of these chosen clusters are sampled, which can reduce costs. Both methods improve sampling efficiency compared to simple random sampling.
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Step 3
A political party had claimed that it has the support of 23% of the electorate. Of the voters in the sample above, 234 stated that they support the party. Is this sufficient evidence to reject the party's claim, at the 5% level of significance?
Answer
Let\( H_0: \\text{The party has 23% support, } p = 0.23 \) and let\( s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.23(0.77)}{1111}} = 0.01263. \ \ The observed sample proportion is \\\\hat{p} = \frac{234}{1111} = 0.2106.\ \
The z-score is calculated as: At the 5% level of significance, we reject the null hypothesis if the z-score lies outside the interval [-1.96, 1.96]. Since -1.5360 does not fall outside, we do not have enough evidence to reject the party's claim.