Questions: Sylvie surveyed a random sample of 50 subscribers to the fast bike magazines to find the number of bikes they own and the features of them. Of the subscribers, 10 own fewer than 3 vehicles. There are 400 subscribers to the fast bike magazines. Based on the above data, what will be the reasonable estimate for the number of subscribers of fast bike magazine who own fewer than 3 vehicles? What is the type of random sampling preferred to get the sample given that we do not have information of all 400 subscribers? 50, Stratified sampling. 40, Cluster sampling. 30, Simple random sampling. 80, Systematic random sampling.

Solution Steps

To estimate the number of subscribers who own fewer than 3 vehicles, we can use the proportion of such subscribers in the sample and apply it to the entire population. For the type of random sampling, we need to identify the method used based on the given options.

1. Calculate the proportion of subscribers in the sample who own fewer than 3 vehicles.
2. Multiply this proportion by the total number of subscribers to estimate the number of such subscribers in the entire population.
3. Identify the type of random sampling based on the description provided.

To find the proportion of subscribers in the sample who own fewer than 3 vehicles, we use the formula:

\[ \text{Proportion} = \frac{\text{Number of subscribers with fewer than 3 vehicles}}{\text{Total sample size}} = \frac{10}{50} = 0.2 \]

Using the proportion calculated in Step 1, we estimate the number of subscribers in the entire population who own fewer than 3 vehicles by multiplying the proportion by the total number of subscribers:

\[ \text{Estimated number of subscribers} = \text{Proportion} \times \text{Total number of subscribers} = 0.2 \times 400 = 80 \]

Based on the description provided, the sampling method used is simple random sampling, as a random sample of subscribers was surveyed without any additional stratification or clustering.

Final Answer