Roy's Toys received a shipment of 100,000 rubber duckies from the factory. The factory couldn't promise that all rubber duckies are in perfect form, but they promised that the percentage of defective toys won't exceed $5 \%$.

Roy wanted to get an estimation of the percentage of defective toys, and since he couldn't go over the entire 100,000 duckies, he took a random sample of 10 duckies. He found that $10 \%$ of them were defective.

What type of statistical study did Roy use?
Choose 1 answer:
(A) Sample study
(B) Experiment
(c) Observational study

Is the study appropriate for the statistical questions it's supposed to answer?

Mark the most suitable choice.
Choose 1 answer:
(A) Yes, because he sampled the correct population.
(B) Yes, because the sample was obtained randomly.
(c) No, because his sample was too small.
(D) No, because he had to check all toys and not just a sample.

Question

Roy's Toys received a shipment of 100,000 rubber duckies from the factory. The factory couldn't promise that all rubber duckies are in perfect form, but they promised that the percentage of defective toys won't exceed $5 \%$.

Roy wanted to get an estimation of the percentage of defective toys, and since he couldn't go over the entire 100,000 duckies, he took a random sample of 10 duckies. He found that $10 \%$ of them were defective.

What type of statistical study did Roy use?
Choose 1 answer:
(A) Sample study
(B) Experiment
(c) Observational study

Is the study appropriate for the statistical questions it's supposed to answer?

Mark the most suitable choice.
Choose 1 answer:
(A) Yes, because he sampled the correct population.
(B) Yes, because the sample was obtained randomly.
(c) No, because his sample was too small.
(D) No, because he had to check all toys and not just a sample.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Identify the type of statistical study used by Roy based on the description provided. ‖ ‖ step 2 ⋮ A sample study is conducted when a part of the population is selected to represent the whole. An experiment involves manipulating variables to observe the effects. An observational study involves observing subjects without intervention. ‖ ‖ step 3 ⋮ Roy took a random sample of 10 duckies from a shipment to estimate the percentage of defective toys, which indicates he conducted a sample study. ‖ ∻1 Answer∻ ***A*** ∻Key Concept∻ ⚹Sample Study⚹ ∻Explanation∻ ⚹Roy used a sample study because he took a random sample from the population to make inferences about the entire population.⚹ ‖ step 4 ⋮ Determine if the sample size and method are appropriate for the statistical question Roy wants to answer. ‖ ‖ step 5 ⋮ The appropriateness of a sample study depends on the sample size, randomness of the selection, and the representativeness of the sample to the population. ‖ ‖ step 6 ⋮ A sample of 10 duckies out of 100,000 is too small to provide a reliable estimate of the percentage of defective toys. ‖ ∻2 Answer∻ ***C*** ∻Key Concept∻ ⚹Appropriateness of Sample Size⚹ ∻Explanation∻ ⚹The study is not appropriate for the statistical question because the sample size of 10 is too small to accurately represent the population of 100,000 rubber duckies.◊What is the formula to calculate the margin of error in a sample study like Roy's Toys scenario?⍭ Generate me a similar question◊⚹

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