We know that proportion of diamond cards in a regular deck of cards is 13/52=0.25. Assume for a moment that we do not know it and we wish to use statistical methods to find a confidence interval for proportion of red cards in a deck. We will use 10 regular decks of card and select random sample of 100 cards. The population will consider of 10 regular decks of cards well shuffled..

Question

As described, we randomly draw 100 cards from the population and record a sample (D - diamond card, ND - not diamond card}. In the sample we have 24 diamond cards and 76 of the other suite.



Answer the following questions:

Number of elements in the population is

Number of elements in the sample is

Proportion of diamond cards in the sample is (express it as a decimal)

Answer 1

Let's address each of your questions step by step:

1. Number of elements in the population:

   • Since we are considering 10 regular decks of cards, and each deck contains 52 cards, the total number of elements in the population is calculated as: \[ 10 \text{ decks} \times 52 \text{ cards/deck} = 520 \text{ cards} \]

2. Number of elements in the sample:

   • From the information you provided, we are taking a random sample of 100 cards. Therefore, the number of elements in the sample is: \[ 100 \text{ cards} \]

3. Proportion of diamond cards in the sample:

   • In your sample, you found 24 diamond cards. To calculate the proportion of diamond cards, we can use the formula: \[ \text{Proportion} = \frac{\text{Number of diamond cards}}{\text{Total number of cards in the sample}} = \frac{24}{100} = 0.24 \]

In summary:

• Number of elements in the population: 520 cards
• Number of elements in the sample: 100 cards
• Proportion of diamond cards in the sample: 0.24 (as a decimal)