Question

An automatic character recognition device successfully reads about ​83% of handwritten credit card applications. To estimate what might happen when this device reads a stack of​ applications, the company did a simulation using samples of size​ 20, 50,​ 75, and 100. For each sample​ size, they simulated 1000 samples with success rate p=0.83 and constructed the histogram of the 1000 sample proportions. Explain what these histograms say about the sampling distribution model for sample proportions.

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1) What is the​ shape, center, and spread of the sampling distribution for samples of size​ 20?

a. The shape of the sampling distribution is ▼_____________- Skewed right? Skewed Left? Normal?

b. The sampling distribution is centered between ▼_________- 0.8-0.9? 0.9-1? 0.6-0.7? 0.7-0.8?

c. The sampling distribution has a ▼________ spread.- Relatively Narrow (0.25> range> 0.10)? Relatively Wide (0.50 > range> 0.25)? Narrow (range< 0.10)? Wide (range> 0.50)?

2) What is the​ shape, center, and spread of the sampling distribution for samples of size​ 50?

a. The shape of the sampling distribution is ▼ Skewed right? Skewed Left? Normal?

b. The sampling distribution is centered between ▼______- 0.65-0.70? 0.70-0.75? 0.75- 0.80? 0.80-0.85? 0.85- 0.90? 0.90-0.95?

c. The sampling distribution has a ▼____ spread.- Relatively Narrow (0.25> range> 0.10)? Relatively Wide (0.50 > range> 0.25)? Narrow (range< 0.10)? Wide (range> 0.50)?

3) What is the​ shape, center, and spread of the sampling distribution for samples of size​ 75?

a. The shape of the sampling distribution is ▼_______. - Skewed right? Skewed Left? Normal?

b. The sampling distribution is centered between ▼_____. 0.75- 0.775? 0.80-0.825? 0.85- 0.875? 0.80-0.85? .875- 0.90? 0.9- 0.925?

c. The sampling distribution has a ▼____ spread. Relatively Narrow (0.25> range> 0.10)? Relatively Wide (0.50 > range> 0.25)? Narrow (range< 0.10)? Wide (range> 0.50)?

4. What is the​ shape, center, and spread of the sampling distribution for samples of size​ 100?

a. The shape of the sampling distribution is ▼______. Skewed right? Skewed Left? Normal?

b. The sampling distribution is centered between ▼_____. 0.78-0.80? 0.80-0.82? 0.82-0.84? 0.84- 0.86? 0.86-0.88? 0.88-0.9? 0.90-0.92?

c. The sampling distribution has a ▼_____ spread. Relatively Narrow (0.25> range> 0.10)? Relatively Wide (0.50 > range> 0.25)? Narrow (range< 0.10)? Wide (range> 0.50)?

Answer 1

The histograms of the sample proportions for different sample sizes show that the sampling distribution models for sample proportions are approximately normal with centers and spreads that vary depending on the sample size.

Step-by-step explanation:

When considering the sampling distribution model for sample proportions, we can analyze the shape, center, and spread of the distribution for different sample sizes.

1. For samples of size 20, the shape of the sampling distribution is approximately normal. The center of the distribution is between 0.8 and 0.9, and the spread of the distribution is relatively narrow.
2. For samples of size 50, the shape of the sampling distribution is also approximately normal. The center of the distribution is between 0.70 and 0.75, and the spread of the distribution is relatively narrow.
3. For samples of size 75, the shape of the sampling distribution is again approximately normal. The center of the distribution is between 0.80 and 0.825, and the spread of the distribution is relatively narrow.
4. For samples of size 100, the shape of the sampling distribution remains approximately normal. The center of the distribution is between 0.82 and 0.84, and the spread of the distribution is relatively narrow.