7.2 Estimating a Population Proportion

Identify the confidence interval used in the figure below if each shaded area is equal to 0.05.

• 90%

• 95%

• 98%

• 99%

Answer explanation

The confidence interval used in the figure is 90% because each shaded area represents 0.05, totaling 0.1 for both sides, leaving 0.9 or 90% for the interval.

The symbol for the sample proportion is __________.

• Z_c

• p̂

• E

• q

Answer explanation

The symbol for the sample proportion is p̂, which represents the sample proportion in statistics.

Find the value of z_c for a 90% confidence interval.

• -1.96 
• 1.645
• 1.440
• -1.598

A recent study of 750 Internet users in Europe found that 35% of Internet users were women. What is the 95% confidence interval of the true proportion of women in Europe who use the Internet?

• 0.321 < p < 0.379

• 0.316 < p < 0.384

• 0.309 < p < 0.391

• 0.305 < p < 0.395

A survey of 800 women shoppers found that 17% of them shop on impulse. What is the 98% confidence interval for the true proportion of women shoppers who shop on impulse?

• 0.148 < p < 0.192

• 0.136 < p < 0.204

• 0.144 < p < 0.196

• 0.139 < p < 0.201

Answer explanation

The correct confidence interval is 0.139 < p < 0.201 because it captures the true proportion of women shoppers who shop on impulse with 98% confidence.

What is the critical value z_c for a 99% confidence interval?

• 2.33

• 1.96

• 2.58

• 1.645

Answer explanation

The critical value z_c for a 99% confidence interval is 2.58, which corresponds to the z-score for a 99% confidence level in a standard normal distribution.

In a study of 500 people, 60% indicated they prefer online shopping. What is the 90% confidence interval for the true proportion of people preferring online shopping?

• 0.556 < p < 0.644

• 0.560 < p < 0.640

• 0.554 < p < 0.646

• 0.562 < p < 0.638

Answer explanation

The correct confidence interval is 0.556 < p < 0.644 as it captures the true proportion with 90% confidence.

The margin of error (E) in a confidence interval calculation is determined by which of the following?

• Sample size and standard deviation

• Critical value and standard error

• Sample mean and population mean

• Population proportion and sample proportion

Answer explanation

The margin of error (E) in a confidence interval calculation is determined by the critical value and standard error.

For a 95% confidence interval, what is the z-value used in the calculation?

• 1.96

• 2.33

• 1.645

• 2.58

Answer explanation

The correct z-value for a 95% confidence interval is 1.96, which is used in the calculation of the interval.

Which of the following best describes the purpose of a confidence interval in statistical analysis?

• To estimate the range within which the true population parameter lies with a certain level of confidence

• To calculate the exact value of the population parameter

• To determine if the sample mean is equal to the population mean

• To test the significance of the sample data

Answer explanation

The purpose of a confidence interval is to estimate the range within which the true population parameter lies with a certain level of confidence.