STATPRO HUMSS11-D W10 Review

If a distribution is normal, then it is not possible to randomly select a value that is more than 4 standard deviations from the mean.

• True

• False

Answer explanation

It is very unlikely, but still possible. The normal distribution curves extends infinitely to the left and right.

If x represents a random variable coming from a normal distribution and P(x > 15.7) = 0.04, then P(x < -15.7) = 0.04.

• True

• False

Answer explanation

This would only be true if the mean was 0.

Given a standard normal distribution, which of the following is the value of the probability, P(z>1.48)?

• 0.0694

• 0.0721

• 0.9279

• 0.9306

Answer explanation

Refer to the standard normal distribution table.

The heights of students in a certain city are normally distributed with a mean of 174.5 centimeters and a standard deviation of 6.9 centimeters. A random sample of 36 students were selected and the probability that their mean height will be below 172 centimeters is to be determined. Which of the following is true?

Answer explanation

When an inference about the sample mean is concerned, the Central Limit Theorem applies

The average life of a rechargeable battery is 25 years, with standard deviation of 2.5 years. Assuming that lives of these batteries follow approximately a normal distribution and a random sample of 35 machines was selected. What is the standard error of the sampling distribution of the mean?

• 0.4226

• 0.1000

• 0.0714

• 2.5

Answer explanation

The standard error is the scaled version of the standard deviation following the sample size.

What is the t-score associated with 95% confidence level when the sample size is 20?

• 1.7291

• 2.0930

• 2.0860

• 1.7247

Answer explanation

Refer to the t-distribution table at 19 degrees of freedom.

Which case of interval estimation is the scenario below about?

The manager of a theme park wishes to estimate the mean amount of money visitors spend at the park. A random sample of 49 visitors has a mean of Php 3700 and a standard deviation of Php 600. Construct a 95% confidence interval for the true mean amount of money spent by park visitors.

• Confidence interval for μ, unknown σ, n≥30

• Confidence interval for μ, known σ

• Confidence interval for p, np>5 and n(1-p)>5

• Confidence interval for μ, unknown σ, n<30

Answer explanation

This requires the estimation of the population mean with a sufficiently large sample size.

Which case of interval estimation is the scenario below about?

In a random sample of 500 teenagers with ages 12 to 17 years old, 330 have regular access to the internet. Construct a 95% confidence interval for the true proportion of teenagers with regular access to the internet.

• Confidence interval for μ, unknown σ, n≥30

• Confidence interval for μ, known σ

• Confidence interval for p, np>5 and n(1-p)>5

• Confidence interval for μ, unknown σ, n<30

Answer explanation

This requires the estimation of the population proportion.

Sometimes, it appears that the cereal box you bought from the grocery is not quite full. To be sure that you are getting your money’s worth, a sample of ten cereal boxes were collected. It is advertised that the cereal boxes weigh 330 g, but the sample mean is 329.93 g, with a standard deviation of 0.21 g. What is the 90% confidence interval for the true mean weight?

• 329.81 g to 330.05 g

• 330.05 g to 331.81 g

• 328.01 g to 330.85 g

Answer explanation

This is an interval that estimates the population mean with a small sample size and uses the t-distribution.

An article says that the trendy color in 2024 is Apricot Crush. Suppose that a group conducted a survey to three hundred students and 225 of them agreed with the article. 

1. If another article says that less than 70% of the students agree that Apricot Crush is the trendy color for 2023, is this valid at 95% confidence?

• Yes, because less than 70% is within the 95% confidence interval.

• No, because less than 70% is NOT within the 95% confidence interval.

• Not enough information to answer.

Answer explanation

There is enough information to estimate the population proportion. At 95% confidence, the population proportion is from 70.1% to 79.9%.