Chapter 7 AP Stats

According to the U.S. Census bureau, 23.5% of people in the United States are under the age of 18. In a random sample of 250 residents of a small town in Ohio, 28% of the sample was under 18. Which one of the following statements is true?

• 23.5% and 28% are statistics, 250 and 18 are parameters

• 23.5% and 28% are parameters, 250 and 18 are statistics

• 23.5% and 28% are parameters, 18 is a statistic.

• 28% is a parameter and 23.5% is a statistic.

• 23.5% is a parameter and 28% is a statistic.

The best statistic for estimating a parameter has which of the following characteristics?

• High bias, no variability

• High bias, low variability

• High bias, high variability

• Low bias, low variability

• Low bias, high variability

Olive weights are classified according to a unique set of adjectives implying great size. For example, the mean weight of olives classified as “Colossal” is 7.7 grams. Suppose a particular company’s crop of “Colossal” olives is approximately Normally distributed with a mean of 7.7 grams and a standard deviation of 0.2 grams. Which of the following represents the probability that the mean weight of a random sample of 3 olives from this population is greater than 8 grams?

• 0.0047

• 0.0668

• 0.0970

• 0.1932

• 0.9953

Population 1 is Normally distributed with a mean of 40 and a standard deviation of 4, and population 2 is Normally distributed with a mean of 25 and a standard deviation of 7. Suppose we select independent SRSs of n1 = 100 and n2 = 85 from population 1 and 2 respectively. Which of the following are the values of the mean and the standard deviation of the sampling distribution of   ˉx1 − ˉx2?

• 
• 
• 
• 
• 

An electronic prize wheel is programmed to land on “win” 25% of the time on weekdays and 10% of the time on weekends, and consecutive plays produce winners independently. Suppose we observe a random sample of 50 outcomes from this machine on weekdays and 100 outcomes from this machine on weekends. Let pˆWD and pˆWE be the sample proportions of winners on weekdays and weekends, respectively. Which of the following describes the shape, mean, and standard deviation of the sampling distribution of pˆWD − pˆWE ?

• Shape = approximately normal, mean = 0.15, standard deviation = 0.07

• Shape = approximately normal, mean = 0.15, standard deviation = 0.05

• Shape = approximately normal, mean = 0.35, standard deviation = 0.07

• Shape = skewed right, mean = 0.35, standard deviation = 0.05

• Shape = skewed right, mean = 0.35, standard deviation = 0.07

A local news story claims that 53% of high school males agree with the statement “I am ok with a girl playing on the football team because there is not a football team for girls.” To investigate this claim, an SRS of 100 males from a large local high school is selected. In the sample, 38 males agreed with the statement. We used technology to simulate choosing 240 SRSs of size n = 100 from a population of males where 53% agreed with the statement. The dotplot shows statement for each of the 240 samples. pˆ = the sample proportion of males who agree with the statement for each of the 240 samples.

Is there convincing evidence that less than 53% of all males at the school agree with the statement?

• Yes. It would be very surprising to get a sample proportion of pˆ = 0.38 or less in an SRS of size 100 when p = 0.53.

• No, the sampling distribution is centered at 0.53, so this validates the claim made in the news story.

• Yes, 38% is less than 53% so this proves that the claim made by the news story is false.

• No, 38% is a plausible value based upon the dotplot, so we cannot reject the claim made in the news story.

• No, because pˆ = 0.53 was one of the most common values in the sampling distribution.

Which of the following distributions has a mean that varies?

I. The population distribution

II. The distribution of sample data

III. The sampling distribution of the sample mean

• I only

• II only

• III only

• II and III

• all three distributions

There are 120 students at Francis Howell North High School. Mr. Willott conducts a poll that asks 20 randomly selected students how many hours of sleep they got last night. They find that the mean amount of sleep is 6.7 hours. The population standard deviation is σ = 2 hours. Can we estimate the standard deviation of the sampling distribution of means by using

σ/√ n = 2/√ 20 = 0.447 hours?

• No, because “hours of sleep” is not a continuous variable.

• No, because we can’t be sure that the central limit theorem applies to this situation.

• No, because we don’t know that the distribution of sleep hours for the population is approximately Normal.

• No, because the sample is more than 10% of the population.

• Yes, because all the conditions for using this formula have been met.

You take a simple random sample of size 25 from a very large population in which the true proportion is p = 0.1. Which statement below best describes what you know about the sampling distribution of pˆ ?

• µ pˆ = 0.1; σ pˆ= √[(0.1)(0.9)/25] ; the distribution is skewed right.

• µ pˆ = 0.1; σ pˆ= √[(0.1)(0.9)/25] ; the distribution is skewed left.

• µ pˆ = 0.1; σ pˆ= √[(0.1)(0.9)/25] ; the distribution is approximately Normal.

• µ pˆ = 0.1; we cannot use the formula σ pˆ = √[(0.1)(0.9)/25] ; the distribution is not approximately Normal.

• µ pˆ = 0.1; we cannot use the formula σ pˆ = √[(0.1)(0.9)/25] ; the distribution is approximately Normal.

The number of siblings an individual has varies from student to student. The distribution of number of siblings is strongly skewed to the right. The central limit theorem says that

• as we look at more and more students, their mean number of siblings gets ever closer to the mean 𝜇𝜇 for all students.

• the mean number of siblings for any number of students has a distribution of the same shape (strongly skewed) as the distribution for individual students.

• the mean number of siblings for any number of students has a distribution that is close to Normal.

• the mean number of siblings for a large number of students has a distribution of the same shape (strongly skewed) as the distribution for individual students.

• the mean number of siblings for a large number of students has a distribution that is close to Normal.