# MATHEMATICS

Which one of the following statements is false?

A) The standard error measures the variability of a population parameter.

B) The standard error of a sample statistic measures, roughly, the average difference between the values of the statistic and the population parameter.

C) Assuming a fixed value of s = sample standard deviation, the standard error of the mean decreases as the sample size increases.

D) The standard error of a sample proportion decreases as the sample size increases.

Which of the following statements is correct about a parameter and a statistic associated with repeated random samples of the same size from the same population?

A) Values of a parameter will vary from sample to sample but values of a statistic will not.

B) Values of both a parameter and a statistic may vary from sample to sample.

C) Values of a parameter will vary according to the sampling distribution for that parameter.

D) Values of a statistic will vary according to the sampling distribution for that statistic.

In a random sample of 1000 students, 80% were in favor of longer hours at the school library. The standard error of ρ-hat is approximately:

A) 0.013

B) 0.160

C) 0.640.

D) 0.800

Based on the 2000 Census, 31.8% of grandparents in California are the primary caregivers for their grandchildren. Suppose n = 1000 persons are to be sampled from this population and the sample proportion of grandparents as primary caregivers (ρ-hat) is to be calculated. What is the mean of the sampling distribution of ρ-hat?

A) 0.0002

B) 0.0147

C) 0.2169

D) 0.3180

Every student taking elementary statistics at a large university (about 1,100 students) participated in a class project by rolling a 6-sided die 100 times. Each individual student determined the proportion of his or her 100 rolls for which the result was a “1”. The instructor plans to draw a histogram of the 1,100 sample proportions. What will be the approximate shape of this histogram?

A) Skewed

B) Uniform

C) Normal (bell-shaped)

D) Chi-square

If the size of a sample randomly selected sample from a population is increased from n = 100 to n = 400, then the standard deviation of ρ-hat will

A) remain the same.

B) increase by a factor of 4.

C) decrease by a factor of 4.

D) decrease by a factor of 2.

For a random sample of 10 men, the mean head circumference is x = 57.3 cm and the sample standard deviation is s = 2 cm. The standard error of the sample mean is

A) 0.200

B) 0.447

C) 0.500

D) 0.632

A store manager is trying to decide whether to price oranges by weight, with a fixed cost per pound, or by the piece, with a fixed cost per orange. He is concerned that customers will choose the largest ones if there is a fixed price per orange. For one week the oranges are priced by the piece rather than by weight, and during this time the mean weight of the oranges purchased is recorded for all customers who buy 4 of them. The manager knows the population of weights of individual oranges is bell-shaped with mean of 8 ounces and a standard deviation of 1.6 ounces. If the 4 oranges each customer chooses are equivalent to a random sample, what should be the approximate mean and standard deviation of the distribution of the mean weight of 4 oranges?

A) mean = 32 ounces, standard deviation = 6.2 ounces

B) mean = 8 ounces, standard deviation = 1.6 ounces

C) mean = 8 ounces, standard deviation = 0.8 ounces

D) mean = 2 ounces, standard deviation = 0.4 ounces