Sample Exam One (Stats)
A machine produces metal springs for computer lids. Over a long period of time it has been found that 10% of the springs produced by the machine are defective. After some adjustments to the machine, a random sample of 200 springs is selected and it is found that 16 of the springs in the sample were defective. The appropriate significance test is carried out in order to determine whether the proportion of defective springs has changed. Which of the following is the correct p-value for the test?
A. 2 x P( Z < 0.08 - 0.1 / √(0.1)(0.9)/200 )
A researcher is studying an old edition of an encyclopedia. She wishes to estimate the proportion of the printed matter in the encyclopedia that is diagrams and pictures (as opposed to text). The encyclopedia consists of 30 volumes, and she observes that the proportion of printed matter that is diagrams and pictures is roughly the same in each of the volumes. The researcher randomly selects four of the volumes, and then studies every page in those four volumes. This is an example of which type of sampling?
A. Cluster
A company produces cloth for use in airplane seats. The company claims that the mean breaking strength μ for specimens of the cloth is 80 lbs of force, but the airlines who buy the cloth are concerned that the cloth might be weaker than that. A group working on behalf of the airlines takes a random sample of specimens of the cloth and finds the breaking strength of each specimen in the sample. What hypotheses should the group use to test the manufacturer's claim?
A. Ho: μ = 80, Ha: μ < 80
The scatterplot above shows 52 points with the associated least squares regression line for predicting values of x. One of the two labeled points - either P or Q - will be removed. Which of the following is true?
A. Removal of the point P would substantially increase the slope of the least squares regression line. Removal of the point Q would have little effect on the slope of the least squares regression line.
On any given evening, what is the minimum number of places that she should set at the dinner table for the children in order to be at least 80% sure that all the children can be seated?
B. 7
A track and field coach wants to find out whether a particular hammer thrower performs better, on average, in the morning or afternoon. The coach observes a random sample of the athlete's morning throws and random sample of the athlete's afternoon throws. Which one of the following significance tests could be used to analyze the results?
C. Paired t-test
In a particular country it is known that 40% of the residents have blue eyes, 35% of the residents have brown eyes, and 25% of the residents have green eyes. A student carries out a study to determine whether, in terms of color, the eyes of dolls manufactured in that country are representative of the residents of the country. The student takes a random sample of 40 brands of doll, and finds that 10 of them have blue eyes, 19 of them have brown eyes, and 11 of them have green eyes. She then carries out the appropriate significance test and obtains the p-value for the test. Which of the following is true?
C. The p-value is between 0.1 and 0.15
In a company, 78% of the employees opt for medical insurance and 42% of the employees opt for at least one of these benefits. What percent of the employees opt for both of these benefits?
D. 38%
A company has recently given some pay raises. The distribution of the amounts by which the employees' salaries have been increased is illustrated by the boxplot below. Which of the following best describes the shape of the distribution and the interquartile range (IQR) of the salary increases?
D. positively skewed; IQR is approximately $2000
A society has 160 members. A relative cumulative frequency graph of their ages is shown in the figure above. Approximately how many of the society's members are over 43 years old?
E. 120
