In a metal fabrication process, metal rods are produced to a specified target length of 15 feet. Suppose that the lengths are normally distributed. A quality control specialist collects a random sample of 16 rods and finds the sample mean length to be 14.8 feet and a standard deviation of 0.65 feet. The standard error of the mean is

A 0.65 ft.

B 0.1625 ft.

C 0.0098 ft.

D 0.346 ft.

E 1.625 ft.

EU (European Union) countries report that 46% of their labor force is female. The United Nations wants to determine if the percentage of females in the U.S. labor force is the same. Based on a sample of 500 employment records, representatives from the United States Department of Labor find that the 95% confidence interval for the proportion of females in the U.S. labor force is 0.357 to 0.443. Which of the following is the correct interpretation?

A We are 95% confident that between 35.7% and 44.3% of the persons in the U.S. labor force is female

B The margin of error for the true percentage of females in the U.S. labor force is between 35.7% and 44.3%

C The percentage of females in the U.S. labor force is between 35.7% and 44.3%

D All samples of size 500 will yield a percentage of females in the U.S. labor force that falls within 35.7% and 44.3%

E None of these

In a metal fabrication process, metal rods are produced to a specified target length of 15 feet. Suppose that the lengths are normally distributed. A quality control specialist collects a random sample of 16 rods and finds the sample mean length to be 14.8 feet and a standard deviation of 0.65 feet. Which of the following statements is true?

A The sampling distribution for the sample mean follows the t-distribution with 15 degrees of freedom

B The mean of the sampling distribution for the sample mean is 14.8 feet

C The standard error is 0.65 feet

D The sampling distribution for the sample mean follows the t-distribution with 16 degrees of freedom

E The sampling distribution for the sample mean is Normal with a mean of 14.8 feet and standard deviation of 0.65 feet