Question

question 5
a company that produces socks wants to estimate the percent of the socks produced in a typical week that are defective. a random sample of 310 socks produced in a certain week were inspected. based on the sample, it is estimated that 12% of all socks produced by the company in this week are defective, with an associated margin of error of 3.62%. based on the estimate and associated margin of error, which of the following is the most appropriate conclusion about all socks produced by the company during this week?
a) 3.62% of the socks are defective.
b) it is plausible that between 8.38% and 15.62% of the socks are defective.
c) 12% of the socks are defective.
d) it is plausible that more than 15.62% of the socks are defective.

question 6
a special camera is used for underwater ocean research. the camera is at a depth of 39 fathoms. what is the cameras depth in feet? (1 fathom = 6 feet)
a) 234
b) 117
c) 45
d) 7

Explanation:

Question 5

Step1: Recall margin - of - error concept

The estimated proportion of defective socks is 12% with a margin of error of 3.62%. The confidence interval is calculated as the estimate plus and minus the margin of error.

Step2: Calculate lower and upper bounds

Lower bound = 12% - 3.62%=8.38%
Upper bound = 12% + 3.62% = 15.62%
This means it is plausible that the true proportion of defective socks lies within this interval.

Step1: Use conversion factor

Given that 1 fathom = 6 feet, and the camera is at a depth of 39 fathoms.

Step2: Calculate depth in feet

We multiply the number of fathoms by the conversion factor. So, the depth in feet is 39×6.
39×6 = 234

Answer:

B. It is plausible that between 8.38% and 15.62% of the socks are defective.

Question 6