Statistics Confidence Interval

What is the point estimate, p̂, of this sample?

• 0.28

• 0.14

• 0.342

• 0.684

What is the margin of error of this sample?

• 0.28

• 0.14

• 0.342

• 0.684

2000 children were surveyed and the report that followed said, "With 98% confidence, between 20% and 50% of all parents make their children eat breakfast." What does 98% confidence mean in this situation?

• We can be 98% confident that the method used to get the intervals always gives the correct answer

• 98% of all parents will make their kids eat breakfast

• When used repeatedly, the method used to find the interval produces intervals which include the true proportion about 98% of the time

• The kids were 98% confident that they ate breakfast that day.

Which of the following would not decrease the width of a confidence interval?

• I only

• II only

• III only

• I and II only

• II and III only

An irate patient complained that the cost of a doctor's visit was too high.  She randomly surveyed 20 other patients and found that the mean amount of money they spent on each doctor's visit was $44.80.  The standard deviation of the sample was $3.53.  Find the 95% confidence interval of the population mean.

• $43.15 - $46.45

• $44.53 - $48.21

• $42.65 - $48.25

• $43.15 - $48.25

In a study of 150 accidents that required treatment in an emergency room, 36% involved children under 6 years of age.  Find the 90% confidence interval of the true proportion of accidents that involve children under the age of 6.

• 0.331 - 0.413

• 0.275 - 0.433

• 0.295 - 0.425

• 0.255 - 0.455

A 90% confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. The interval was ($139,048, $154,144). Give a practical interpretation of the interval.

• 90% of the sampled CEOs have salaries that fell in the interval $139,048 to $154,144

• We are 90% confident that the mean salary of all CEOs in the electronics industry falls in the interval $139,048 to $154,144. 

• 90% of all CEOs in the electronics industry have salaries that fall between $139,048 to $154,144

• We are 90% confident that the mean salary of the sampled CEOs falls in the interval $139,048 to $154,144.

A study found that in a sample of 44 subjects, 9 of them agree that children under 6 shouldn’t be taken to nice restaurants.
The 95% confidence interval for p is (0.082, 0.318). Interpret this interval.

• 95% of the time the proportion of people who believe children under 6 shouldn't be taken to nice restaurants will be between 8.2% and 31.8%.

• The population proportion of people who believe children under 6 shouldn't be taken to nice restaurants is between 8.2% and 31.8%.

• The probability that the proportion of people who believe children under 6 shouldn't be taken to nice restaurants will be between 8.2% and 31.8% is 95%.

• Based on this sample, I am 95% confident that the proportion of people who believe children under 6 shouldn't be taken to nice restaurants is between 8.2% and 31.8%.

Which z-value is used for a 95% confidence interval?

• 1.65

• 1.96

• 2.58

• 2.33

A survey of a random sample of 2500 adults who have a credit card found that 570 had a balance of $1000 or more on their credit card.

What would NOT be a condition we need to verify before constructing the interval?

• np̂ ≥ 10 and n(1-p̂) ≥ 10

• n ≥ 30

• 10% condition

• random sample