Confidence Interval and MOE

Suppose that $51,759 was the median income for all households in 2012. Does the interval ($51,484, $52,394) provide convincing evidence that the median household income increased in 2013? 

• Yes
• No

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.6

CCSS.HSS.ID.A.2

CCSS.HSS.ID.A.3

A sample size of n = 64 is drawn from a population whose standard deviation is σ = 5.6.

Find the margin of error for a 99% confidence interval for µ.

• 1.799

• 1.798

• 1.803

Tags

CCSS.HSS.IC.B.4

We want to know if students work too much (and thus spend less time on their classes). Previous studies show that the standard deviation for work time is 3 hours, and a survey of 40 students has a mean of 9.8 work hours.

The 95% confidence interval is…

• (8.84, 10.76)

• (8.87, 10.73)

• (9.02, 10.58)

• (9.00, 10.60)

Tags

CCSS.HSS.IC.B.4

Suppose that a confidence interval for hours worked by students was computed to be (8.82, 10.78). Which of these is a valid interpretation of this confidence interval?

• There is a 95% probability that the average number of hours worked by all students is between 8.82 and 10.78 hours.

• There is a 95% probability that a randomly selected student worked between 8.82 and 10.78 hours.

• We are 95% confident that the population average number of hours worked by all students is between 8.82 and 10.78 hours.

• We are 95% confident that the average number of hours worked by the students in our sample is between 8.82 and 10.78 hours.

Tags

CCSS.HSS.IC.B.4

A factory that produces manhole covers took a random sample of 800 manhole covers and found that 40 out of the covers were defective. What is the 95% CI for the proportion of defective manhole covers?

• (37.26, 42.74)

• (.035, .065)

• (.047, .053)

• (.015, .085)

Tags

CCSS.HSS.IC.B.4

We wish to obtain a 95% confidence interval for the average SAT score for Midlo students. The standard deviation of all SAT scores is 180. We should sample ____ students if we wish the margin of error to be within 40 points. ROUND ANSWER TO THE NEAREST TEN (for example, 20, 120, etc.)

Tags

CCSS.HSS.IC.B.4

We plan to survey college seniors to see what proportion plan to attend grad school next year. Using 98% confidence, how many students should we survey if we wish the margin of error to be within 3%?

• approximately 1170

• approximately 1500

• approximately 1050

• approximately 40

The symbol for the sample proportion is __________.

• Z_c
• p̂
• E
• q

Tags

CCSS.HSS.IC.B.4

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

• 1.65
• 1.96
• 2.58
• 2.33

Tags

CCSS.HSS.ID.A.4

In a crash test of 15 troopers, collision repair costs are found to have a distribution that is approximately normal, with a mean of $1800 and a sample standard deviation of $950. Construct a 99% confidence interval for the repair cost. 

• (1069.77, 2530.23)
• (1077.13, 2522.87)
• (1167.15, 2432.85)
• None of these.