6-Estimating the Population Mean When the Population Standard Deviation Is Known

Question 1

What is a point estimate ?

Answer 1

a single number that estimates a population parameter. In other words, a point estimate is a statistic.

Question 2

What is an interval estimate ?

Answer 2

is a range of values believed to contain the population parameter.

Question 3

What is a confidence interval ?

Answer 3

when we can express the confidence we have that it contains the parameter. Confidence is expressed as a percentage.

Question 4

Whats the formula to calculate a 95% confidence interval ?

Answer 4

m+-1,96(om)

*m= the SAMPLE mean
1,96 = to the za/2 of 95%

Question 5

True or false : If the arms around µ capture m, then the same arms around m will capture µ. Therefore, whenever the arms around µ capture m, the same arms around m will capture µ.

Answer 5

True. We can calculate by u+-1,96(om) for m or m+-1,96(om) to find u

Question 6

what is the formula for (1−α)100% confidence interval?

Answer 6

m+-za/2(om)

Question 7

True or false. As σ increases (and n remains constant), σm will increase. Conversely, as n increases (and σ remains constant), σm will decrease.

Answer 7

True

Question 8

True or false: I have 95% confidence that µ lies in the interval m ± zα/2(σm) = [16.8, 28.4] because 95% of all possible intervals

Answer 8

True

Question 9

True or false. (1−α)100% intervals computed as m ± zα/2(σm) will capture m.

Answer 9

False. Because m is always at the center of the interval, 100% of intervals computed as m ± zα/2(σm) will capture m.

Question 10

What is the formula for sample standard deviation ?

Whats the formula for an approximative confidence interval ?

Answer 10

sm= squ.rt of s^2/n

m+-za/2 (sm)

Question 11

True or false. 3. Confidence intervals computed with sm will capture µ more often than those computed with σm.

Answer 11

False

Question 12

What is the formula for the margin of error (moe) ?

Answer 12

moe= za/2 (om)

Question 13

In the general case, we could say we want the moe to be ƒ(σ), where ƒ is some number less than … and greater than ….

Answer 13

a) 1

b) 0

Question 14

What formula shows the sample size required to produce an moe of ƒ(σ) ?

Answer 14

n=(za/2) / f )^2

Question 15

What are valid assumptions ?

Answer 15

1) Normality (when o is known or when it is unknown but with large sample size)
2) Random sampling