Statistics Sect. 10.2 Worksheet #1
Name ______________________________
INFERENCE ABOUT POPULATION MEAN (CONFIDENCE INTERVALS)
1.
x is called the ………………… …………… and is a …………………… (parameter/statistic).
2.
 is called the ………………… …………… and is a …………………… (parameter/statistic).
3.
For the sampling distribution of x , the mean = ……… and the standard deviation
x
= …………
4. The Central Limit Theorem tells us that for large sample sizes, the sampling distribution of x is
approximately …………………, regardless of the shape of the sampling distribution of X.
5.
For the sampling distribution of x , as n increases, the standard deviation  x ……………………
(increases/decreases)
6.
When using the t distribution for inference about the mean, the formula for the degrees of freedom is
……………, where n = …………………………
7.
In general, as the confidence level increases, the margin of error and the length of the interval
both …………………… (increase/decrease/stay the same).
8. In general, if all other values remain the same but the sample size increases, then the margin of error and the
length of the interval both …………………… (increase/decrease/stay the same).
9. What critical t* from Table C should be used for a confidence interval for the population mean μ for each of the
following situations?
a. A 90% confidence interval for an SRS of 15 observations
………………
b. A 99% confidence interval for a random sample of 12 observations
………………
c.
………………
A 95% confidence interval for a random sample of 20 observations
10. A simple random sample of 20 overweight people who have agreed to participate in an experiment for a new
weight loss program were weighed and the amount of excess was calculated for each based on gender, height
and body frame. These were the excess weights:
32
52
56
48
73
49
52
46
51
62
58
62
57
55
70
37
45
62
71
50
a. Compute x . ……………
Compute s. …………
b. What critical t* from Table C should be used for a 95% confidence interval for the population mean excess
weight of all overweight people?
……………
c. Construct a 95% confidence interval for the mean excess weight of all overweight people. Show your work.
……………………
d. Write an interpretation of this interval. …………………………………………………………………………