Math 146 - Statistics - Hybrid – Spring 2016
Quiz 5 (total points: 10)
May 19, 2016
Name: ___Anne Sers _____________________
1. (2 pt) True or False.
a) One is estimating a population mean  If n < 30 a point estimate is more accurate. If n ≥ 30
an interval estimate is more accurate. False
b) If the level of confidence increases, the width of the confidence interval increases. True
c) If all other quantities remain the same, a decrease in sample size will narrow the confidence
interval. False
d) One constructs a 96% confidence interval for a population mean using a random sample. The
confidence interval is 24.3 < µ < 26.8. The probability that µ is in this interval is .96. False
2. (1 pt) The symbol/notation for the unbiased estimate of µ is:
̅
𝒙
3. (1 pt)a) If c = 0.88, find the critical value, zc, necessary to form a confidence interval.
Zc = ± 1.555
b) If c = 0.95 and n =40 , find the critical value, tc, necessary to form a confidence interval.
tc = 2.023
4. (1 pt) a) Give 2 (only!!) distinct properties of the t-distribution.
Mean = mode = median = 0
Bell-shaped, symmetric about zero
Curve never touches x-axis
Area under curve = 1
Tails are “thicker” than Standard Normal
Family of curves define by degrees of freedom
As degrees of freedom increases (df ≈30), the distribution is very like the Standard
Normal
̅ = 𝟏𝟖. 𝟔 𝝈 = 𝟏𝟎. 𝟎 𝒏 = 𝟒𝟕
5. (1 pt) c = 0.95, 𝒙
Construct the confidence interval for the population mean. Give an expression (all numbers, do
not simplify), in interval form.
(𝟏𝟖. 𝟔 − 𝟏. 𝟗𝟔 ∗
𝟏𝟎
√𝟒𝟕
,
𝟏𝟖. 𝟔 + 𝟏. 𝟗𝟔 ∗
𝟏𝟎
√𝟒𝟕
)
6. (1 pt) A scientist reports a confidence interval for a population mean to be (14.6, 14.8).
a) What is the margin of error?
b) What is the sample mean?
0.1
14.7
̅ = 𝟐𝟓. 𝟗, s = 5.2, n = 48 The population is normally distributed with
7. (1 pt) c = 0.95, 𝒙
unknown population standard deviation.
Find the margin of error (not the confidence interval!) to be used in a confidence interval.
(Give an expression, do not simplify)
E = 𝟐. 𝟎𝟏𝟒 ∗
𝟓.𝟐
√𝟒𝟖
8. (1 pt) In a random sample of 5 microwave ovens, the mean repair cost was $65.00 and
the standard deviation was $13.00.
Assume the population is normally distributed normally distributed.
a) Does one use the normal distribution or t-distribution (or neither!) to construct a confidence
interval for the population mean µ?
t-distribution
b) Explain.
The repair costs are Normally distributed
- and σ is unknown
9. (1 pt) A college admissions director wishes to estimate the mean age of all students
currently enrolled. In a random sample of 20 students, the mean age is found to be 22.9
years. From past studies, the standard deviation is known to be 1.5 years, and the
population is normally distributed.
A 90% confidence interval is:
( 22.3, 23.5 )
Interpret the results.
We are 90% confident that the mean age of all students currently enrolled is between 22.3
and 23.5 years