Review of Statistical Inference from STA 2023
Confidence Intervals and Significance Tests for:
 one mean
 matched paired differences
 difference of two independent means
 one proportion
 difference of two independent proportions
Chapter 7: CI and Significance Tests for means using the t distribution
1. Why do we use the t table?
2. What assumptions do we need to make? How do we check them?

Random Samples

Population is Normal
3. Find Formulas on tables.
Confidence Interval:
Significance Test:
Ho:
Ha:
TS:
p-value:
4. Read Minitab Output
5. Interpret Results

CI does NOT include # from Ho → Supports Ha

p-value small → Supports Ha
Chapter 8 : CI and Sig. Tests for p and p1-p2 using the z
1. Why do we use the z table?
2. What assumptions do we need to make?
 Random Samples
 Check specific assumption for that test
OR Use the most restrictive one for all cases and you will be ok.
 One Sample Proportion CI -sample size must be at least equal
to 5.
 One Sample Proportion ST - must have at least ten successes and
ten failures.
 Two Sample Proportion CI - both sample sizes must be at least
equal to 10.
 Two Sample Proportions ST – at least 5 successes and 5 failures
must in each of the samples.
3. Which estimator of p do we use?

One Sample Proportion (Confidence Interval)

One Sample Proportion (Significance Test)

Two Sample Proportion (Confidence Interval)

Two Sample Proportions (Significance Test)
4. Make and interpret CI and ST.
5. Read Minitab Output
6. Interpret Results
Examples: For each of the following examples, we will first determine which kind of
problem it is. Then we will set the problem up as if to do by hand. We will interpret
the Minitab output given for each problem.
1. Suppose that in a random sample of 50 babies conceived by an in vitro fertilization
process (test tube babies), 35 are girls. Does this sample evidence show convincingly
that the in vitro process favors the female gender? Explain.
 Which kind of problem is this?

Interpret the results of the Minitab output from the last page.
2. Four sets of identical twins were selected at random. One child was selected at
random from each pair to form an "experimental group"- these four children were sent to
school. The other four children were kept at home as a control group. At the end of the
school year the IQ scores presented below were obtained. Does this evidence justify the
conclusion that lack of school experience has a depressing effect on IQ scores?
Experimental
Control
Pair
Group
Group
A
110
111
B
125
120
C
139
128
D
142
135

Which kind of problem is this?

Interpret the results of the Minitab output from the last page.
3. A restaurant has recently started using a dessert cart that is pushed around the eating
area for diners to view and, it is hoped, be unable to resist. On the first ten evenings the
cart was used, the average expenditure per night for desserts was $130 compared to an
average of $110 prior to the use of the cart. The standard deviation for the ten evenings
was $65. Does it look like the cart will improve sales significantly?

Which kind of problem is this?

Interpret the results of the Minitab output from the last page.
4. A social scientist believes that the fraction of Republicans in favor of the death
penalty is greater than the fraction of Democrats in favor of the death penalty. She asked
random samples of 200 Republicans and 200 Democrats and found 46 Republicans and
34 Democrats favoring the death penalty. Do these data support the social scientist's
belief?

Which kind of problem is this?

Interpret the results of the Minitab output from the last page.
5. The effect of alcohol consumption on the body appears to be much greater at high altitudes
than at sea level. To test this theory, a scientist randomly selects 12 subjects and randomly
divides them into two groups of six each. One group is transported to an altitude of 12,000
feet, where each subject ingests a drink containing 100 cc of alcohol. The second group
receives the same drink at sea level. After two hours, the amount of alcohol in the blood
(grams per 100 cc) for each subject is measured. The data are shown in the table. Do the data
provide sufficient evidence to support the theory that retention of alcohol in the blood is
greater at high altitudes?
Sea Level
0.07
0.10
0.09
0.12
0.09
0.13
12,000 Feet
0.13
0.17
0.15
0.14
0.10
0.14

Which kind of problem is this?

Interpret the results of the Minitab output from the last page.
Test and Confidence Interval for One Proportion
Test of p = 0.5 vs p > 0.5
Exact
X N Sample p
95.0 % CI
P-Value
35 50 0.700000 (0.553918, 0.821382)
0.003
Test and CI for One Proportion
Sample
X
N Sample p
1
37
54 0.685185
95.0% CI
(0.544476, 0.804761)
Paired T-Test and Confidence Interval
Paired T for exp - control
N
Mean
StDev
SE Mean
exp
4
129.00
14.67
7.34
control
4
123.50
10.34
5.17
Difference
4
5.50
5.00
2.50
95% CI for mean difference: (-2.46, 13.46)
T-Test of mean difference = 0 (vs >0):
T-Value = 2.20 P-Value =
0.058
T-Test of the Mean
Test of mu = 110.0 vs mu > 110.0
Variable N
Mean StDev SE Mean
T
P
dessert 10 130.0
65.3
20.6 0.97 0.18
T Confidence Intervals
Variable N
Mean StDev SE Mean
95.0 % CI
dessert 10 130.0
65.3
20.6 (83.3,176.7)
Test and Confidence Interval for Two Proportions
Sample
X
N
Sample p
1
46 200
0.230000
2
34 200
0.170000
Estimate for p(1) - p(2): 0.06
95% CI for p(1) - p(2): (-0.0181778, 0.138178)
Test for p(1) - p(2) = 0 (vs > 0): Z = 1.50 P-Value = 0.066
Test and CI for Two Proportions
Sample
X
N Sample p
1
47
202 0.232673
2
35
202 0.173267
95% CI for p(1) - p(2): (-0.0188205, 0.137632)
Two Sample T-Test and Confidence Interval
Two sample T for sea level vs 12000ft
N
Mean
StDev
SE Mean
sea leve 6
0.1000 0.0219
0.0089
12000ft 6
0.1383 0.0232
0.0095
95% CI for mu sea leve - mu 12000ft:( -0.0678, -0.0089)
T-Test mu sea leve = mu 12000ft (vs <): T = -2.94 P = 0.0082 DF = 9